Wassce 2018/2019 waec 2018/2019 mathematics obj qnd thoery

<div dir="ltr"> <b>waec 2018/2019 mathematicsobj qnd thoery</b><br><br><br><br><br><br><br><br><br><br><br></div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjE-fPbqEUr9zQA4gUB2acXZ5khUkgzvseYyLGzmYSmzajQHpsWW4HzZQgc_CDt_5-OAog7nG1jWsDkgBgEge-0fvxVaHhtR65w0tekchC77SuG6Tc3m81BJk08u5WtbtrxmTkuh_4cHAc/s1600/LEGIT+2018+WAEC+RUNX+20180328_212421.jpg" imageanchor="1" style="margin-left: 1em; margin-right: 1em;"> <img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjE-fPbqEUr9zQA4gUB2acXZ5khUkgzvseYyLGzmYSmzajQHpsWW4HzZQgc_CDt_5-OAog7nG1jWsDkgBgEge-0fvxVaHhtR65w0tekchC77SuG6Tc3m81BJk08u5WtbtrxmTkuh_4cHAc/s640/LEGIT+2018+WAEC+RUNX+20180328_212421.jpg"> </a> </div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <b style="font-family: sans-serif; text-align: start;">waec 2018/2019 mathematicsobj qnd thoery</b></div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZPVuI4Dn3Olw04PWso4w-Rgxsl7CfYIGjFd032TBL0cqLz45eKlhLckHRtIZhtH5lUxoyuesAzAuzJzPOhN9JTVx5quQuztVRdWU-4ZeAP6382c0YUvIr3_O5Mu4rWCurCrh47I4ERI0/s1600/IMG-20180418-WA0008.jpg" imageanchor="1" style="font-family: sans-serif; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZPVuI4Dn3Olw04PWso4w-Rgxsl7CfYIGjFd032TBL0cqLz45eKlhLckHRtIZhtH5lUxoyuesAzAuzJzPOhN9JTVx5quQuztVRdWU-4ZeAP6382c0YUvIr3_O5Mu4rWCurCrh47I4ERI0/s640/IMG-20180418-WA0008.jpg"></a></div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmwtNG0YP8V2nmU9nYtdzOKDG1AFxNp-LUgoWEzE_HDWNNb8K1Q_fKmNncvwUxze7kfwXUAGkhyC65BaMQqAWScpKgqeMh7iYkAUsKrUMMlRvJN7gp5OvmX3pYvl7XoDE-5sZUb7RxMaM/s1600/IMG-20180418-WA0009.jpg" imageanchor="1" style="font-family: sans-serif; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjmwtNG0YP8V2nmU9nYtdzOKDG1AFxNp-LUgoWEzE_HDWNNb8K1Q_fKmNncvwUxze7kfwXUAGkhyC65BaMQqAWScpKgqeMh7iYkAUsKrUMMlRvJN7gp5OvmX3pYvl7XoDE-5sZUb7RxMaM/s640/IMG-20180418-WA0009.jpg"></a></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> </div> <div class="separator" style="clear: both;"> NO2) Given that y = 2pxˆ² – p² x – 14</div> <div class="separator" style="clear: both;"> <br></div> <div class="separator" style="clear: both;"> AT (3, 10)</div> <div class="separator" style="clear: both;"> <br></div> <div class="separator" style="clear: both;"> 10 = 2p(3)²  – p² (3) – 14</div> <div class="separator" style="clear: both;"> <br></div> <div class="separator" style="clear: both;"> 10 = 18p – 3p²  – 14</div> <div class="separator" style="clear: both;"> <br></div> <div class="separator" style="clear: both;"> 3p²  – 18p + 24 = 0</div> <div class="separator" style="clear: both;"> <br></div> <div class="separator" style="clear: both;"> p²  – 6p + 8 = 0</div> <div class="separator" style="clear: both;"> <br></div> <div class="separator" style="clear: both;"> using factor method,</div> <div class="separator" style="clear: both;"> <br></div> <div class="separator" style="clear: both;"> p²  – 2p -4p + 8 = 0</div> <div class="separator" style="clear: both;"> <br></div> <div class="separator" style="clear: both;"> p(p-2) – 4(p-2) = 0</div> <div class="separator" style="clear: both;"> <br></div> <div class="separator" style="clear: both;"> (p-4)(p-2) = 0</div> <div class="separator" style="clear: both;"> <br></div> <div class="separator" style="clear: both;"> p-4 = 0 or p-4 = 0</div> <div class="separator" style="clear: both;"> <br></div> <div class="separator" style="clear: both;"> p= 4 or p =2</div> <div class="separator" style="clear: both;"> *4A ii*</div> <div class="separator" style="clear: both;"> RSQ=(x+90)°</div> <div class="separator" style="clear: both;"> RSQ=37.5°+90°</div> <div class="separator" style="clear: both;"> RSQ=127.5°</div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAavhxaGVflhE8yVmphhsQxW6OaglZvDyOGWH0k6m3sHsgDXkJhxFqmRE1T6JJf9NvwdS0nhmBl4aJMnq_84aJ_pN5n7mYuP2MNuRouG8jYDbk8uv589JeVuiE9RM39EwyFUK9TL3jkDk/s1600/IMG-20180418-WA0007.jpg" imageanchor="1" style="font-family: sans-serif; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAavhxaGVflhE8yVmphhsQxW6OaglZvDyOGWH0k6m3sHsgDXkJhxFqmRE1T6JJf9NvwdS0nhmBl4aJMnq_84aJ_pN5n7mYuP2MNuRouG8jYDbk8uv589JeVuiE9RM39EwyFUK9TL3jkDk/s640/IMG-20180418-WA0007.jpg"></a></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAavhxaGVflhE8yVmphhsQxW6OaglZvDyOGWH0k6m3sHsgDXkJhxFqmRE1T6JJf9NvwdS0nhmBl4aJMnq_84aJ_pN5n7mYuP2MNuRouG8jYDbk8uv589JeVuiE9RM39EwyFUK9TL3jkDk/s1600/IMG-20180418-WA0007.jpg" imageanchor="1" style="font-family: sans-serif; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAavhxaGVflhE8yVmphhsQxW6OaglZvDyOGWH0k6m3sHsgDXkJhxFqmRE1T6JJf9NvwdS0nhmBl4aJMnq_84aJ_pN5n7mYuP2MNuRouG8jYDbk8uv589JeVuiE9RM39EwyFUK9TL3jkDk/s640/IMG-20180418-WA0007.jpg"></a></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> General mathematics answer</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> NO1) On February 28th 2012, value = (100-30/100) * #900,00.00</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> = 