MCQ Questions

Question No. 1

Round off each number to the nearest 10 000.

Answer :

a) 6 237 714

b) 552 459

c) 846 010

Question No. 2

Round off each number to the nearest 100.

Answer :

a) 46 762

b) 93 417

c) 50 094

Question No. 3

Write each number correct to one d.p.

Answer :

a) 17.7108

b) 0.9575

c) 31.013

Question No. 4

Write each number correct to three d.p.

Answer :

a) 0.28456

b) 17.0407

c) 1.2644

Question No. 5

Write each number correct to two s.f.

Answer :

a) 52 913 900

b) 1.9523

c) 0.00284

Question No. 6

Write each number correct to four s.f.

Answer :

a) 41 632 509

b) 71.20437

c) 0.18947

Question No. 7

Write each of the following numbers in expanded form.

Answer :

a) 1.86 × 10³

b) 3.047 × 10⁻²

c) 2.1982 × 10⁷

d) 5.58 × 10⁻⁵

e) 1.296 × 10⁶

f) 8.404 × 10⁻⁶

g) 6.0339 × 10⁵

h) 9.515 × 10⁻⁴

Question No. 8

Write each of the following numbers in standard form.

Answer :

a) 218.5

b) 0.523

c) 417 000

d) 0.008272

e) 84 040

f) 0.000093658

g) 6 217 400

h) 0.00000030011

Question No. 9

Write this expression in index form: 3 × p × 2 × q × p × q × p.

Answer :

Question No. 10

Use the laws of indices to simplify each of the following. Write your answers with positive indices, where necessary.

Question No. 11

Write each of the following in index form.

Answer :

a) ∛p

b) ∜y³

c) √x⁷

d) ∜4b

Question No. 12

Write each of the following in root form.

Answer :

a) x^(⅓)

b) (6b)^(½)

c) y^(²⁄ⁿ)

d) z^(⁶⁄₅)

Question No. 13

Write each of the following in logarithm form.

Answer :

a) 2⁵ = 32

b) 3⁷ = 2,187

c) 4ᵖ = q

d) xʸ = z

Question No. 14

Simplify each of the following.

Question No. 15

Use the logarithmic tables to find the logarithms of each of the following (correct to four d.p.).

Answer :

a) 5.945

b) 59.45

c) 1.189

d) 118.9

e) 4.374

f) 4 374

g) 7.491

h) 74 910

Question No. 16

Use the logarithmic tables to find the antilogarithms of each of the following.

Answer :

a) 0.973

b) 1.973

c) 0.1658

d) 3.1658

e) 0.6612

f) 2.6612

g) 0.4202

h) 4.4202

Question No. 17

Use the logarithmic tables to calculate each of the following (correct to four s.f.).

Answer :

a) 6.651 × 5.12

b) 99.44 ÷ 32.31

c) 33.39 × 12.95

d) 839.2 ÷ 101.2

e) 74.6 × 29.69

f) 62.3 ÷ 3.482

g) 630.7 × 2.226

h) 47.93 ÷ 8.724

Question No. 18

Solve:

Answer :

a) Make P the subject of the formula A = P(1 − r/100)ⁿ

b) Make t the subject of the formula SI = P·r·t/100

c) Make h the subject of the formula V = ½·b·h·H

d) Make r the subject of the formula x² + y² = r²

e) Make s the subject of the formula V = s³

f) Make a the subject of the formula Tₙ = a·rⁿ⁻¹

g) Make r the subject of the formula S∞ = a/(1 − r)

h) Make v the subject of the formula 1/u + 1/v = 1/f

Question No. 19

Solve each of the following quadratic equations by factorising

Answer :

a) x² − 5x + 4 = 0

b) 2x² − 24x + 54 = 0

c) 6x² + 13x + 6 = 0

d) 3x² − 23x − 8 = 0

Question No. 20

Solve each quadratic equation (correct to two d.p.) using the quadratic formula

Answer :

a) x² + x − 10 = 0

b) x² + 7x + 2 = 0

c) 2x² + 11x + 6 = 0

d) 3x² − x − 9 = 0

Question No. 21

Solve each quadratic equation (correct to two d.p.) by completing the square

Answer :

a) x² − 2x − 5 = 0

b) x² + 8x + 3 = 0

c) 2x² − 9x − 4 = 0

d) 6x² − 18x + 1 = 0

Question No. 22

Find the equation of each of the following quadratic functions.

