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

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Calculus

If y = (1 - 2x)3, find the value of  $\frac{dy}{dx}$  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. $\frac{17}{50}$     B. $\frac{3}{25}$     C. $\frac{1}{50}$     D. $\frac{7}{10}$

Algebra

If P = $\begin{pmatrix}&space;1&space;&&space;3&space;&&space;2\\&space;4&space;&&space;5&space;&&space;-1\\&space;-3&space;&&space;2&space;&&space;0&space;\end{pmatrix}$ 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 = $4\frac{2}{3}$ and L = 54, find d in terms of W and L.

A. $\sqrt{\frac{42W}{5L}}$     B. $\sqrt{\frac{5L}{42W}}$     C. $4\frac{42W}{5L}$     D. $4\frac{5L}{42W}$

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  $\frac{\sqrt{12}-\sqrt{3}}{\sqrt{12}+\sqrt{3}}$

A. 0     B. $\frac{1}{3}$     C. $\frac{3}{5}$     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. $-\frac{9}{4}$     B. $-\frac{7}{4}$     C. $-\frac{3}{2}$     D. $-\frac{1}{2}$

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. $\frac{1}{20}$    B. $\frac{1}{3}$    C. $\frac{3}{20}$    D. $\frac{7}{10}$

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 = $\frac{22}{7}$ ]

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. $\frac{17}{6}$ units (sq)      B. $\frac{7}{6}$ units (sq)     C. $\frac{5}{6}$ units (sq)     D. $\frac{1}{6}$ 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   $3\frac{1}{2}-\left&space;(&space;2\frac{1}{3}\times&space;1\frac{1}{4}&space;\right&space;)+\frac{3}{5}$

A. $2\frac{11}{60}$     B. $2\frac{1}{60}$     C. $1\frac{11}{60}$     D. $1\frac{1}{60}$

Calculus

Differentiate $\left&space;(&space;x^{2}-\frac{1}{x}&space;\right&space;)^{2}$ with respect to x.

A. $4x^{3}-4x-\frac{2}{x}$      B. $4x^{3}-2+\frac{2}{x^{3}}$      C. $4x^{3}-2-\frac{2}{x^{3}}$      D. $4x^{3}-3x+\frac{2}{x}$

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  $\frac{1}{3}$  of the oranges and the second received  $\frac{2}{3}$  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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