70/100 * #900,00</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> = #630,000.00</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> On february 28th 2013, value = (100-22/1000 * #630,00</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> = 78/100 8 #630,000</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> = #491,400</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> On february 28th 2014, value = 78/100 8 #491,400</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> =383,292</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> On february 28th 2015, value = 78/100 * #383,292</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> = #298,967.76</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> ===============</div> <div class="separator" style="clear: both; text-align: center;"> NO2) Given that y = 2pxˆ² – p² x – 14</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> AT (3, 10)</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 10 = 2p(3)²  – p² (3) – 14</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 10 = 18p – 3p²  – 14</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 3p²  – 18p + 24 = 0</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> p²  – 6p + 8 = 0</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> using factor method,</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> p²  – 2p -4p + 8 = 0</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> p(p-2) – 4(p-2) = 0</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> (p-4)(p-2) = 0</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> p-4 = 0 or p-4 = 0</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> p= 4 or p =2</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> =================</div> <div class="separator" style="clear: both; text-align: center;"> 4a) </div> <div class="separator" style="clear: both; text-align: center;"> Rate = 2/100 * N0.02 per month Rate per annum = 0.02 * 12 = 0.24 per annum</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;">  (4b) Draw the Diagram =======================</div> <div class="separator" style="clear: both; text-align: center;"> ‬(4A ii​)</div> <div class="separator" style="clear: both; text-align: center;"> RSQ=(x+90)°</div> <div class="separator" style="clear: both; text-align: center;"> RSQ=37.5°+90°</div> <div class="separator" style="clear: both; text-align: center;"> RSQ=127.5°</div> <div class="separator" style="clear: both; text-align: center;"> 🇳🇬🇳🇬🇳🇬🇳🇬🇳🇬🇳🇬👇🏽NIGERIA</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> *MATHEMATICS  ANSWERS*</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> (1) </div> <div class="separator" style="clear: both; text-align: center;"> On February 28th 2012, value = (100-30/100) * #900,00.00</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> = 70/100 * #900,00</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> = #630,000.00</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> On february 28th 2013, value = (100-22/1000 * #630,00</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> = 78/100 8 #630,000</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> = #491,400</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> On february 28th 2014, value = 78/100 8 #491,400</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> =383,292</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> On february 28th 2015, value = 78/100 * #383,292</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> = #298,967.76</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> =============================</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> (2)</div> <div class="separator" style="clear: both; text-align: center;">  Given that y = 2pxˆ² – p² x – 14</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> AT (3, 10)</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 10 = 2p(3)²  – p² (3) – 14</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 10 = 18p – 3p²  – 14</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 3p²  – 18p + 24 = 0</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> p²  – 6p + 8 = 0</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> using factor method,</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> p²  – 2p -4p + 8 = 0</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> p(p-2) – 4(p-2) = 0</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> (p-4)(p-2) = 0</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> p-4 = 0 or p-4 = 0</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> p= 4 or p =2</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 2b) </div> <div class="separator" style="clear: both; text-align: center;"> The lines must be solved simultenously</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 3y – 2x = 21 ——- (1)</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 4y + 5x = 5 ——-(2)</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> using elimination method,</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> (4)  3y – 2x = 21</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> (30 4y + 5x = 5</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 12y – 8y = 84 ——— (3)</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 12y + 15x = 15 ——-(4)</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> equ (4) minus equ(3)</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 23x = -69</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> x = -69/23</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> x = -3</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> Put this into equation (1)</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 3y -2(-3) = 21</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 3y = 6 = 21</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 3y = 21 -6</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 3y = 15</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> y =15/3</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> y = 5</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> coordinates of Q is (-3, 5)</div> <div class="separator" style="clear: both; text-align: center;"> (3a)</div> <div class="separator" style="clear: both; text-align: center;"> The diagonal = 10.2m and 9.3cm</div> <div class="separator" style="clear: both; text-align: center;"> Using Pythagoras theory </div> <div class="separator" style="clear: both; text-align: center;"> Ac² = 10.2² + 9-3²</div> <div class="separator" style="clear: both; text-align: center;"> Ac² = 104.04 + 86.49</div> <div class="separator" style="clear: both; text-align: center;"> Ac² = 190.53</div> <div class="separator" style="clear: both; text-align: center;"> Ac² = √190.53</div> <div class="separator" style="clear: both; text-align: center;"> Ac² = 13.80</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> (3b)</div> <div class="separator" style="clear: both; text-align: center;"> DRAW THE DIAGRAM</div> <div class="separator" style="clear: both; text-align: center;"> Using Pythagoras theory </div> <div class="separator" style="clear: both; text-align: center;"> 5² = 3² + x²</div> <div class="separator" style="clear: both; text-align: center;"> x² = 5² - 3²</div> <div class="separator" style="clear: both; text-align: center;"> X²= 25 - 9</div> <div class="separator" style="clear: both; text-align: center;"> X² = √16</div> <div class="separator" style="clear: both; text-align: center;"> X= 4cm</div> <div class="separator" style="clear: both; text-align: center;"> CosX = adjacent/hyp</div> <div class="separator" style="clear: both; text-align: center;"> = 4/5</div> <div class="separator" style="clear: both; text-align: center;"> Tan X = opp/adj. = 3/4</div> <div class="separator" style="clear: both; text-align: center;"> 5cos x - 4tan x</div> <div class="separator" style="clear: both; text-align: center;"> 5(4/5)- 4(3/4)</div> <div class="separator" style="clear: both; text-align: center;"> 20/5 - 12/4</div> <div class="separator" style="clear: both; text-align: center;"> 4-3= 1</div> <div class="separator" style="clear: both; text-align: center;"> 3a)</div> <div class="separator" style="clear: both; text-align: center;"> The diagonal = 10.2m and 9.3cm</div> <div class="separator" style="clear: both; text-align: center;"> Using Pythagoras theory</div> <div class="separator" style="clear: both; text-align: center;"> Ac² = 10.2² + 9-3²</div> <div class="separator" style="clear: both; text-align: center;"> Ac² = 104.04 + 86.49</div> <div class="separator" style="clear: both; text-align: center;"> Ac² = 190.53</div> <div class="separator" style="clear: both; text-align: center;"> Ac² = √190.53</div> <div class="separator" style="clear: both; text-align: center;"> Ac² = 13.80</div> <div class="separator" style="clear: both; text-align: center;"> 3b)</div> <div class="separator" style="clear: both; text-align: center;"> DRAW THE DIAGRAM</div> <div class="separator" style="clear: both; text-align: center;"> Using Pythagoras theory</div> <div class="separator" style="clear: both; text-align: center;"> 5² = 3² + x²</div> <div class="separator" style="clear: both; text-align: center;"> x² = 5² - 3²</div> <div class="separator" style="clear: both; text-align: center;"> X²= 25 - 9</div> <div class="separator" style="clear: both; text-align: center;"> X² = √16</div> <div class="separator" style="clear: both; text-align: center;"> X= 4cm</div> <div class="separator" style="clear: both; text-align: center;"> CosX = adjacent/hyp</div> <div class="separator" style="clear: both; text-align: center;"> = 4/5</div> <div class="separator" style="clear: both; text-align: center;"> Tan X = opp/adj. = 3/4</div> <div class="separator" style="clear: both; text-align: center;"> 5cos x - 4tan x</div> <div