GCSE Foundation Revision Booklet
AREA FORMULAE
SQUARE
RECTANGLE
Length
Width
Length
Length
AREA = Length x Length
AREA = Length x Width
TRIANGLE
PARALLELOGRAM
Height
Height
Base
Base
AREA = Base x Height
2
TRAPEZIUM
AREA = Base x Height
CIRCLE
A
Height
Radius
R
Diameter
B
AREA = ( A + B ) x Height
2
Diameter = 2 x Radius
Circumference = π x Diameter
Area = π x Radius x Radius
GCSE Foundation Revision Booklet
VOLUME FORMULAE
CUBE
CUBOID
Height
Length
Width
Length
Length
Length
Volume = Length x Length x Length
TRIANGULAR PRISM
Volume = Length x Width x Height
CYLINDER
Radius
Height
Height
Length
Base
Volume = Base x Height x Length
2
Volume = π x Radius x Radius x Height
VOLUME OF ANY PRISM
Volume = Cross Sectional Area x Length
Cross Sectional
Area
Length
GCSE Foundation Revision Booklet
WORDS ASSOCIATED WITH GEOMETRY
ANGLES
Acute
less than 90º
Obtuse
between 90º and 180º
Right-angled
equal to 90º
Reflex
more than 180º
TRIANGLES
SIDES
ANGLES
Scalene – all sides different lengths
Acute – all angles acute
Isosceles – 2 sides equal length
Right – 1 angle = 90º
Equilateral – all sides equal length
Obtuse – 1 angle more than 90º
Congruent shapes are identical to each other, they may be
reflected or rotated
Tessellate means to tile shapes like on a bathroom or kitchen wall
GCSE Foundation Revision Booklet
QUADRILATERALS
Square
Rectangle
Rhombus
Parallelogram
Kite
Trapezium
PROPERTIES OF QUADRILATERALS
SQUARE
4 equal sides and angles
RECTANGLE
2 pairs of parallel equal sides and all angles equal
PARALLELOGRAM 2 pairs of parallel equal sides and 2 pairs of non
right-angled equal angles (non-right)
KITE
2 pairs of non-parallel equal sides
RHOMBUS
4 equal sides and and 2 pairs of non right-angled
equal angles (non-right)
TRAPEZIUM
2 pairs of non-equal parallel sides
GCSE Foundation Revision Booklet
ANGLE RULES
Straight Line
At a Point
X
X
Y
Y Z
Angles add to 180o
Angles add to 360
In a Triangle
Right Angle
X
Y
X
Z
Y
Angles add to180
Angles add to 90
Vertically Opposite
Corresponding (F – Angles)
X
X
Y
Y
Angles are equal
Angles are equal
Alternate (Z – Angles)
Internal (C – Angles)
X
X
Y
Angles are equal
Y
Angles add to 180
GCSE Foundation Revision Booklet
POLYGONS
Name
No. of
Sides
3
4
5
6
7
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Angle
Total
180
360
540
720
900
Name
Octagon
Nonagon
Decagon
Undecagon
Icosagon
No. of
Sides
8
9
10
11
12
Angle
Total
1080
1260
1440
1620
1800
REGULAR POLYGONS
Name
Equilateral Triangle
Square
Regular Pentagon
Regular Hexagon
Regular Heptagon
Regular Octagon
Regular Nonagon
Regular Decagon
No. of Sides
3
4
5
6
7
8
9
10
Angle Total
180
360
540
720
900
1080
1260
1440
Interior Angle
60
90
108
120
128.6
135
140
144
Exterior Angle
120
90
72
60
51.4
45
40
36
Pythagoras’ Theorem
Use this to find the longest side
c
a
c² = a² + b²
Use this to find one of the short sides
b
b² = c² - a²
GCSE Foundation Revision Booklet
Algebra Glossary of Terms (solutions in italics)
 Solve – Find the value of x usually applies to equations or
inequalities (below are likely questions)
i.e. Solve the following for x
1)
2x + 1 = 5
2x = 4
x=2
2)
3x – 1 = x + 7
2x – 1 = 7
2x = 8
x=4
OR
Solve the following inequalities for x
1)
3x – 5 < 13
3x < 18
x<6
2)
11 – 3x > 2
11 > 2 + 3x
9 > 3x
3>x
 Simplify – Write in a shorter way (below are likely
questions)
Simplify
1)
5a + 2b – 2a + 7b
= 3a + 9b
2)
x² + 3x + 2x² - x
= 3x² + 2x
2)
(5b)² = 25b²
OR
Simplify
1)
(3a²) x (2a) = 6a³
GCSE Foundation Revision Booklet
 Expand – Remove brackets (below are likely questions)
Expand
1)
3(x + 5) = 3x + 15
2)
x(2x – 3) = 2x² - 3x
2)
(3x – 1)(2x + 5)
= 6x² + 15x – 2x – 5
= 6x² + 13x – 5
OR
Expand and Simplify
1)
(x + 2)(x + 3)
= x² + 3x + 2x + 6
= x² + 5x + 6
 Factorise – Put into brackets (below are likely questions)
Factorise completely
1)
2x + 6 = 2(x + 3)
2)
8x²- 12x = 4x(2x – 3)
2)
x² - x – 12
= (x – 4)(x + 3)
OR
Factorise the following quadratics
1)
x² + 6x + 8
= (x + 2)(x + 4)