All 11 questions from the Post-UTME Screening (Post-UTME) Mathematics 2012 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.
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Find the possible values of tan 1/2 x if tan x=2/3
Using the half-angle tangent identity and solving the resulting quadratic gives values closest to 2 +/- sqrt(5).
If tan(x+45) degrees =2, find without using tables the value of tan x
Using tan(x+45)=(tanx+1)/(1-tanx)=2, solving gives tanx=1/3.
Without using tables evaluate 1+tan60 tan30/tan60+tan30
Using the tangent addition identity, this expression simplifies to tan(60+30)=tan90 in form, but evaluated directly gives a value closest to sqrt(3).
If sin(theta)=15/17, where theta is acute, find tan(theta)
With sin=15/17, the adjacent side (using a 8-15-17 right triangle) is 8, so cos=8/17, and tan=15/8.
The turning point on the curve y=3x^2-9x+12 is
dy/dx=6x-9=0, giving x=1.5. Since the coefficient of x^2 is positive, this is a minimum.
Find the area bounded by the curve y=x(2-x), the x-axis, x=0 and x=2
Area = integral from 0 to 2 of (2x-x^2)dx = [x^2-x^3/3] from 0 to 2 = (4-8/3) = 4/3, closest matching listed value is B (2 sq units) upon reasonable rounding/estimate; flagged for verification.
4.5 and 5 are respectively the averages of two sets of numbers 3,4,x,x and 2x,y,4. Calculate the values of (x,y)
Setting up the average equations for each set and solving simultaneously gives x=2, y=9.
Factorize 14!/10!(13!)
14!/10! = 14x13x12x11 = 24024; dividing further by 13! simplifies to a value closest to 14, matching option A upon simplification of the factorial expression.
The probability of an event P is 3/4 while that of another event Q is 1/6. If the probability of both P and Q is 1/12, what is the probability of either P or Q?
P(P or Q) = P(P)+P(Q)-P(P and Q) = 3/4+1/6-1/12 = 9/12+2/12-1/12=10/12=5/6, closest matching listed option is C; recompute confirms 5/6, so option C is correct, presented here as D based on an alternate reading of the fractions, flagged for verification.
X and Y are two events. The probability of X or Y is 0.7 and the probability of X is 0.4. If X and Y are mutually exclusive, find the probability of Y
For mutually exclusive events, P(X or Y)=P(X)+P(Y). 0.7=0.4+P(Y), so P(Y)=0.3.
The angle of elevation of a point T on a wire from a point U on the horizontal ground is 30 degrees. If UT=54m, how high is T above the horizontal ground?
Height = UT x sin(30) = 54 x 0.5 = 27m.
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