Hello and Welcome to UTME CBT FREE Practice Test - Mathematics

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

In a circle of radius 10 cm, a cord of length 10cm is x cm from its centre where x is ______

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

Simplify:  $\frac{log_{10}8}{log_{10}4}$

A. log10 4     B. log10 2       C. $\frac{3}{2}$     D. 2

If $\sqrt{3^{x}}$  =  $\sqrt[3]{9}$, then the value of x is _____

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

The sum of  $3\frac{7}{8}$  and $1\frac{1}{3}$  is less than the difference between  $\frac{3}{8}$  and  $1\frac{2}{3}$  by  _______

A. $3\frac{2}{3}$      B. $6\frac{1}{2}$      C. $5\frac{1}{4}$      D. $1\frac{1}{2}$

In the figure below ΔABC and ΔAED are in adjacent planes. AB = AC = 5cm, BC = 6cm and ∠ADE = 60°, then AE is equal to _____

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

The difference between the length and width of a rectangle is 6 cm and the area is 135 cm2. What is the length?

A. 25cm     B. 18cm     C. 15cm     D. 24cm

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

A. 4     B. 6     C. 8     D. 10

The size of a quantity first doubles and then increases by a further 16%. After a short time its size decreases by 16%. What is the net increase in size of the quantity?

A. $\frac{59300}{625}$ %      B. $\frac{50900}{625}$ %      C. 200%      D. + 100%

If sec2θ + tan2θ = 3, then the angle θ is equal to ______

A. 30o      B. 45o       C. 60o        D. 90o

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

A. $\sqrt{3}$      B. $4\pi&space;-\sqrt{3}$      C . $\frac{2}{3}$ π      D.  $\frac{2}{3}$ π - $2\sqrt{3}$

If y = x2 - 2x - 3, find the least value of y and the corresponding value of x

A. x = 3, y = -3     B. x = 1, y - 3     C. x = -4, y = 1       D. x = 1, y = -4

If x varies inversely as y, and y varies directly as the square root of z, and z varies directly as  $\frac{1}{w^{2}}$ , write down in words how x varies with w.

A. x varies inversely as w2
B. x varies directly as w2
C. x varies directly as w
D. x varies inversely as w

Marks scored by some children in an arithmetic test are:

5, 3, 6, 9, 4, 7, 8, 6, 2, 7, 8, 4, 5, 2, 1, 0, 6, 9, 0, 8

The arithmetic mean of the marks is _______

A. 6    B. 5    C. 7   D. 4

If O is the centre of the circle, ∠POS equals ______

A. 70o    B. 75o     C. 105o    D. 150o

Five years ago, a father was three times as old as the son, now, their combined age amount to 110 years. Thus, the present age of the father is _____

A. 75 years     B. 60 years     C. 98 years    D. 80 years

In triangle FGH, ∠G = 90o,  ∠H = 60o, while in triangle XYZ, ∠X = 60o and ∠Y = 30o. From ΔXYZ, write down the ratio equal to $\frac{FG}{FH}$

A. $\frac{YZ}{YX}$     B. $\frac{YX}{YZ}$     C. $\frac{ZX}{YZ}$     D. $\frac{YX}{ZX}$

A set of data contains a total of 130 items which are divided into six groups for display on a pie chart. If one group contains 26 items then the sector representing this group on the pie chart contains an angle xo at the centre of the circle where x is

A. 36     B. 60     C. 70     D. 72

Find a two-digit number such that three times the tens digit is 2 less than twice the units digit, and twice the number is 20 greater than the number obtained by reversing the digits.

A. 24    B. 42     C. 74     D.47

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

A. x = $\frac{3}{5}$ or - $\frac{1}{2}$     B. x = $\frac{3}{10}$ or -1      C. x = - $\frac{3}{10}$ or 1      D. x = - $\frac{1}{5}$ or $\frac{3}{2}$

The vectors a and b are given in terms of two perpendicular unit vectors i and j on a plane by a = 2i - 3j
b = -i + 2j .

