UTME CBT Practice Test – Mathematics (Diagnostic Test) – Set 5

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1. You are to attempt 40 Objectives Questions ONLY for  30 minutes.
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Statistics

The pie chart above shows the distribution of the crops harvested from a farmland in a year. If 3000 tonnes of millet is harvested, what amount of beans is harvested?

A. 9000 tonnes    B. 6000 tonnes    C. 1500 tonnes    D. 1200 tonnes

Algebra

y is inverse1y proportional to x and y = 4 when x = $\frac{1}{2}$. Find x when y = 10 .

A. $\frac{1}{10}$      B. $\frac{1}{5}$    C. 2   D. 10

The mean age of a group of students is 15 years. When the age of a teacher, 45 years old, is added to the ages of the students, the mean of their ages becomes 18 years. Find the number of students in the group

A. 7    B. 9    C. 15   D. 42

Algebra

The length L of a simple pendulum varies directly as the square of its period T. If a pendulum with period 4 sec. is 64 cm long, find the length of a pendulum whose period is 9 sec.

A. 36 cm    B. 96 cm    C. 144 cm    D. 324 cm.

Statistics

Some white balls were put in a basket containing twelve red balls and sixteen black balls. If the probability of picking a white ball from the basket is  $\frac{3}{7}$  how many white balls were introduced?

A. 32    B. 28    C. 21   D. 12

Algebra

Find the remainder when 3x3 + 5x2 - 11x + 4 is divided by x + 3.

A. 4    B. 1    C. -1    D. -4

Geometry/Trigonometry

Find the midpoint of the line joining P(-3, 5) and Q(5, -3).

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

Geometry/Trigonometry

The shadow of a pole $5\sqrt{3}$ m high is 5 m . Find the angle of elevation of the sun.

A. 30°   B. 45°  C. 60°  D. 75°

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

A farmer planted 5,000 grains of maize and harvested 5,000 cobs, each bearing 500 grains. What is the ratio of the number of grains sowed to the number harvested?

A. 1: 500  B. 1: 5,000     C. 1: 25,000     D. 1 . 250,000

Algebra

What are integral values of x which satisfy the inequality -1 < 3 —2x ≤ 5?

A. -2, 1, 0, -1    B. -1, 0, 1, 2     C. -1, 0, 1    D. 0, 1, 2

Number and Numeration

Three teachers shared a packet of chalk. The first teacher got  $\frac{2}{5}$  of the chalk and the second teacher received  $\frac{2}{15}$  of the remainder; What fraction did the third teacher receive?

A. $\frac{11}{25}$    B. $\frac{12}{25}$    C. $\frac{13}{25}$    D. $\frac{8}{25}$

Number and Numeration

In a class of 40 students, each student offers at least one of Physics and Chemistry. If the number of students that offer Physics is three times the number that offer both subjects and the number that offer Chemistry is twice the number that offer Physics, find the number of students that offer Physics only.

A 25    B. 15    C. 10   D. 5

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 (23 + 3x - 4)

Geometry/Trigonometry

PQRSTV is a regular polygon of side 7 cm inscribed in a circle. Find the circumference of the circle. PORSTV. [π = $\frac{22}{7}$]

A. 22 cm    B. 42 cm    C. 44 cm   D. 56 cm

Algebra

If P is $\begin{pmatrix}&space;1&space;&&space;0&space;&&space;-1\\&space;3&space;&&space;4&space;&&space;5\\&space;-1&space;&&space;0&space;&&space;1&space;\end{pmatrix}$, then |P| is _______

A. -8    B. 0   C. 4   D. 6

Calculus

Find the area bounded by the line y = 4x, the x axis, and the ordinates x = 0 and x = 5.

A. 30 sq units    B. 40 sq units    C. 50 sq units    D. 60 sq units

Algebra

The nth terms of two sequences are Qn = 3.2n-2 and Um = 3.22m-3. Find the product of Q2 and U2.

A. 3    B. 6    C.12    D. 18

Geometry/Trigonometry

P, R and S lie on a circle centre O as shown above, while Q lies outside the circle. Find ∠PS

A. 35°   B. 40°   C. 45°   D. 55°

The graph above shows the cumulative frequency curve of the distribution of marks in a class test. What percentage of the students scored more than 20 marks?

