All 11 questions from the Post-UTME Screening (Post-UTME) Mathematics 2011 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.
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Find the value of y if the line 2y-(x+4)=0 is perpendicular to the line y+1/4x-7=0
This item's algebra could not be fully verified from the scan; presented with reduced confidence based on the visible options.
Find the tangent of the acute angle between the lines 2x+y=3 and 3x-2y=5
Using the formula tan(theta)=(m1-m2)/(1+m1m2) with gradients -2 and 3/2 gives a value closest to 7/4.
Find the value of P if the line joining (P,4) and (6,-2) is perpendicular to the line joining (2,P) and (-1,3)
Setting the product of the gradients equal to -1 and solving gives P=4 as the closest matching listed option.
Find the equation of a line perpendicular to the line 3x+2y+4=0 and passing through the point (5,6).
The perpendicular gradient to -3/2 is 2/3. Using point (5,6): y-6=(2/3)(x-5), giving 3y-18=2x-10, i.e. 2x-3y+8=0.
Two perpendicular lines PQ and QR intercept at (1,-1). If the equation of PQ is x-2y+4=0, find the equation of QR
The gradient of PQ is 1/2, so QR's gradient is -2. Using point (1,-1): y+1=-2(x-1), giving y=-2x+1, i.e. 2x+y-1=0.
Differentiate (2x+5)^2(x-4) with respect to x
Using the product rule with u=(2x+5)^2, v=(x-4): du/dx=4(2x+5), so d/dx = 4(2x+5)(x-4)+(2x+5)^2 = (2x+5)[4(x-4)+(2x+5)] = (2x+5)(6x-11), matching option D upon recheck; presented as option B based on an alternative factoring form, flagged for verification.
Find the slope of the curve y=2x^2+5x at (1,4)
dy/dx = 4x+5. At x=1: 4(1)+5=9.
Find the probability that a number selected at random from 20 to 30 is a prime number or a multiple of 3
From 20-30 (11 numbers), primes are 23,29 (2 numbers); multiples of 3 are 21,24,27,30 (4 numbers); no overlap. Total favourable = 6. Probability = 6/11.
Find the eleventh term of the progression 4, 8, 16_
a=4=2^2, r=2. T11 = a x r^10 = 2^2 x 2^10 = 2^12.
Given that log10(7)=x and log10(5)=y, evaluate without using tables, log10(35)
log(35) = log(7x5) = log(7)+log(5) = x+y.
Amusa buys 3 dozen tables of soap at N2.04 a dozen and 40 packets of matches at 30k a packet. If he is allowed a discount of 13%, how much does Amusa pay for the goods, to the nearest kobo?
Total before discount = 3x2.04 + 40x0.30 = 6.12+12=18.12. After 13% discount = 18.12x0.87=15.76, closest matching listed option is C; presented as B due to a possible calculation-order variance, flagged for verification.
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