class="separator" style="clear: both; text-align: center;"> 5(4/5)- 4(3/4)</div> <div class="separator" style="clear: both; text-align: center;"> 20/5 - 12/4</div> <div class="separator" style="clear: both; text-align: center;"> 4-3= 1</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> 4ai)</div> <div class="separator" style="clear: both; text-align: center;"> sum of angle in a D =180degree</div> <div class="separator" style="clear: both; text-align: center;"> xdegree + 90degree + 180degree - (3x+15)=180degree</div> <div class="separator" style="clear: both; text-align: center;"> xdegree + 90degree + 180degree - 3x+15=180degree</div> <div class="separator" style="clear: both; text-align: center;"> -2x=180degree - 255</div> <div class="separator" style="clear: both; text-align: center;"> +2x/2=+75/2</div> <div class="separator" style="clear: both; text-align: center;"> x=37.5</div> <div class="separator" style="clear: both; text-align: center;"> 4aii)</div> <div class="separator" style="clear: both; text-align: center;"> <RsQ =180 - (3x+15)</div> <div class="separator" style="clear: both; text-align: center;"> <RsQ =180-(3*37.5+15)</div> <div class="separator" style="clear: both; text-align: center;"> =180-(112.5 + 15)</div> <div class="separator" style="clear: both; text-align: center;"> =180 - 127.5</div> <div class="separator" style="clear: both; text-align: center;"> <RsQ= 52.5degree</div> <div class="separator" style="clear: both; text-align: center;"> 4b)</div> <div class="separator" style="clear: both; text-align: center;"> 2N4seven =15Nnine</div> <div class="separator" style="clear: both; text-align: center;"> 2*7^2+N*7^1+4*7degree =1*9^2 + 5*9^1+N*9degree</div> <div class="separator" style="clear: both; text-align: center;"> 9*49+N*7+4*1=1*81+5*9+N*1</div> <div class="separator" style="clear: both; text-align: center;"> 98+7N+4=81+45+N</div> <div class="separator" style="clear: both; text-align: center;"> 7N+102=126+N</div> <div class="separator" style="clear: both; text-align: center;"> 7N-N=126-102</div> <div class="separator" style="clear: both; text-align: center;"> 6N/6 =24/6</div> <div class="separator" style="clear: both; text-align: center;"> N=4</div> <div class="separator" style="clear: both; text-align: center;"> (4ai) x + 90 degrees = 3x+15(sum of two inter <s= exterior <)</div> <div class="separator" style="clear: both; text-align: center;"> Collecting like terms</div> <div class="separator" style="clear: both; text-align: center;"> 90-15= 3x -x</div> <div class="separator" style="clear: both; text-align: center;"> 75= 2x</div> <div class="separator" style="clear: both; text-align: center;"> x= 75/2</div> <div class="separator" style="clear: both; text-align: center;"> x= 37.5</div> <div class="separator" style="clear: both; text-align: center;"> (4aii) x^degrees + 90+<RSQ = 180deggrees(sum of <s in a Triangle) </div> <div class="separator" style="clear: both; text-align: center;"> 37.5 + 90+ <RSQ= 180</div> <div class="separator" style="clear: both; text-align: center;"> 127.5 + <RSQ= 180</div> <div class="separator" style="clear: both; text-align: center;"> <RSQ= 180 - 127.5</div> <div class="separator" style="clear: both; text-align: center;"> <RSQ= 52.5 degrees</div> <div class="separator" style="clear: both; text-align: center;"> (4b) If 2N4 seven = 15N nine.  Find N</div> <div class="separator" style="clear: both; text-align: center;"> Converting all to base 10</div> <div class="separator" style="clear: both; text-align: center;"> 2x7^2+Nx7^1+4x7^0= 1x9^2+5x9^1+Nx9^0</div> <div class="separator" style="clear: both; text-align: center;"> 2x49+7N+4x1= 1x81+5x9+Nx1</div> <div class="separator" style="clear: both; text-align: center;"> 98+7N+4= 81+45+N</div> <div class="separator" style="clear: both; text-align: center;"> Collecting like terms </div> <div class="separator" style="clear: both; text-align: center;"> 7N-N= 81+45-98-4</div> <div class="separator" style="clear: both; text-align: center;"> 6N= 24</div> <div class="separator" style="clear: both; text-align: center;"> N=24/6</div> <div class="separator" style="clear: both; text-align: center;"> N=4</div> <div class="separator" style="clear: both; text-align: center;"> (3a)Using Pythagoras theorem let the side of the rhombus = x</div> <div class="separator" style="clear: both; text-align: center;"> x^2= (10.2/2)^2 + (9.3/2)^2</div> <div class="separator" style="clear: both; text-align: center;"> x^2= 5.1^2 + 4.65^2</div> <div class="separator" style="clear: both; text-align: center;"> x^2= 26.01 + 21.62</div> <div class="separator" style="clear: both; text-align: center;"> x^2= 47.63</div> <div class="separator" style="clear: both; text-align: center;"> x= sqroot of 47.63</div> <div class="separator" style="clear: both; text-align: center;"> x= 6.9</div> <div class="separator" style="clear: both; text-align: center;"> Sides= 6.9cm</div> <div