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2019 WAEC Further Mathematics Theory (a) P(-1, 4), Q(2, 3), R(x, y) and S(-2, 3) are the verticles of a...

Further Mathematics
WAEC 2019

(a) P(-1, 4), Q(2, 3), R(x, y) and S(-2, 3) are the verticles of a parallelogram. Find the value of x and y. 

(b) A particle starts from rest and moves in a straight line. It attains a velocity of 20ms\(^{-1}\) after travelling a distance of 8 metres. Calculate;

(ii) Iis acceleration

(ii) the time taken to travel 40 metres

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Explanation

\(\over{PS}\) = \(\over{OS}\) - \(\over{OP}\) = (\(^{-2}_3\)) - (\(^{-1}_4\)) = (\(^{-1}_{-1}\)) 

Similarly \(\over{QR}\) = \(\over{OR}\) - \(\over{OQ}\) = (\(^x_y\)) - (\(^2_3\)) = (\(^{x - 2}_{y - 3}\))

Since \(\over{PS}\) = \(\over{QR}\), it flows that (\(^{x - 2}_{y - 3}\)) = (\(^{-1}_{-1}\)). Therefore, x - 2 = -1 which solved will yield x = 1.

Also, y - 3 = -1 which implies that y = 2

 

(b)(i), Since the particle starts from rest, the initial velocity (u) = 0 and substituting for final velocity (v) and distance (s) into the formula v\(^2\) = u\(^2\) + 2as to obtain 20\(^2\) = 0 + 2a(8) and when simplifies and solved for acceleration (a), to get a = 25ms\(^{-2}\) 

(b)(ii), S = ut + \(\frac{1}{2}\)at\(^2\), where s = 40, u = 0 and a = 25

Substituting these values into the equation we obtain 40 = 0 + \(\frac{1}{2}\) x 25t\(^2\) and solving for t gave t = 1.79 seconds. 


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Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts
WAEC offline past questions - with all answers and explanations in one app - Download for free
WAEC May/June 2024 - Practice for Objective & Theory - From 1988 till date, download app now - 99995
WAEC Past Questions, Objective & Theory, Study 100% offline, Download app now - 24709
WAEC offline past questions - with all answers and explanations in one app - Download for free
WAEC May/June 2024 - Practice for Objective & Theory - From 1988 till date, download app now - 99995
WAEC Past Questions, Objective & Theory, Study 100% offline, Download app now - 24709
Post-UTME Past Questions - Original materials are available here - Download PDF for your school of choice + 1 year SMS alerts