MCQ Questions

Question No. 1

Simplify, leaving your answer in index form.

Answer :

a) v⁷ × v⁸

b) p³ × p⁵

c) q⁶ × q¹¹

Question No. 2

Write down the value of these numbers.

Answer :

a) 10⁰

b) 17⁰

c) (−20)⁰

d) 1 500⁰

e) 3 000⁰

Question No. 3

Solve:

Answer :

a) 9⁵ × 9⁷

b) 8⁶ × 8¹⁰

c) 2⁸ × 2¹⁰

Question No. 4

Write these numbers in index form, with negative indices.

Answer :

a) 1 ⁄ 3¹⁰

b) 1 ⁄ 5⁴

c) 1 ⁄ 1 000

d) 1 ⁄ 6⁴

e) 1 ⁄ 34³

Question No. 5

Write these numbers as reciprocals, with positive indices.

Answer :

a) 3⁻⁷

b) 7⁻⁴

c) 11⁻⁴

Question No. 6

Simplify the following fractions, leaving your answers in index form with negative indices.

Answer :

a) y⁷ ⁄ y⁹

b) x⁵ y⁷ ⁄ x⁷ y¹²

Question No. 7

Use Law 4 and Law 5 to simplify the following numbers. Leave your answer in index form.

Answer :

d) (2⁻⁸)⁻¹⁄₂

e) (7³)⁻²

a) (5³)⁷

b) (8⁶)⁵

c) (2⁻³)⁻⁶

Question No. 8

Put these numbers in order of size, starting with the largest number.

Answer :

a) 6 × 10⁰, 0.076, 9.2 × 10⁴, 4 × 10⁻³, 67 000

b) 2 × 10⁻¹, 203, 47.6, 3.1 × 10¹, 0.09

c) 45 000, 4 × 10⁵, 5.7 × 10⁻⁶, 9 × 10⁻⁸, 2 × 10⁷

d) 0.004, 3 × 10⁻², 0.9, 8 × 10⁻⁴, 6.4 × 10⁻³

e) 0.09, 5 × 10⁻³, 0.5, 8 × 10⁻⁴, 5.4 × 10⁻²

Question No. 9

These numbers are written in standard form. Convert them to ordinary numbers.

Answer :

a) 1.4 × 10²

b) 2 × 10³

c) 6.3 × 10¹

d) 4.52 × 10²

Question No. 10

Write these numbers in standard form.

Answer :

a) 23.5

b) 93 400

c) 207

d) 7 210 000

e) 1.32

f) 930 000 000

Question No. 11

These numbers are given in standard form. Write them as ordinary numbers.

Answer :

a) 2 × 10⁻¹

b) 4.1 × 10⁻⁵

c) 5.63 × 10⁰

d) 3.1 × 10⁻⁴

e) 6 × 10⁻²

f) 1.8 × 10⁻³

Question No. 12

A crowd at a football match is estimated to be 46 300 people. Write this number in standard form.

Answer :

Question No. 13

It takes light approximately 3.05 × 10⁻⁷ seconds to travel 100 m. Write this in normal decimal form.

Answer :

Question No. 14

The fastest fighter jet on the planet travels at a speed of Mach 3, approximately 3.675 × 10⁶ km/h. What is Mach 3 as a whole number?

Answer :

Question No. 15

List all the factors of the following.

Answer :

a) 10

b) 18

c) 37

d) 52

e) 120

Question No. 16

The Sieve of Eratosthenes is an ancient method for finding all prime numbers up to a specified number. It was created by Eratosthenes (275–194 B.C.), an ancient Greek mathematician. The numbers from 1 to 100 are listed in the table below. We use the Sieve of Eratosthenes to find all prime numbers up to the number 100. Follow the directions: • Cross out 1 because it is not prime. • Circle 2 because it is the smallest prime number. Cross out every multiple of 2. • Circle the next open number, 3. N

Answer :

Question No. 17

List the first seven prime numbers.

Answer :

Question No. 18

Say whether the following numbers are prime, composite or neither. Give a reason for your answer.