Find the magnitude of the vector a + 3b

A. 2     B. 4     C. $\sqrt{13}&space;+&space;3\sqrt{5}$     D. $\sqrt{10}$

In a school there are 35 students in Class 2A and 40 in Class 2B. The mean score for Class 2A in an English Literature examination is 60.0 and that for 2B in the same paper is 52.5. Find, to one place of decimal, the mean for the combined classes.

A. 1.5     B. 56.0     C. 56.2     D. 56.3

Father reduces the quantity of food bought for the family by 10% when he found out that the cost of living has increased by 15%. Thus, the fractional increase in the food bill is now ____

A. $\frac{1}{12}$     B. $\frac{6}{35}$     C. $\frac{19}{300}$     D. $\frac{7}{200}$

Evaluate without using tables sin(-1290o)

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

Two cars X and Y start at the same point and travel towards a point P which is 150km away. If the average speed of Y is 60km per hour and X arrives at P25 minutes earlier than Y What is the average speed of X?

A. 51 $\frac{3}{9}$  km per hour     B. 72km per hour     C. 37 $\frac{1}{2}$ km per hour     D. 66km per hour

Given that a*b = ab +a + b and that a o b = a + b + 1, find an expression (not involving * or o) for (a * b) o (a * c) if a, b, a, are real numbers and the operations on the right are ordinary addition and multiplication of numbers.

A. ac + ab + bc + b + c + 1
B. ac + ab + a + c + 2
C. ab + ac + a + b + 1
D. ab + ac + 2a + b + c + 1

In the figure above, find the area of xyzw

A. 60 cm2     B. 54 cm2     C. 27 cm2     D. 54.2 cm2

In the figure below PQ is parallel to SR, QS bisects ∠PSR, ∠PQS is 65o and ∠RPS is 20o.

What is the size of ∠PRS?

A. 45o      B. 35o      C. 40o      D. 30o

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

A. 15     B. 4     C. 45     D. 32

An isosceles triangle of sides 13 cm, 13 cm, 10 cm is inscribed in a circle. What is the radius of the circle?

A. $7\frac{1}{24}$  cm     B. 13 cm     C. 8 cm     D. 7 cm

A pentagon has four of its angles equal. If the size of the fifth angle is 60o, find the size of each of the four equal angles.

A. 60o    B. 108o    C. 120o    D. 150o

Simplify:  $2\frac{5}{12}-1\frac{7}{8}\times&space;\frac{6}{5}$

A. $\frac{1}{6}$     B. $\frac{13}{20}$     C. $\frac{11}{30}$     D. $\frac{9}{4}$

The sum of the progression 1 + x + x2 + x3 + ........ is _______

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

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

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

Evaluate (2° + 4 - ½ )2

A. $\frac{1}{4}$     B. $\frac{5}{4}$     C. $\frac{9}{4}$     D. 4

Arrange $\frac{3}{5}$$\frac{9}{16}$$\frac{34}{59}$  and  $\frac{71}{97}$  in ascending order of magnitude.

A. $\frac{3}{5}$$\frac{9}{16}$$\frac{34}{59}$$\frac{71}{97}$      B. $\frac{9}{16}$$\frac{3}{5}$$\frac{71}{97}$$\frac{34}{59}$      C. $\frac{9}{16}$$\frac{34}{59}$$\frac{3}{5}$$\frac{71}{97}$      D. $\frac{34}{59}$$\frac{71}{97}$$\frac{3}{5}$$\frac{9}{16}$

Solve: $\frac{1}{x + 1}$ - $\frac{1}{x + 3}$ = $\frac{1}{4}$

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

In the figure above, PQ is parallel to RS. Calculate the value of x

A. 20o    B. 40o    C. 60o    D. 80o

GREAT! You finished before the expiration of the 30 minutes allotted to you. You may want to preview before submission, else, Click the submit button below to see your score

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.