Gcse Aqa Maths Numbers Review

Numbers Review

You may only use a calculator if the question says so. Otherwise, do not use one.

Types of Numbers

Five numbers include -12, 4.25, 0.27272727... and 6...

a.) Which number is an integer?

b.) Which numbers are non-integers?

c.) Which number has a terminating decimal?

d.) Which number has a recurring decimal (always the same)? Using the number you chose, write it in a convenient, shorter form (2 marks).

e.) Which number is an irrational number? Write one more example of an irrational number (2 marks).

Squares, Cubes, and Powers of 0 and 1

a.) Write the first 15 square numbers.

b.) Write the first 5 cubic numbers, including zero cubed and ten cubed.

c.) Using a calculator, what is 7⁵?

d.) What is 4⁰? Also, explain the rule for powers of zero (2 marks).

e.) What is 16¹? Also, explain the rule for powers of one (2 marks).

Multiples

Remember to show all your workings:

a.) Find the LCM of 5 and 8. (2 marks).

b.) Find the LCM of 8, 12 and 16.

c.) A student was writing an answer to a multiples question. The left side of her page was destroyed by a fire, and only this fragment remains:

*burn marks*, 78, 91, 104, 117

Which number is she using for her multiples? How many multiples did she probably have written down before the page was burned? (2 marks).

Factors

a.) Find the HCF of 20 and 24.

b.) Find the HCF of 48, 60 and 72.

c.) Is it possible the find the factors of a non-integer? Explain your answer (2 marks).

Prime Numbers and Prime Factors

a.) Write the first fifteen prime numbers.

b.) What is the 9th prime number?

c.) Show that 87 is not a prime number.

d.) Show that 143 is not a prime number.

e.) Which factors do all prime numbers have?

f.) Explain the difference between factors and prime factors (2 marks).

g.) Find the prime factors of 1025. Prove that your final answer is correct (3 marks).

Simplifying Fractions

Simplify the following fractions:

a. 16/32

b. 27/36

c. 64/512

d. 65/104

Mixed Fractions and Improper Fractions

Convert the mixed fractions to improper fractions:

a. 4 1/4

b. 9 3/11

c. 11 1/2

d. 6 8/9

Convert the improper fractions to mixed fractions:

a. 17/4

b. 36/6

c. 91/11

d. 103/13

Comparing Fractions

Complete the following inequalities using >, < or =.

a. 4/9 and 1/2

b. 3/4 and 7/10

c. 1/7 and 1/6

d. 7/8 and 17/20

Place the following fractions in ascending order:

a. 1/3, 1/4, 1, 5/6, 1/2, 3/4

b. 3/4, 1, 7/5, 2, 13/20, 3/5, 15/8

Fraction Quantities

Solve the following.

a. 1/4 of 35kg

b. 1/3 of 87.9mL

c. 4/5 of £19.85

d. 8/9 of 68.59g (You may use a calculator. Round your answer to 2 d.p.)

Decimals to Percentages

Convert the decimals into percentages:

a. 0.7

b. 0.07

c. 1.8

d. 0.026

Percentages to Decimals

Convert the percentages into decimals:

a. 34%

b. 2%

c. 0.8%

d. 150%

Fractions to Decimals

Convert the following fractions into decimals. Show all your work

a. 28/100

b. 31/1000

c. 26/200

d. 5/24

e. 5/9

f. 11/12

g. 27/99

Decimals to Fractions

Convert the following terminating decimals to fractions:

a. 0.9

b. 0.007

c. 2.47

d. 0.045

Convert the following recurring decimals to fractions:

(For example, 0.25... on this worksheet means 0.252525252525...)

a. 0.6...

b. 0.17...

c. 0.028...

d. 0.117...

Fractions Arithmetic

Add or Subtract the following fractions:

a. 5/8 + 3/8

b. 1/3 + 13/15

c. 1/9 + 1/6

d. 11/12 - 7/12

e. 3/4 - 1/8

f. 5/7 - 5/8

Multiply or Divide the following fractions:

Find 30% of 78g

Find 57% of 82mL

Find 11.5% of 208kg

26 : 52

5/2 : 15/4

7.2 : 11.7

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