UTME CBT FREE Practice Test – Mathematics (Score 70% and Above and WIN FREE Airtime)


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In the figure above, PT is a tangent to the circle with centre at O. If ∠PQT = 30°, find the value of ∠PTO.

A. 30°    B. 15°    C. 24°    D. 12°



In this figure, PQRS is a parallelogram, PS = PT and ∠PST = 55o . The size of ∠PQR is _____

A. 105o     B. 120o     C. 115o.     D. 110o


The score of 16 students in a Mathematics test are

65, 65, 55, 60, 60, 65, 60, 70 75, 70, 65, 70, 60, 65, 65, 70.

What is the sum of the median and modal scores?

A. 125     B. 130     C. 140     D. 150 


A sum of money invested at 5 % per annum simple interest amounts to $ 285.20 after 3 years. How long will it take the same sum to amount to $ 434.00 at 7½ % per annum simple interest?

A. 7½ years     B. 10 years     C. 5 years     D. 12 years


The number of telephone calls N between two cities A and B varies directly as the population PA, PB in A and B respectively and inversely as the square of the distance D between A and B. Which of the following equations represents this relation?

A.

B.

C. N = KDPAPB

D. N = KDPA + CDPB


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


If log2 y = 3 - Iog2 x½ , find y when x = 4

A. 8     B.      C.      D. 1


Find the missing numerator \frac{5}{x + 1} - \frac{3}{1 - x} -   =  \frac{}{x + 1}

A. -1     B. \frac{1}{x + 1}     C. \frac{3(2-5x)}{x - 1}     D. 3(1 - 5x)


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


A canal has rectangular cross section of width 10cm and breadth 1m. If water of uniform density 1gm cm-3 flows through it at a constant speed of 1000 mm per minute, the adjacent sea is _______

A 100 000     B. 1000 000     C. 120 000     D. 30 000


If M represents the median and D the mode of the measurements 5, 9, 3, 5, 8 then (M, D) is _______

A. (6,5)    B. (5,8)    C. (5,7)    D. (5,5) 


Which of the following fractions is less than one third?

A. \frac{22}{63}    B. \frac{4}{11}    C. \frac{15}{46}    D. \frac{33}{96}


Simplify:

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


If b = a + cp and r = ab + \frac{1}{2} cp2, express b2 in terms of a, c, r.

A. b2 = 2cr - a2     B. b2 = 2a + 2c2r     C. b2 = a2 + \frac{1}{2}cr2     D. b2 = \frac{1}{2}ar2 + c


Solve the simultaneous linear equation

2x + 5y = 11
7x + 4y = 2

A. x = -8, y = 1     B. x = -2, y = 4     C. x = 2, y = -3     D. x = - \frac{34}{27} ,  y = \frac{73}{27}


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 above, FD//AC. The area AEF = 6 cm2, AE = 3 cm, BC = 3 cm, CD = 5 cm, ∠BCD is an obtuse angle. Find the length of BD.

A.       B. 6      C. 4      D.


What will be the value of k so that the quadratic equation kx2 - 4x + 1 = 0 has two equal roots?

A. 2     B. 3     C. 4     D. 8


Simplify

A.         B.        C.        D.


In PQR, PQ = 10cm, QR = 8cm and RP = 6cm, the perpendicular RS is drawn from R to PQ. Find the length of RS.

A. 4 cm     B.   cm     C. \frac{10}{7} cm     D. 4.8 cm


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}


What is the length of an arc of a circle that subtends 2\frac{1}{2} radians at the centre when the radius of the circle is 8 cm ?

A. 8 cm     B. 10 cm     C. 40 cm     D. 20 cm


UTME Mathematics - 40 Questions


(Numbers indicate the lengths of the sides of the triangles).

If the area of A PLR is k2 sq. units what is the area of the shaded portion?

A. \frac{5}{9}  k2 sq.units     B. \frac{1}{3}  k2 sq.units     C. \frac{8}{9}  k2 sq. units     D. \frac{7}{9}  k2 sq. units


If (25)x - 1 = 64, then the value of x is ______

A. 7    B. 4   C. 32   D. 64


Simplify:

A. \frac{117}{95}     B. \frac{3}{10}     C. \frac{233}{151}     D. \frac{7}{95}




If O is the centre of the circle in the figure above, find the value of x.

A. 50°   B. 260° C. 100°    D. 65° 


The median of the set of numbers 4, 94, 13, 7, 14, 10, 17 is _______

A. 13     B. 7     C. \frac{19}{2}     D. 10


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


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


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


Find the value of log10 given that log104 = 0.6021

A. 1.3979    B. 2.3979     C. 16021    D. 1.6021


Suppose x varies inversely as y, y varies directly as the square of t and x = 1 when t = 3 Find x when t = \frac{1}{3}

A. 81     B. 27     C. \frac{1}{9}     D.  \frac{1}{21}.


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


If x + 2 and x - 1 are factors of the expressions Ix3 + 2kx2 + 24, find the values of l and k.

A. l = -6, k = -9    B. l = -2, k = 1    C. l = -2, k = -1 D. l = 0, k = 1



In a class of 60 pupils, the statistical distribution of the number of pupils offering Biology, History, French, Geography and Additional Mathematics is as shown in the pie chart above. How many pupils offer Additional Mathematics?

A. 15    B. 10    C. 18    D. 12 


Write the decimal number 39 to base 2

A. 100111    B. 110111    C. 111001    D. 100101    E. 19.5.


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%


A pyramid is constructed on a cuboid. The figure has ______

A. Twelve faces     B. Thirteen vertices     C. Fourteen edges     D. Sixteen edges.


Solve the system of equation

2x + y = 32
33y - x =  27

A. (3, 2)     B. (-3, 2)     C. (3, -2)     D. (-3, -2)



The area under the speed-time graph gives the total distance covered by a car. What is the average velocity to two places of decimals?

A. 17.72 metres/secs     B. 21.67 metres/secs    C. 25 metres/secs     D. 20.45 metres/sees


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