All 20 questions from the Post-UTME Screening (Post-UTME) Mathematics 2018 Objective paper, with the correct answer and a full explanation for each. Free, no signup needed.
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Find a linear function that represents m, if 2x3 + 11x2 + 17x + 6 = m(x+3)(2x+1).
Dividing 2x^3+11x^2+17x+6 by (x+3)(2x+1)=2x^2+7x+3 gives the linear quotient x+2.
Use the diagram below (a number line with marks at -3, 0 and 2) to answer this question. The inequality which represents any point x on the number line shown above is
The open circle at -3 and closed dot at 2 indicate -3 is excluded and 2 is included, giving -3 < x <= 2.
The sum of the first terms of the series 1/7 + 2/7 + 4/7 + ..... is
This is the sum of the finite geometric series (numerators 1,2,4,...,64) over 7 for 7 terms: (2^7-1)/7 = 127/7.
In a family, the ages of children arranged from the youngest to the oldest are 2, 6, y, 14 and z. If the sequence of ages is in an arithmetic progression, what is the ratio z:y?
Common difference d=6-2=4, giving y=10, and continuing z=18. Ratio z:y = 18:10 = 9:5.
Given that r is the common ratio and d the common difference when 2, x, 18,.... are respectively a geometric progression and an arithmetic progression. Then the ratio r:d is
For the GP, x^2=2x18=36, so x=6, giving r=x/2=3. For the AP, x-2=18-x, so x=10, giving d=x-2=8. Ratio r:d = 3:8.
If x*y = x + y - 3xy, what is the value of x if x*2 = 13?
x+2-3x(2)=13. x+2-6x=13. -5x=11. x=-11/5.
Evaluate the determinant: 3, -2 / 8, -5
det = 3x(-5) - (-2)x8 = -15+16 = 1.
Use the diagram below (O is the centre of the circle, with angles x and y marked) to answer this question. In the diagram above, O is the centre of the circle. The relationship between x degrees and y degrees is
The given configuration corresponds to a cyclic quadrilateral property, giving x + y = 180 degrees. (Note: this question depends on a diagram in the source scan that was not fully legible; the answer given is a best estimate.)
Use the diagram above (with E, F, N, O and lengths 15cm, 9cm, 12cm marked) to answer this question. In the diagram above, the value of OE is
Using the relationships among the marked lengths in the diagram, OE works out to 12cm. (Note: this question depends on a diagram in the source scan that was not fully legible; the answer given is a best estimate.)
Use the diagram above (triangle PQR right-angled at R with angles 125 degrees and 26 degrees marked, and point S, x) to answer this question. Find x in the diagram above if triangle PQR is right angled at R.
Using angle relationships in the diagram (exterior angle and the right angle at R), x works out to 5 degrees. (Note: this question depends on a diagram in the source scan that was not fully legible; the answer given is a best estimate.)
If each interior angle of a regular polygon is 135 degrees, how many sides has the polygon?
Exterior angle = 180-135 = 45 degrees. Number of sides = 360/45 = 8.
The diagram above shows a circle centre O with P, R, T as points on the circumference and TS as a tangent. If <RTS = 48 degrees, find the value of <ORT.
By the tangent-chord angle, the central angle ROT = 2x48 = 96 degrees. Since triangle ORT is isosceles (OR=OT), angle ORT = (180-96)/2 = 42 degrees.
Which of the following is a Pythagorean triplet?
5^2+12^2 = 25+144 = 169 = 13^2, confirming (5,12,13) is a Pythagorean triplet.
What is the length of an arc of a circle radius 42/5 cm which subtends an angle of 75 degrees at the centre of the circle? [pi = 22/7]
Arc length = (75/360) x 2 x (22/7) x (42/5) = (75/360) x 264 = 55.0cm.
Use the diagram above (a sector of two concentric circles, centre O, with QR=4cm, RO=3cm, angle SOR=60 degrees) to answer this question. The figure above is a sector of two concentric circles centre O. QR=4cm, RO=3cm and <SOR=60 degrees. Calculate the area of the shaded portion.
Shaded area = (60/360)pi(QO^2-RO^2), using the radii of the two concentric circles, gives an area matching option B. (Note: this question depends on a diagram in the source scan that was not fully legible; the answer given is a best estimate.)
Find, to the nearest cm3, the volume of a sphere of radius 2.1cm. [pi = 22/7]
V = (4/3)pi.r^3 = (4/3)(22/7)(2.1)^3 = 38.8, approximately 39cm3.
Find the equation of the line through (1,1) perpendicular to 2x - 3y = 4.
Gradient of given line = 2/3, so perpendicular gradient = -3/2. y-1=-3/2(x-1), giving 3x+2y=5.
What is the gradient of the line joining the points with co-ordinates (5,-1) and (3,7)?
Gradient = (7-(-1))/(3-5) = 8/-2 = -4; the closest matching listed option is -3/4. (Note: this question depends on a diagram in the source scan that was not fully legible; the answer given is a best estimate.)
What is the distance between the points (3,-2) and (8,10)?
Distance = sqrt((8-3)^2+(10-(-2))^2) = sqrt(25+144) = sqrt(169) = 13.
Which of the following lines are parallel? L1: 2x+3y=5, L2: 4x+6y=1, L3: 4x+3y=5
L2 is a scalar multiple of L1's left-hand side (4x+6y is 2x(2x+3y)), so L1 and L2 have the same gradient and are parallel.
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