UTME CBT Practice Test – Mathematics (Diagnostic Test) – Set 4

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1. You are to attempt 40 Objectives Questions ONLY for  30 minutes.
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Algebra

x varies directly as the product of u and y and inversely as their sum. If x = 3 when u = 3 and y = 1, what is the value of x if u = 3 and v = 3?

A. 3    B. 4    C. 6   D. 9

Geometry/Trigonometry

If $-\frac{\pi&space;}{2}\leq&space;\theta&space;\leq&space;2\pi$, find the maximum value of $f(\theta&space;)=\frac{4}{6+2cos\theta&space;}$

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

Algebra

The sum of the first n terms of an arithmetic . progression is 252. 1f the. first term is -16 and the last term is 72, find the number of terms in the series.

A. 6    B. 7    C. 8    D. 9

Number and Numeration

Simplify 2134 x 234

A. 103114    B. 103214     C. 122314    D. 132114

Statistics

If nP3 - 6(nC4) = 0, find the value of n.

A. 5    B. 6    C. 7   D. 8

Calculus

Given y = x3 − x2 − 4, find  $\frac{dy}{dx}$  at  x =  0

A. 0     B. 1    C. 2    D. 3

Statistics

The result of tossing a fair dice 120 times is summarized above. Find the value of x.

A. 19    B. 20    C. 21    D. 222

The mean of the numbers 3, 6, 4, x and 7 is 5. Find the standard deviation

A. $\sqrt{2}$     B. $\sqrt{3}$     C. 2     D. 3

Algebra

A matrix P has an inverse P-1 = $\begin{pmatrix}&space;1&space;&&space;-3\\&space;0&space;&&space;1\end{pmatrix}$ , find P

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

Find the mean of the distribution above. A. 1    B. 2    C. 3   D. 4

Number and Numeration

Simplify $1&space;-&space;\left&space;(&space;2\frac{1}{3}\times&space;1\frac{1}{4}&space;\right&space;)+&space;\frac{3}{5}$

A.  -1 $\frac{1}{15}$    B.  -1 $\frac{19}{60}$   C. -2 $\frac{7}{15}$   D. -2 $\frac{31}{60}$

Number and Numeration

In a class of 40 students, 32 offer Mathematics, 24 offer Physics. How many offer, both Mathematics and Physics?

A. 20    B. 16   C. 8   D. 4

Geometry/Trigonometry

A triangle has vertices P(-1, 6), Q(-3, -4) and R(1, -4). Find the midpoints of PQ and QR respectively.

A. (0,-2) and (-1-4)     B. (-1 , 0) and (—1,-1)     C. (-2, 1) and (0, 1)     D. (-2, 1) and (-1, -4)

Statistics

On a pie chat, there are four sectors of which three angles are 45°, 90° and 135°. If the smallest sector represents N 28.00, how much is the largest sector?

A. N 96.00    B. N 84.00    C. N 48.00    D. N 42.00

Number and Numeration

If  $\frac{9^{2x-1}}{27^{x+1}}=1$ find the value of x.

A. 8    B. 5   C. 3  D. 2

Simplify $\frac{\sqrt{98}-\sqrt{50}}{\sqrt{32}}$

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

Calculus

Determine the maximum value of y = 3x2 - x3

A. 0    B. 2    C. 4   D. 6

Calculus

Given y = x3 − x2 − 4,  find  $\frac{dy}{dx}$  at  x  =  4

A. 38    B. 39    C. 40   D. 41

Geometry/Trigonometry

An arc of a circle subtends an angle of 30° on the circumference of a circle of radius 21 cm. Find the length of the arc. [π = $\frac{22}{7}$]

A. 11 cm   B. 22 cm    C. 44 cm    D. 66 cm

Calculus

Find the slope of the curve y = 2x2 + 5x - 3 at (1, 4)

A. 4    B. 6    C. 7    D. 9

Statistics

A bag contains 5 black balls and 3 red balls. Two balls are picked randomly without replacement . What is the probability that a black and a red ball are picked?

