# UTME CBT Practice Test – Mathematics (Diagnostic Test) – Set 3

UTME CBT Practice Test – Mathematics (Diagnostic Test) – Set 3

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Algebra

Find the range of values of x for which  $\frac{x+2}{4}-\frac{2x-3}{3}<&space;4$

A. x > -6    B. x > -3     C. x < 8    D. x < 4

Algebra

Solve for x in the equation x3 - 5x2 - x + 5 = 0

A. 1, -l or 5    B. 1, 1 or -5    C. -1, 1 or- 5    D. 1, 1 or 5

If a function is defined by f(x + 1) = 3x2 - x + 4, find f(0)

A. 4 B. 6 C. 8 D. 10

Calculus

The inverse of the function f(x) = 3x + 4 is _____

A. $\frac{1}{3}$ (x - 4)    B. $\frac{1}{5}$ (x — 5)    C. $\frac{1}{4}$ (x + 3)    D. $\frac{1}{3}$ (x + 4)

Algebra

If The 9th term of an AP is five times the 5th term, find the relationship between a and d.

A. 2a + d = 0     B. 3a + 5d = 0     C. a + 3d = 0     D. a + 2d = 0

Geometry/Trigonometry

A bucket is 12 cm in diameter at the top, 8 cm in diameter at the bottom and 4cm deep. Calculate its volume.

A. $\frac{304}{3}$ π cm3    B. 144 π cm3      C. $\frac{128}{3}$ π cm3    D. 72 π cm3

Algebra

The sum to infinity of the series 1 + $\frac{1}{3}$ + $\frac{1}{9}$ + $\frac{1}{27}$ + ...... is ______

A. $\frac{11}{3}$     B. $\frac{10}{3}$     C. $\frac{5}{2}$     D. $\frac{3}{2}$

Geometry/Trigonometry

If tan θ = $\frac{4}{3}$, calculate sin2θ - cos2θ

A. $\frac{16}{25}$    B. $\frac{24}{25}$    C. $\frac{7}{25}$    D. $\frac{9}{25}$

Number and Numeration

Simplify $\left&space;(&space;\sqrt{0.7}+\sqrt{70}&space;\right&space;)^{2}$

A. 84.7   B. 70.7    C. 217.7    D. 168.7

Geometry/Trigonometry

In the diagram above, PST is a straight line, PQ = QS = RS. If ∠RST = 72°, find x.

A. 36°    B. 18°    C. 72°    D. 24°

Statistics

Find the mean of the data: 7, -3, 4, -2, 5, 9, 4, 8, -6, 12

A. 3   B. 4   C. 1   D. 2

Geometry/Trigonometry

The sum of the interior angles of a polygon is 20 right angles. How many sides does the polygon have?

A. 12     B. 20    C. 40    D. 10

Calculus

lf  $\frac{dy}{dx}$  = 2x - 3 and y = 3 when x = 0, find y in terms of x.

A. 2x2 - 3x      B. x2 - 3x      C. x2 - 3x - 3       D. x2 - 3x + 3

Number and Numeration

A trader bought goats for N 4000 each. He sold them for N 1801000 at a loss of 25%. How many goats did he buy?

A. 60  B. 50   C. 45   D. 36

Number and Numeration

The Venn diagram above shows the number of students offering Music and History in a class of 80 students. If a student is picked at random from the class, what is the probability that he offers Music only?

A. 0.38    B. 0.13    C. 0.50    D. 0.25

Statistics

Calculate the mean deviation of the set of numbers 7, 3, 14, 9, 7 and 8

A. 2 $\frac{1}{6}$    B. 2 $\frac{1}{2}$    C. 1 $\frac{1}{6}$    D. 2 $\frac{1}{3}$

Algebra

If $\begin{pmatrix}&space;2&space;&&space;1\\&space;3&space;&&space;0&space;\end{pmatrix}$ and I is a 2 X 2 unit matrix, evaluate P2 - 2P + 4I

A. $\begin{pmatrix}&space;9&space;&&space;4\\&space;-12&space;&&space;1&space;\end{pmatrix}$     B. $\begin{pmatrix}&space;-3&space;&&space;0\\&space;0&space;&&space;-3&space;\end{pmatrix}$     C. $\begin{pmatrix}&space;1&space;&&space;0\\&space;0&space;&&space;1&space;\end{pmatrix}$    D. $\begin{pmatrix}&space;1&space;&&space;4\\&space;4&space;&&space;1&space;\end{pmatrix}$

Calculus

The slope of the tangent to the curve y = 3x2 - 2x + 5 at the point (1, 6) is ______

A. 4     B. 1   C. 6    D. 5

Calculus

Find the derivative of y = sin2(5x) with respect to x.

