GCSE Maths possible questions from basics to hard

GCSE MATHEMATICS

Aiming for Grade 7
REVISION BOOKLET
Exam Dates:
________________
________________
________________




Name: ______________________________




1

,Contents
Page:
Number:
Surds 3
Bounds calculations 7

Algebra:
Parallel and perpendicular graphs 11
Transformations of graphs 16
Algebraic fractions - simplifying 20
Algebraic fractions – solving 23
Solving quadratic inequalities 26

Shape, Space and Measure:
Circle theorems 28
Vectors 32
Sine and cosine rules 40

Data Handling:
Cumulative frequency and box plots 44
Histograms 51

Probability:
Set theory 59

Ratio and Proportion:
Proportion 62
Percentages – compound interest 66
Percentages – reverse 68




2

,Surds

Things to remember:
 √ means square root;
 To simplify surds, find all its factors;
 To rationalise the denominator, find an equivalent fraction where the denominator is
rational.

Questions:
1. Work out
(5 + √3)(5− √3)
√22
Give your answer in its simplest form.




……………………………………
(Total 3 marks)

1
2. (a) Rationalise the denominator of
√3



……………………………………
(1)
(b) Expand (2 + √3)(1 + √3)
Give your answer in the form 𝑎 + 𝑏√3 where a and b are integers.




……………………………………
(2)
(Total 3 marks)
3

, 1
3. (a) Rationalise the denominator of
√7




……………………………………
(2)
(b) (i) Expand and simplify (√3 + √15)2
Give your answer in the form 𝑎 + 𝑏√3 where a and b are integers.




……………………………………

(ii) All measurements on the triangle are in centimetres.
ABC is a right-angled triangle.
k is a positive integer.

A  C
Diagram NOT
accurately drawn
k 3 + 


B

Find the value of k.




k = ……………………………………
(5)
(Total 7 marks)


4