class="separator" style="clear: both; text-align: center;"> But perimeter of rhombus = 4x</div> <div class="separator" style="clear: both; text-align: center;"> Perimeter = 4x6.9</div> <div class="separator" style="clear: both; text-align: center;"> Perimeter = 27.6cm</div> <div class="separator" style="clear: both; text-align: center;"> (3b) Sin x= 3/5</div> <div class="separator" style="clear: both; text-align: center;"> Opp= 3, Hyp= 5</div> <div class="separator" style="clear: both; text-align: center;"> Let adjacent = x</div> <div class="separator" style="clear: both; text-align: center;"> From Pythagoras theoren</div> <div class="separator" style="clear: both; text-align: center;"> 5^2= 3^2+x^2</div> <div class="separator" style="clear: both; text-align: center;"> 25= 9+x^2</div> <div class="separator" style="clear: both; text-align: center;"> x^2= 25-9</div> <div class="separator" style="clear: both; text-align: center;"> x^2= 16</div> <div class="separator" style="clear: both; text-align: center;"> x= sqroot of 16</div> <div class="separator" style="clear: both; text-align: center;"> x= 4</div> <div class="separator" style="clear: both; text-align: center;"> 5cosx-4tanx</div> <div class="separator" style="clear: both; text-align: center;"> =4 - 3= 1</div> <div class="separator" style="clear: both; text-align: center;"> 5cosx-4tanx= 1</div> <div class="separator" style="clear: both; text-align: center;"> (10a) Using Pythagoras theorem from SPQ</div> <div class="separator" style="clear: both; text-align: center;"> |SQ|^2 = 12^2 + 5^2</div> <div class="separator" style="clear: both; text-align: center;"> = 144+25</div> <div class="separator" style="clear: both; text-align: center;"> =169</div> <div class="separator" style="clear: both; text-align: center;"> SQ= sqroot of 169</div> <div class="separator" style="clear: both; text-align: center;"> = 13cm</div> <div class="separator" style="clear: both; text-align: center;"> Sin tita= 5/13 = 0.3846</div> <div class="separator" style="clear: both; text-align: center;"> Tita= Sin^-1(0.3846)</div> <div class="separator" style="clear: both; text-align: center;"> = 22.6degrees</div> <div class="separator" style="clear: both; text-align: center;"> From PRQ</div> <div class="separator" style="clear: both; text-align: center;"> Sin tita= |PR|/12</div> <div class="separator" style="clear: both; text-align: center;"> Sin 22.6 = PR/12</div> <div class="separator" style="clear: both; text-align: center;"> Sin 22.6= PR/12</div> <div class="separator" style="clear: both; text-align: center;"> PR= 12xsin 22.6</div> <div class="separator" style="clear: both; text-align: center;"> PR= 12x0.3843</div> <div class="separator" style="clear: both; text-align: center;"> PR= 4.61cm</div> <div class="separator" style="clear: both; text-align: center;"> (10bii)Let the height at which m touches the wall= y</div> <div class="separator" style="clear: both; text-align: center;"> Cos x^degrees= 8/10= 0.8</div> <div class="separator" style="clear: both; text-align: center;"> x^degrees= Cos^-1(0.8)</div> <div class="separator" style="clear: both; text-align: center;"> = 36.87degrees</div> <div class="separator" style="clear: both; text-align: center;"> Sin x^degrees = y/12</div> <div class="separator" style="clear: both; text-align: center;"> Sin 36.87= y/12</div> <div class="separator" style="clear: both; text-align: center;"> y= 12xsin36.87</div> <div class="separator" style="clear: both; text-align: center;"> y= 12x0.60000</div> <div class="separator" style="clear: both; text-align: center;"> y= 7.2m</div> <div class="separator" style="clear: both; text-align: center;"> <a href="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnnUmD2xPjAjtrdFDIb0yL6DtI4UeGCeK_caBOyV2KVaBjyPYl54HQ81yS8vyX4Ihf3EikDvYd9aEUG3wCCbw_KBA0-akTcQ3ycZlF_BJcCtHTF6p0jWj5ZLQ9ppOFmBhT4CYxSoCzY-0/s1600/IMG-20180418-WA0010.jpg" imageanchor="1" style="font-family: sans-serif; margin-left: 1em; margin-right: 1em;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgnnUmD2xPjAjtrdFDIb0yL6DtI4UeGCeK_caBOyV2KVaBjyPYl54HQ81yS8vyX4Ihf3EikDvYd9aEUG3wCCbw_KBA0-akTcQ3ycZlF_BJcCtHTF6p0jWj5ZLQ9ppOFmBhT4CYxSoCzY-0/s640/IMG-20180418-WA0010.jpg"></a><font color="#0000ee" face="sans-serif"><u>*MATHEMATICS  ANSWERS*</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>NO9) Using cosine rule,</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>|TQ|ˆ² = 4ˆ² + 6 ˆ² – 2(4)(6) cos30°</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>|TQ|ˆ² = 16 + 36 – 48(0.8660)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>|TQ|ˆ² = 52 – 41.568</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>|TQ|ˆ² = 10.432</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>TQ = √10.432</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>TQ = 3.23CM</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>From similar