A. 10 sin 5x cos 5x     B. 5 sin 5x cos 5x     C. 2 sin 5x cos 5x    D. 15 sin 5x cos 5x

Statistics

The probability of a student passing any examination is  $\frac{2}{3}$.  If the student takes three examinations, what is the probability that he will not pass any of them?

A. $\frac{2}{3}$    B. $\frac{4}{9}$    C. $\frac{8}{27}$    D. $\frac{1}{27}$

Algebra

If x varies directly as $\sqrt{n}$ and x = 9 when n = 9, find x when n = $\frac{17}{9}$

A. 4    B. 27    C. $\sqrt{3}$    D. $\sqrt{17}$

Calculus

If y = $x^{2}-\frac{1}{x}$  find  $\frac{dy}{dx}$

A. $2x-\frac{1}{x^{2}}$     B. 2x + x2     C. 2x - x2     D. $2x+\frac{1}{x^{2}}$

Geometry/Trigonometry

In the diagram above, XZ is the diameter of the circle XYZW, with centre O and radius $\frac{15}{2}$ cm. If XY = 12 cm, find the area of the triangle XYZ.

A. 54 cm2    B. 45cm2    C. 27cm2     D. 75cm2

Calculus

A circle with a radius 5 cm has its radius increasing at the rate at 0.2cms-1. What will be the corresponding increase in the area?

A. 2 π   B. 5 π   C. π   D. 4 π

Algebra

The binary operation * is defined on the set of integers p and q by p*q = pq + p + q. Find 2*(3*4).

A. 59   B. 19    C. 67    D. 38

Statistics

The mean of a set of six numbers is 60. If the mean of the first five is 50, find the sixth number in the set.

A. 105    B. 100    C. 95    D. 110

Statistics

The acres for rice, pineapples, cassava cocoa and palm oil in a certain district are given respectively as 2, 5, 3, 11 and 9. What la the angle of the sector for cassava in a pie chart?

A. 108°    B. 180°    C. 36°    D. 60°

Geometry/Trigonometry

The triangle POR above is _______

A. an obtuse-angled triangle    B. a scalene triangle    C. an isosceles triangle    D. an equilateral triangle

Geometry/Trigonometry

Find the value of α if the line 2y - αx + 4 = 0 is perpendicular to the line y + $\frac{1}{4}$  -  7 = 0

A. -4    B. 4    C. 8     D. -8

Number and Numeration

Simplify 52.4 - 5.7 - 3.45 - 1.75

A. 41.4    B. 41.5   C. 42.1   D. 42.2

Number and Numeration

Without using tables, evaluate $\left&space;(&space;343&space;\right&space;)^{\frac{1}{3}}&space;\times&space;\left&space;(&space;0.14&space;\right&space;)^{-1}$

A. 10   B. 12 .  C. 8 .   D. 7

Calculus

Evaluate $\int&space;Sin\:&space;3x\:&space;dx$

A. $\frac{2}{3}cos3x+C$     B. $\frac{1}{3}cos3x+C$     C. - $\frac{1}{3}cos3x+C$    D. - $\frac{2}{3}cos3x+C$

Number and Numeration

Evaluate  $\frac{0.21\times&space;0.072\times&space;0.00054}{0.006\times&space;1.68\times&space;0.063}$  correct to four significant figures.

A. 0.01286   B. 0.01285    C. 0.1286    D. 0.1285

Number and Numeration

In a school 220 students offer Biology or Mathematics or both. 125 offer Biology and 110 Mathematics. How many offer Biology but, not Mathematics?

A. 95    B. 80    C. 125    D. 110

Calculus

Find the maximum value of y in the equation y = 1 - 2x - 3x2

A. $\frac{5}{4}$    B. $\frac{5}{3}$    C. $\frac{3}{4}$    D. $\frac{4}{3}$

Algebra

Make r the subject of the formula $\frac{x}{r+a}&space;=\frac{a}{r}$

A. $\frac{a^{2}}{x-a}$    B. $\frac{a^{2}}{x+a}$    C. $\frac{a}{x-a}$    D. $\frac{a}{x+a}$

Geometry/Trigonometry

In the diagram above, a cylinder is surmounted by a hemispherical bowl. Calculate the volume of the solid.

A. 180 π cm3    B. 162 π cm3    C. 216 π cm3    D. 198 π cm3

Statistics

The range of the data k + 2, k - 3, k + 4, k - 2, k, k + 5, k + 3, k - 1 and k + 6 is ______

A. 10   B. 11    C. 6   D. 8

Statistics

How many three-digit numbers can be formed from 32564 without any digit being repeated?

A. 120    B. 10    C. 20    D. 60

For the set of numbers 2, 3, 5, 6, 7, 7, 8

A. the median is greater than the mode ,
B. the mean is less than the median.
C. the mean is greater than the median
D. the median is equal to the mean

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