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


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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 , find the maximum value of

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.      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 \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  find the value of x.

A. 8    B. 5   C. 3  D. 2


Simplify

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  =   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 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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