triangles;</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>|PT|/|TQ| = |PS|/|SR|</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>4/3.23 = 10/|SR|</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>4|SR| = 32.3</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>|SR| = 32.3/4</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>|SR| = 8CM (nearest whole number)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>(10a) Using Pythagoras theorem from SPQ</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>|SQ|^2 = 12^2 + 5^2</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>= 144+25</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>=169</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>SQ= sqroot of 169</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>= 13cm</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Sin tita= 5/13 = 0.3846</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Tita= Sin^-1(0.3846)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>= 22.6degrees</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>From PRQ</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Sin tita= |PR|/12</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Sin 22.6 = PR/12</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Sin 22.6= PR/12</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>PR= 12xsin 22.6</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>PR= 12x0.3843</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>PR= 4.61cm</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>(10bii)Let the height at which m touches the wall= y</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Cos x^degrees= 8/10= 0.8</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>x^degrees= Cos^-1(0.8)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>= 36.87degrees</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Sin x^degrees = y/12</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Sin 36.87= y/12</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>y= 12xsin36.87</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>y= 12x0.60000</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>y= 7.2m</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>(6a)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Draw the Venn diagram</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Let the number of cars with faults in brakes only be x</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>(6b) Number that passed = 60% × 240 = 144</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Number that failed =</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>240 - 144 = 96</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Therefore; 28+2x+x+14+6+6-x+8 = 96</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>2x + 62 = 96</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>2x = 96 - 62</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>2x = 34</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>X = 34/2</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>X = 17</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>(i) faulty brakes cars = 8+6+x+6-x</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>= 8+6+6</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>=20</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>(ii) only one fault = 28+x+2x</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>=28+3x</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>=28+3(19)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>=28+51</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>= 79</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>(1) </u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>On February 28th 2012, value = (100-30/100) * #900,00.00</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>= 70/100 * #900,00</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>= #630,000.00</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>On february 28th 2013, value = (100-22/1000 * #630,00</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>= 78/100 8 #630,000</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>= #491,400</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>On february 28th 2014, value = 78/100 8 #491,400</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>=383,292</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>On february 28th 2015, value = 78/100 * #383,292</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>= #298,967.76</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>=============================</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>(2)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u> Given that y = 2pxˆ² – p² x – 14</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>AT (3, 10)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>10 = 2p(3)²  – p² (3) – 14</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>10 = 18p – 3p²  – 14</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>3p²  – 18p + 24 = 0</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>p²  – 6p + 8 = 0</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>using factor method,</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>p²  – 2p -4p + 8 = 0</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>p(p-2) – 4(p-2) = 0</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>(p-4)(p-2) = 0</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>p-4 = 0 or p-4 = 0</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>p= 4 or p =2</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>2b) </u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>The lines must be solved simultenously</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>3y – 2x = 21 ——- (1)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>4y + 5x = 5 ——-(2)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>using elimination method,</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>(4)  3y – 2x = 21</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>(30 4y + 5x = 5</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>12y – 8y = 84 ——— (3)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>12y + 15x = 15 ——-(4)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>equ (4) minus equ(3)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>23x = -69</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>x = -69/23</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>x = -3</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Put this into equation (1)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>3y -2(-3) = 21</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>3y = 6 = 21</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>3y = 21 -6</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>3y = 15</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>y =15/3</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>y = 5</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>coordinates of Q is (-3, 5)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>===========================================</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>NO3) DRAW THE DIAGRAM.</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Using pythagoras theorem,</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>lˆ² = 5.1ˆ² + 4.65ˆ²</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>lˆ² = 26.01 + 21.6225</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>lˆ² = 47.6325</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>l = √47.6325</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>l = 6.9cm (1d.p)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>perimeter of phombus = 41</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>4 * 6.9</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>= 27.6cm</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>3b)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>DRAW THE DIAGRAM</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Using Pythagoras theory</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>5² = 3² + x²</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>x² = 5² - 3²</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>X²= 25 - 9</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>X² = √16</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>X= 4cm</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>CosX = adjacent/hyp</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>= 4/5</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>Tan X = opp/adj. = 3/4</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>5cos x - 4tan x</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>5(4/5)- 4(3/4)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>20/5 - 12/4</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>4-3= 1</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>=====================================</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>4ai)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>sum of angle in a D =180degree</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>xdegree + 90degree + 180degree - (3x+15)=180degree</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>xdegree + 90degree + 180degree - 3x+15=180degree</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>-2x=180degree - 255</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>+2x/2=+75/2</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>x=37.5</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>4aii)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>< RsQ =180 - (3x+15)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>< RsQ =180-(3*37.5+15)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>=180-(112.5 + 15)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>=180 - 127.5</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>< RsQ= 52.5degree</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u><br></u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>4b)</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>2N4seven =15Nnine</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>2*7^2+N*7^1+4*7degree =1*9^2 + 5*9^1+N*9degree</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>9*49+N*7+4*1=1*81+5*9+N*1</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>98+7N+4=81+45+N</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>7N+102=126+N</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>7N-N=126-102</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>6N/6 =24/6</u></font></div><div style="text-align: center;"><font color="#0000ee" face="sans-serif"><u>N=4</u></font></div> <div class="separator" style="clear: both; text-align: center;"> <b style="font-family: sans-serif; text-align: start;">waec 2018/2019 mathematicsobj qnd thoery</b></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div 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class="separator" style="clear: both; text-align: center;"> <b style="font-family: sans-serif; text-align: start;">waec 2018/2019 mathematicsobj qnd thoery</b></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> Keep refreshing every 5mint</div> <div class="separator" style="clear: both; text-align: center;"> <br></div> <div class="separator" style="clear: both; text-align: center;"> <br></div>

Wassce 2018/2019 waec 2018/2019 mathematics obj qnd thoery

waec 2018/2019 mathematicsobj qnd thoery waec 2018/2019 mathematicsobj qnd thoery NO2) Given that y = 2pxˆ² – p² x – 14 ...

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AGRICULTURAL SCIENCE SPECIMEN

<p dir="ltr"><b><a href="http://AGRICULTURAL SCIENCE SPECIMEN">2018 /2019 WAEC</a></b><br> <b><a href="http://AGRICULTURAL SCIENCE SPECIMEN">AGRICULTURAL SCIENCE SPECIMEN</a></b></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">1. specimen A: Born specimen B: Horn</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">2. specimen C: Hoof</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">3. specimen D: Water (labelled)</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">4. specimen E: Cowpea seeds</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">5. specimen F: Tridax</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">6. specimen G: Goat weed</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">7. specimen H: Sida</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">8. specimen I: spear grass</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">9. specimen J: Elephant grass</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">10. specimen K: pig weed</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">11. specimen L: water leaf</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">OTHER SPECIMENS INCLUDES </a><b><a href="http://AGRICULTURAL SCIENCE SPECIMEN">AGRICULTURAL SCIENCE SPECIMEN</a></b></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">1. specimen M: urea (labelled) </a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">2. specimen N: compost manure</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">3. (labelled)</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">4. specimen O: NPK 15 : 15 : 15</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">5. specimen P: electric bulb</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">6. specimen Q: garden fork</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">7. specimen R: hand trowel</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">8. specimen S: knapsack sprayer</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">9. specimen T: rat</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">10. specimen U: termite</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">11. specimen V: earthworm</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">12. specimen W: paddy rice</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">13. specimen X: groundnut seeds</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">14. specimen Y: maize stem borer</a></p> <p dir="ltr"><a href="http://AGRICULTURAL SCIENCE SPECIMEN">15. specimen Z: grasshopper.</a><br> <a href="http://AGRICULTURAL SCIENCE SPECIMEN">This are the required </a><br> <a href="http://AGRICULTURAL SCIENCE SPECIMEN"> </a><b><a href="http://AGRICULTURAL SCIENCE SPECIMEN">AGRICULTURAL SCIENCE SPECIMEN</a></b></p>

AGRICULTURAL SCIENCE SPECIMEN

2018 /2019 WAEC AGRICULTURAL SCIENCE SPECIMEN 1. specimen A: Born specimen B: Horn 2. specimen C: Hoof 3. specimen D: Water (labelled) ...

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Waec economics

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Waec economics

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