Answer :

a)

b)

Question No. 23

Draw the graph of each of the following on its own system of axes. Show all the intercepts with the axes, as well as the coordinates of the vertex. Use a dotted line to indicate the line of symmetry and give the equation of the line of symmetry.

Answer :

a) y = −x² + 3x + 4

b) y = 3x² − 12x + 9

Question No. 24

Copy and complete the following truth tables.

Answer :

a)

b)

Question No. 25

Given the statements P: ‘It is Saturday’ and Q: ‘The market is busy’, write down a simple sentence that describes each of the following logical statements.

Answer :

a) ¬P

b) ¬Q

c) P ∧ Q

d) P ∨ Q

e) ¬¬Q

f) P ⇒ Q

g) Q ⇔ P

h) P ⇒ ¬Q

Question No. 26

Eya constructed a circle with a radius of 20 cm and then shaded a sector of the circle with an angle θ at the centre. Calculate each of the following, correct to two decimal places.

Answer :

b) the area of the sector, if θ = 205°

a) the length of the arc of the sector, if θ = 60°

c) the perimeter of the arc of the sector, if θ = 130°

Question No. 27

A sector of a circle is shown in the diagram. If the angle θ of the sector is chosen so that the length of the arc equals the radius r of the circle, calculate the size of θ, correct to the nearest tenth of a degree.

Answer :

Question No. 28

Use the trigonometric tables or a calculator to calculate each of the following, correct to two decimal places.

Answer :

a) sin 29°

b) cos 78.3°

c) tan 42.7°

d) sin 65.6°

e) cos 38°

f) tan 85.8°

Question No. 29

Use the trigonometric tables or a calculator to calculate the value of θ in each of the following, correct to one decimal place.

Answer :

a) sin θ = 0.24

b) cos θ = 0.43

c) tan θ = 6

d) sin θ = 0.75

e) cos θ = 0.57

f) tan θ = 1.2

Question No. 30

In the diagram below, two points on the ground, A and B, are in line with the base of a water tower WT, such that B is exactly halfway between A and T. The angle of elevation from B to W is 36° and the height of the water tower is 15 m.

Answer :

a) Calculate the distance between A and the foot of the tower, correct to the nearest metre.

b) Calculate the angle of elevation from A to W, correct to the nearest degree.

Question No. 31

Points P, Q and R form the vertices of an equilateral triangle, as shown. If the bearing of point Q from point P is 145°, calculate:

Answer :

a) the bearing of point R from point Q

b) the bearing of point P from point R

Question No. 32

For the diagram below, calculate, giving reasons, the sizes of the angles marked a to i, in that order.

Answer :

Question No. 33

In the diagram below, ∠ABC = 90° and BD ⟂ AC with D on BC.

Answer :

a) State which two other triangles are similar to △ABC. Write your answer in the form △ABC ||| △… ||| △….

b) If AB : BD : AD = 7 : 6 : 3 and BC = 51 mm, use similarity (not Pythagoras) to calculate, correct to the nearest tenth of a millimetre: (i) AC (ii) AB (iii) CD (iv) BD

Question No. 34

In the diagram below, PQRS is a parallelogram and RT/ST = 1/2. Determine the following ratios.

Answer :

a) RU/UV

b) RU/RV

c) RU/PR

d) UV/PV

Question No. 35

A post was advertised and a number of applicants submitted their CVs. The personnel manager analysed these CVs to see how many previous jobs each applicant had held. The results are summarised in this frequency table.

Answer :

a) Write down the numbers and tallies that are missing in the table.

b) How many applicants applied for the position?

c) How many applicants had no previous experience?

d) Calculate: (i) the mean (ii) the median (iii) the mode (iv) the range of previous jobs held by the applicants.

Question No. 36

The ages of the applicants in Exercise 1.14 are summarised in the table below.

Answer :

a) Estimate the mean age of the applicants.

b) Estimate the median age of the applicants.

c) Find the modal class of this data.

d) Comment on possible values of the range for this data.

Question No. 37

Represent the data in the frequency table below in a histogram.

Answer :

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