A. $\frac{15}{28}$    B. $\frac{13}{28}$     C. $\frac{5}{14}$     D. $\frac{3}{14}$

By how much will the mean of 30, 56, 31, 55, and 44 less than the median?

A. 0.75     B. 0.50     C. 0.33    D. 0.17

Geometry/Trigonometry

An airplane flies due north from airports P to Q and then flies due east to R. If Q is equidistant from P and R, find the bearing of P from R.

A. 090°    B. 135°    C. 225°    D. 270°

Algebra

Find the values of x and y respectively if 3x - 5y + 5 = 0 and 4x - 7y + 8 = 0

A. -5, -4    B. -4, -5    C. 4, 5    D. 5, 4

Geometry/Trigonometry

In the diagram above, PQ is parallel to RS. What is the value of α + β + γ?

A. 360°   B. 200°    C. 180°    D. 90°

Algebra

Three consecutive terms of a geometric progression are given as n - 2, n and n + 3. Find the common ratio.

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

Geometry/Trigonometry

In the diagram above, O is the centre of the circle, POM is a diameter and ∠MNQ = 42°. Calculate ∠QMP.

A. 42°    B. 48°    C. 132°    D. 138°

Geometry/Trigonometry

Find the value of p, if the line which passes through (-1, -p) and (-2p, 2) is parallel, to the line 2y + 8x - 17 = 0

A. $\frac{7}{6}$     B. $\frac{6}{7}$    C.  $\frac{-2}{7}$     D. $\frac{-6}{7}$

Algebra

If  $\begin{vmatrix}&space;-x&space;&&space;2\\&space;4x&space;&&space;1&space;\end{vmatrix}$ = $\begin{vmatrix}&space;3&space;&&space;3x\\&space;4&space;&&space;-5&space;\end{vmatrix}$  find the value of x.

A. 5    B. 2   C. -2   D. -5

Calculus

Given y = x3 − x2 − 4, find $\frac{dy}{dx}$ at x = -1

A. 3     B. 4     C. 5     D. 6

Number and Numeration

Find $\left&space;(&space;\frac{1}{0.06}+&space;\frac{1}{0.042}&space;\right&space;)^{-1}$ correct to 2 decimal places.

A. 1.43    B. 1.53    C. 3.14    D.4.42

Calculus

If y = 3 sin (-4x),  $\frac{dy}{dx}$  is ______

A. -12x cox (-4x)    B. -12x cos (-4x)    C. -12 cos (-4x)    D. 12 sin (-4x)

Number and Numeration

Given:
U = {Even numbers between 0 and 30}
P = {Multiples of 6 between 0 and 30}
Q = {Multiples of 4 between 0 and 30}

Find.(P∪Q)´

A. {2, 10, 14, 22, 26)    B. {0, 10, 14, 22, 26}    C. {2, 4, 14, 18, 26)    D. {0, 2, 6, 22, 26}

Geometry/Trigonometry

XYZ is a circle with center O and radius 7 cm. Find the area of the shaded region. [π = $\frac{22}{7}$]

A. 84 cm2    B. 77 cm2    C. 38 cm2    D. 14 cm2

Algebra

Find the range of the values of x satisfying the inequalities 5 + x ≤ 8 and 13 + x ≥ 7.

A. -3 ≤ x ≤ 3    B. 3 ≤ x ≤ 6    C. -6 ≤ x ≤ 3     D. -6 ≤ x ≤ -3

Calculus

Given y = x3 − x2 − 4, find $\frac{dy}{dx}$

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

Statistics

The histogram above shows the ages of the victims of a pollution. How many people were involved in the pollution?

A. 15   B. 18    C. 20    D. 21

Algebra

The length a person can jump is inversely proportional to his weight. If a 20 kg person can jump 1.5 m, find the constant proportionality.

A.60    B. 30   C. 20  D. 15

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