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

Hello and Welcome to UTME CBT Practice Test - Mathematics (Diagnostic Test) - Set 4

1. You are to attempt 40 Objectives Questions ONLY for  30 minutes.
2. Supply Your Full Name and Location in the text box below and begin immediately.
Full Name (Surname First):
Location:

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 , find the maximum value of

A. 4     B. 1     C.     D.

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    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.      B.      C. 2     D. 3

Algebra

A matrix P has an inverse P-1 = , find P

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

Number and Numeration

Simplify

A.  -1     B.  -1   C. -2    D. -2

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  find the value of x.

A. 8    B. 5   C. 3  D. 2

Simplify

A. 3    B. 1    C.   D.

Calculus

Determine the maximum value of y = 3x2 - x3

A. 0    B. 2    C. 4   D. 6

Calculus

Given y = x3 − x2 − 4,  find    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 = ]

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.    B.      C.      D.

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.     B.     C.     D.

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.      B.     C.       D.

Algebra

If  =   find the value of x.

A. 5    B. 2   C. -2   D. -5

Calculus

Given y = x3 − x2 − 4, find at x = -1

A. 3     B. 4     C. 5     D. 6

Number and Numeration

Find correct to 2 decimal places.

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

Calculus

If y = 3 sin (-4x),    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 = ]

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

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

To submit your quiz and see your score/performance report; Make sure you supply your Full Name in the form above.

Unable to submit your quiz? . Make sure you supply your Full Name before submission.