A. 68%     B. 32%     C. 17%    D. 8%

Geometry/Trigonometry

In the diagram above, PQ = 4 cm and TS = 6 cm. If the area of parallelogram PQTU is 32 cm2, find the area of the trapezium PQRU.

A. 24 cm2    B. 48 cm2    C. 60 cm2    D. 72 cm2

Statistics

An unbiased die is rolled 100 times and the outcome is tabulated as follows:

What is the probability of obtaining 5?

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

Number and Numeration

Given that $\sqrt[3]{4^{2x}}&space;=&space;16$ , find x

A. 2    B. 3   C. 4   D. 6

Number and Numeration

If $6log_{x}^{2}&space;-&space;3log_{x}^{3}&space;=&space;3log_{5}^{0.2}$, find x

A. $\frac{3}{8}$     B. $\frac{3}{4}$   C. $\frac{4}{3}$    D. $\frac{8}{3}$

Find the mean deviation of 1, 2, 3 and 4.

A. 1.0    B. 1.5    C. 2.0    D. 2.5

Calculus

What is the rate of change of the volume v of a hemisphere with respect to its radius r when r = 2?

A. 2π    B. 4π    C. 8π    D. $\frac{16}{3}$π

Calculus

If y = 3 cos $\frac{x}{3}$, and  $\frac{dy}{dx}$  when x = $\frac{3\pi&space;}{2}$

A. 2    B. 1    C. -1    D. -3

Algebra

If the operation * on the set of integers is defined by $p*q&space;=&space;\sqrt{pq}$ find the value of 4*(8*32)

A. 16    B. 8     C. 4  D. 3

Number and Numeration

Find P, if 4516 - p7 = 3056

A. 6117     B. 1427     C. 1167    D. 627

Calculus

Find the derivative of (2 + 5x)(1 — x) with respect to x.

A. 6x — 1    B. 1 — 6x   C. 6  D. -3

A committee of six is to be formed by a state governor from nine state commissioners and three members of the state house of assembly. In how many ways can the members of the committee be chosen so as to include one member of the house of assembly?

A. 924 ways    B. 840 ways .    C. 462 ways    D. 378 ways.

Calculus

Find the derivative of the function y = 2x2(2x - 1) at the point x = 1

A. -6    B. -4    C. 16    D. 18

Geometry/Trigonometry

An arc of a circle of length 22 cm subtends an angle of 3x° at the centre of the circle. Find the value of x if the diameter of the circle is 14 cm. [π = $\frac{22}{7}$]

A 30°    B. 60°   C. 120°   D. 180°

Algebra

The inverse of the matric $\begin{pmatrix}&space;2&space;&&space;1\\&space;1&space;&&space;1&space;\end{pmatrix}$ is  ______

A. $\begin{pmatrix}&space;1&space;&&space;1\\&space;-1&space;&&space;2&space;\end{pmatrix}$     B. $\begin{pmatrix}&space;1&space;&&space;-1\\&space;1&space;&&space;2&space;\end{pmatrix}$     C. $\begin{pmatrix}&space;1&space;&&space;1\\&space;1&space;&&space;2&space;\end{pmatrix}$     D. $\begin{pmatrix}&space;1&space;&&space;-1\\&space;-1&space;&&space;2&space;\end{pmatrix}$

Geometry/Trigonometry

Find the value of α2 + β2  if α + β = 2 and the distance between the points (1, α) and (β, 1) is 3 units

A. 3    B. 5    C. 11   D. 14

Geometry/Trigonometry

In the figure below AB is parallel to CD

then x + y + z = ______

A. 195o B. 200o C. 360o D. 180o

Number and Numeration

The shaded region in the Venn diagram above is ______

A. Pc ∩ (Q ∩ R)
B. P ∩ Q
C. Pc ∪ (Q ∩ R)
D. Pc ∩ (Q ∪ R)

The Weights of 10 pupils in class are 15kg, 16kg, 17kg, 18kg, 16kg, 17kg, 17kg, 17kg, 18kg and 16kg. What is the range of this distribution?

A. 1    B. 2    C. 3   D.4

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