Answer :

a) 12

b) 19

c) 81

d) 54

e) 250

f) 163

Question No. 19

From the numbers {1, 2, 3, 4, 7, 9, 12, 18, 19, 24, 27, 48, 80, 84, 92, 96}, select the following:

Answer :

a) factors of 12

b) multiples of 12

c) Prime numbers

d) even prime numbers

Question No. 20

Write the following in index notation.

Answer :

a) 2 × 2 × 3

b) 2 × 3 × 3 × 5

c) 5 × 5 × 7 × 13 × 13

Question No. 21

Write the following as the product of prime factors by completing the ladder.

Answer :

a)

b)

c)

Question No. 22

Find the prime factors of the following numbers. Leave your answer in index notation.

Answer :

a) 50

b) 225

c) 216

d) 486

e) 965

Question No. 23

Find the HCF of the following terms.

Answer :

a) 2 × 2 × 3 and 2 × 2 × 3 × 5

b) 2 × 2 × 3 × 3 × 7 and 2 × 3 × 3 × 7

c) 3³ × 3 × 5² and 2² × 5 × 7

d) 2⁴ × 5³ × 7² and 2³ × 5 × 7

Question No. 24

Find the HCF of the following pairs of numbers.

Answer :

a) 75 and 90

b) 84 and 92

c) 216 and 360

d) 288 and 360

Question No. 25

Write down the first six multiples of the following numbers.

Answer :

a) 4

b) 8

c) 9

d) 15

e) 20

Question No. 26

Find the LCM of the following terms.

Answer :

a) 2³ × 3² × 7 and 2² × 3³ × 5

b) 2 × 3 × 3 × 5 and 2 × 2 × 3 × 3 × 3

c) 2 × 2 × 2 × 3 × 3 × 7 and 2 × 2 × 3 × 3 × 3 × 5

d) 2² × 3³ × 5², 2⁴ × 3³ × 5² × 7 and 2 × 3 × 7²

e) 2 × 3² × 5, 2² × 3 × 5 and 2 × 3 × 5²

Question No. 27

Determine the LCM of the following.

Answer :

a) 12 and 18

b) 6 and 16

c) 30 and 128

d) 15, 30 and 45

e) 32, 40 and 48

Question No. 28

Kola is planting trees. He has enough trees to plant 6, 7, or 14 trees in each row. What is the least number of trees Kola could have?

Answer :

Question No. 29

At a dance ceremony, three drums are beaten at intervals of 18 s, 27 s and 36 s respectively. All drums start together. Find how long it will take until the drums next beat together.

Answer :

Question No. 30

A band rehearses with either six or 10 members in every line. What is the least number of people that can be in the marching band?

Answer :

Question No. 31

Determine the following without a calculator, and by using prime factors.

Answer :

a) √81

b) √196

c) √676

d) √484

e) √841

f) √289

Question No. 32

Determine.

Answer :

a) √(25/196)

b) √(81/49)

c) √(121/81)

d) √(5/320)

e) √(384/54)

Question No. 33

Fill in the next three numbers in each sequence. Describe a rule for the number pattern.

Answer :

a) 9, 13, 17, 21, …

b) 25, 31, 37, 43, …

c) 36, 33, 30, 27, …

d) 38, 32, 26, 20, …

Question No. 34

Fill in the missing numbers. Describe a rule for the number pattern.

Answer :

a) ___, ___, 41, 36, 31, 26

b) ___, ___, 49, 55, 61, 67

c) 75, 69, ___, 57, 51, ___

d) ___, 37, ___, 27, ___, 17, 12

Question No. 35

Find the difference between each term. Then, write down the next three terms in the following number patterns:

Answer :

a) 12, 6, 0, ___, ___, ___

b) 15, 10, ___, ___, ___

c) −50, −40, −30, ___, ___, ___

d) 10, 8, 6, ___, ___, ___

e) 2, 4, 8, 16, ___, ___, ___

f) 3, 5, 9, 17, ___, ___, ___

Question No. 36

The next number patterns are more challenging. Find the next term in each pattern and give a reason for your answer.

Answer :

a) 1, 4, 9, 16, …

b) 1, 3, 6, 10, …

c) 2, 2, 4, 6, 10, 16, 26, …

d) 2, 3, 5, 9, 17, 33, …

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