UTME CBT FREE Practice Test – Mathematics

A frustum pyramid with square base has its upper and lower sections as squares of sizes 2 cm and 5 cm respectively and the distance between them is 6 cm. Find the height of the pyramid from which the frustum was obtained.

A. 8.0 m   B. 8.4 m   C. 9.0 m   D. 10.0 m

Find the area of the shaded segment in the figure shown above.

A.       B.       C . π      D.  π -

If 0.0000152 x 0.00042 = A x 10^B , where 1 ≤ A ≤ 10, find A and B.

A. A = 9, B = 6.38      B. A = 6.38, B = -9       C. A = 6.38, B = 9       D. A = 6.38, B = -1

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

A regular hexagon is constructed inside a circle of diameter 12 cm. The area of hexagon is _____

A. 36π cm²      B. cm²      C. 54 cm²     D. cm²

The minimum point on the curve y = x² - 6x + 5  is  at  _______ 

A. (1,5)      B. (2, 3)       C. (3, -4)      D. (-3, 4)

Find the distance between the points and

A.    B. 0    C. 1    D.

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°

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

A. 120    B. 10    C. 20    D. 60

Differentiate with respect to x.

A.      B.      C.      D.

The table above shows the scores of a group of students in a test. If the average score is 3.5, find the value of x.

A. 1    B. 2    C. 3    D. 4

If three unbiased coins are tossed, find the probability that they are all heads.

A.    B.    C.    D.

 lf    = 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

If the operation * on the set of integers is defined by find the value of 4*(8*32)

A. 16    B. 8     C. 4  D. 3

In the diagram above, XZ is the diameter of the circle XYZW, with centre O and radius cm. If XY = 12 cm, find the area of the triangle XYZ.

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

If  , find the value of x.

A. 4    B. 5    C. 2    D. 3

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

In the figure below, if PT is parallel to RS, PQ = PT and angle SQT 90^o  , find. x

A 35^o      B 50^o     C. 55^o     D. 70^o

A regular polygon has 150° as the size of each interior angle. How many sides does it have?

A. 12     B. 10     C. 9     D. 8

Solve: - =  

A. x = -1 or 3     B. x = 1 or 3     C. x = 1 or -5     D. x = -1 or 5

Find the value of sin 45° – cos 30°.

A.     B.      C.      D.

If , find x

A.      B.   C.     D.

The bar chart above shows different colours of cars passing a particular point of a certain street in two minutes. What fraction of the total number of cars is yellow?

A.      B.      C.     D.

If 55_x + 52_x = 77₁₀, find x

A. 5    B. 6    C. 7    D. 10

PQRS is a cyclic quadrilateral with PQ as diameter of the circle. If ∠PQS 15^o find ∠QRS

A. 75^o     B. 37 ½^o     C. 127½^o     D. 105^o

The sum to infinity of the series 1 + + + + ...... is ______

A.      B.      C.      D.

In base ten, the number 101101 (base 2) equals _______

A. 15     B. 4     C. 45     D. 32

If  b = a + cp and r = ab + cp2, express b² in terms of a, c, r.

A. b² = 2cr + 2ab - a²        B. b² = 2a + 2c²r         C. b² = a² + cr²         D. b² = ar² + c

Let K be any number from 0 and -1.

If P = , then _____

A. P > 0    B. P ≥ 0    C. P ≤ 0    D. P < 1

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

A. π cm³    B. 144 π cm³      C. π cm³    D. 72 π cm³

Simplify:

A.       B.       C.       D.

After getting a rise of 15%, a man’s new monthly salary is N345. How much per month did he earn before the increase?

A. N330     B. N396.75     C. N300     D. N293.25

On a square paper of length 2.524375cm is  inscribed square diagram of length 0.524375cm. Find the area of the paper not covered by the diagram correct to 3 significant figures.

A. 6.00 cm²   B. 6.10 cm²    C. 6 cm²   D. 6.09 cm²

Find the roots of the equation 10x² - 13x - 3 = 0

A. x = or -      B. x = or -1      C. x = - or 1      D. x = - or

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. 9   D. 8

y varies partly as the square of x and partly as the inverse of the square root of x. -Write down the expression for y if y = 2 when x = 1 and y = 6 when x = 4.

A.        

B.        

C.        

D.

Determine the maximum value of y = 3x² - x³

A. 0    B. 2    C. 4   D. 6

A man runs a distance of 9km at a constant speed for the first 4km and then 2km/h faster for the rest of the distance. The whole run takes him one hour. His average speed for the first 4km is _____

A. 6 km/h     B. 8 km/h     C. 9 km/h     D. 11 km/h

If the 7th term of an AP is twice the third term and the sum of the first four terms is 42, find the common difference.

A. 6     B. 3     C. 2     D. 1

Correct each of the numbers 59.81798 and 0.0746829 to three significant figures and multiply them, giving your answer to three significant figures.

A. 4.46     B. 4.48     C. 4.47     D. 4.49