UTME CBT Practice Test – Mathematics (Diagnostic Test) – Set 6

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Calculus

If y = (1 - 2x)3, find the value of    at x = -1.

A. 57    B. 27    C. –6    D. –54

Number and Numeration The Venn diagram above shows a class of 40 students with the games they play. How many of the students play two games only?

A. 19    B. 16    C. 15    D. 4

Statistics

A box contains 5 blue balls, 3 red balls and 2 white balls. Two balls are selected from the box with replacement. Find the probability of obtaining two blue or two red balls.

A.     B.     C.     D.

Algebra

If P = find the determinant of matrix P.

A. 75     B. 57     C. –57     D. –75

Statistics

How many possible ways are there of seating seven people P, Q, R, S, T, U and V at a circular table?

A. 360     B. 720     C. 2520     D. 5040

Find the value of t if the standard deviation of 2t, 3t, 4t, 5t and 6t is 2 .

A. 1    B. 2     C. 3     D. 4

Algebra

The weight W kg of a metal bar varies jointly as its length L metres and the square of its diameter d metres. If W = 140 when d = and L = 54, find d in terms of W and L.

A.     B.     C.     D.

Calculus

The radius r of a circular disc is increasing at the rate of 0.5 cm/sec. At what rate is the area of the disc increasing when its radius is 6 cm?

A. 36π cm2/sec    B. 18π cm2/sec    C. 6π cm2/sec    D. 3π cm2/sec

Simplify

A. 0     B.     C.     D. 1

Number and Numeration

If the interest of  N150.00 for 2½ years is  N 4.50, find the interest on N 250.00 for 6 months at the same rate.

A. N 1.50    B. N 7.50    C. N 15.00     D. N 18.00

Calculus

The maximum value of the function f(x) = 2 + x - x2 is ______

A.     B.     C.     D. The histogram above shows the distribution of the monthly incomes of the workers in a company. How many workers earn more than N 700.00?

A. 16     B. 17     C. 8     D. 6

Algebra

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

Algebra The diagram above is the graph of the function f(x). Determine the range of values of x for which f(x) ≤ 0.

A. x ≤ 2    B. 0 ≤ x ≤ 2    C.-2 ≤ x ≤ 0, x ≥ 2    D. x ≤ -2, 0 ≤ x ≤ 2

Geometry/Trigonometry

A chord of a circle subtends an angle of 60° at the centre of a circle of radius 14 cm. Find the length of the chord.

A. 7 cm    B. 14 cm    C. 21 cm    D. 28 cm

Statistics The grades of 36 students in a test are shown in the pie chart above. How many students had ‘excellent’?

A. 7     B. 8     C. 9     D. 12

Calculus

Find the derivative of y = sin (2x3 + 3x - 4).

A. cos (2x3 + 3x - 4)
B. –cos (2x3 + 3x - 4)
C. (6x2 + 3) cos (2x3 + 3x - 4)
D. –(6x2 + 3) cos (2x3 + 3x - 4)

Number and Numeration

If U = {x/x is a positive integer less than 10} and P = {x/x is a prime factor of 30}, find the complement of P.

A. {1, 2, 4, 7, 8, 9}     B. {1, 2, 4, 6, 7, 8, 9}     C. {1, 4, 6, 7, 8, 9)     D. { 1, 4, 7, 8, 9}

Algebra

Divide 6x2 – 13x + 5   by   2x - 1

A. 3x + 5     B. 3x – 5     C. 5x – 3     D. 5x + 3

The modal height and range of heights 1.35, 1.25, 1.35, 1.40, 1.35, 1.45, 1.50, 1.35, 1.50 and 1.20 are m and r respectively. Find m + 2r.

A. 1.35    B. 1.65    C. 1.95    D. 3.00 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

Statistics

What is the probability that an integer x, (1 ≤ x ≤ 20) chosen at random is divisible by both 2 and 3?

A.    B.    C.    D.

Geometry/Trigonometry From the diagram above, find the bearing of R from S.

A. 226°     B. 224°     C. 136°     D. 134°

Geometry/Trigonometry

Find the coordinates of the midpoint of the line joining (3, -4) and (-1, 10).

A. (1, 3)     B. (1, 2)     C. (2, 3)     D. (3, 2)

Geometry/Trigonometry

A sector of a circle has an area of 55 cm2. If the radius of the circle is 10 cm, calculate the angle of the sector. [π = ]

A. 45°    B. 63°    C. 75°    D. 90°

Algebra

An operation * is defined on the set of real numbers by a*b = ab + 2(a + b + 1). Find the identity element.

A. 2    B. 1    C. -1    D. -2

Calculus

Find the area of the figure bounded by the given pair of curves y = x2 – x + 3 and y = 3

A. units (sq)      B. units (sq)     C. units (sq)     D. units (sq)

Number and Numeration

If 3214 is divided by 234 and leaves a remainder r, what is the value of r?

A. 0    B. 1    C. 2    D. 3

Algebra

A polynomial in x whose zeros are –2, -1 and 3 is ______

A. x3 – 7x + 6     B. x3 + 7x – 6     C. x3 + 7x + 6     D. x3 – 7x – 6

Number and Numeration

Simplify

A.     B.     C.     D.

Calculus

Differentiate with respect to x.

A.      B.      C.      D.

Geometry/Trigonometry In the diagram above, calculate the value of x.

A. 60°     B. 100°     C. 120°     D. 140°

Geometry/Trigonometry In the diagram above, O is the centre of the circle, ∠UOT = 70° and ∠RST = 100°. Calculate ∠RUO.

A. 20°     B. 25°     C. 50°     D. 80°

Number and Numeration

Three boys shared some oranges. The first received    of the oranges and the second received    of the remainder. If the third boy received the remaining 12 oranges, how many oranges did they share?

A. 60    B. 54    C. 48    D. 42

Geometry/Trigonometry Three straight lines EF, GH and LK intersect at O as shown above, If ∠KOF = 52° and ∠LOH= 85°, calculate the size of ∠EOG.

A. 26°     B. 43°     C. 52°     D. 85°

Geometry/Trigonometry

Find the equation of the perpendicular at point (4, 3) to the line y + 2x = 5.

A. 2y - x = 4      B. y + 2x = 3      C. y + 2x = 5      D. 2y - x = 2

Calculus

The gradient of a curve is 2x + 7 and the curve passes through point (2, 0). Find the equation of the curve.

A. y = x2 + 7x + 9     B. y = x2 + 7x - 18     C. y = x2 + 7x + 18     D. y = x2 + 14x + 11

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