This document provides a review of key concepts for mathematics exams, including:
- Recording all steps, not crossing anything out, and checking answers and units for full marks.
- Rounding numbers correctly based on decimal places or significant figures.
- Giving answers with the same degree of accuracy as values in exam questions.
- Knowing what algebraic terms like "simplify", "factorize", and "expand" mean.
- Drawing graphs correctly by plotting points neatly and ensuring curves are smooth.
- Remembering formulas for area, perimeter, volume, angles, and bearings.
- Understanding properties of transformations, Pythagoras' theorem, and trigonometric ratios.
- Reading the whole
1. AQA Module 5
Revision Support
Caroline Johnson
Bristol LA Mathematics Consultant
Based on an original by Steve Alexis
(AST at Brislington Enterprise College)
2. Exam Questions – collecting marks
It’s all about getting every possible mark
Remember to:
– record every step in your working
– not cross anything out
– check the sense of your answers
– be aware of the number of marks available
– use the correct terminology
– take note of specific instructions – include
units; give your answer to 2 dp
4. Rounding
• When rounding to a given number of decimal
places count each place after the decimal
point
• When rounding to a given number of
significant figures, begin counting from the
first non-zero digit.
E.g. 27.35
Correct to 1 decimal place is 27.4
Correct to 1 significant figure is 30
5. Sensible answers
If a question says..
‘Give your answer to a sensible degree
of accuracy’
you need to write the answer no more
accurately than the values in the
question.
E.g. If a question has values to 2 s.f.
then give the answer to 2 s.f. or 1.s.f
6. Algebra –what it means!
• Simplify – collect terms together
– E.g. 2a + 3b + 4a – 5b = 6a – 2b
• Factorise – take out a common factor
– E.g. factorise 4x2
+ 6x = 2x(2x + 3)
• Expand - multiply out the brackets
– E.g. 7(p – 4q) = 7p – 28q
7. Algebra – what it means (2)
• Expand and simplify – multiply out the
brackets and then collect terms
– E.g. 2(p + 5q) + 7(p - 4q)
= 2p + 10q +7p – 28q
= 9p – 18q
• Solve – find the exact value of [x] that makes
the equation true.
– E.g. 4(2x – 3) = 20
8x – 12 = 20
8x = 32
x = 4
8. Algebra tips.
If question says ‘do not use trial and
improvement’, then an algebraic
method is expected. Any sign of trial
and improvement will be penalised.
This is particularly true for solving
simultaneous equations.
9. Drawing graphs
• Draw all graphs in pencil.
• Make sure you plot points neatly with a small
cross.
• If the graph has an equation with an x2
term in
it then it will be ‘U’ shaped or ‘∩’ shaped.
E.g. x2
– 3x – 5
If it is not a smooth curve check that you have
worked out your values correctly and/or that
they are plotted accurately.
10. Straight line graphs
If asked to draw the graph of y = 2x+ 3 there
are 2 methods you could use.
(i) draw up a table of values to plot 3 points
(why a minimum of 3?).
You can choose the values of x, but keep
them simple e.g. 0, 2 and 4
(ii) use the gradient and intercept method
11. Perimeter, Area and Volume
• Perimeter measures length, so your answer
should be in km, m, cm or mm
• Area units are squared e.g. m2
• Volume is measured in cubic units e.g. cm3
• Remember that there are two formulae in the
front of the paper. These help you to find the
area of a trapezium and the volume of a
prism.
USE THEM IF YOU NEED THEM.
12. Some useful area formulae
• Area of a rectangle = length x width
• Area of a parallelogram = base x height
• Area of a triangle = base x height
• Area of a circle = πr2
Remember
Circumference of a circle = πd or 2πr
Use the π button on your calculator.
2
1
13. Don’t measure it!
• If a diagram says :
‘Not to scale’ or ‘not drawn accurately’
to work out the answer you will need to
do some calculation(s).
You do not measure lengths
14. Angle properties
Know your angle facts!
• There are 360° in a full turn
• The sum of the angles at a point on a
straight line is 180 °
• The sum of the angles in a triangle is 180°
• The sum of the angles in a quadrilateral is
360 °
15. Angles Between Parallel lines
Parallel lines
remain the same
distance apart.
Transversal
Vertically opposite angles are equal. vert.opp. ∠s
Corresponding angles are equal. corr. ∠s
Alternate angles are equal. alt. ∠s
Interior angles sum to 180o
.(Supplementary) Int. ∠s
16. Bearings
Remember that bearings are:
1. measured from the NORTH
2. in a clockwise direction
3. written with 3 figures e.g. 060°
17. Transformations
Transformation Properties
Reflection A line of reflection
Rotation A centre, an angle (90°,
180°, 270°) and a direction
Translation A vector e.g.
Enlargement A centre and scale factor
(which can be a fraction)
−
−
2
3
18. Pythagoras
Is used for finding lengths in right-angled
triangles
b
c
a
In a right-angled triangle,
the square on the
hypotenuse is equal to
the sum of the squares
on the other two sides.
Hypotenuse
a2
= b2
+c2
19. The Trigonometric Ratios
A
BC
hypotenuse
opposite
A
B C
hypotenuse
opposite
adjacent
adjacent
Opposite
Sine A
Hypotenuse
=
O
SinA
H
=
Adjacent
Cosine A
Hypotenuse
= Cos
A
A
H
=
Opposite
Tangent A
Adjacent
= Tan
O
A
A
=
S O CH A H T O A
Remember
20. In the exam
• Read the whole paper
• Highlight important points (but don’t use a
highlighter pen on your answers)
• Do the questions that you find easy first
• Be aware of the number of marks per
question or part of a question
• Remember units, rounding
• Check your answers thoroughly at the end
