Knowledge Organiser
GCSE MATHS
Years 9-11 (all tiers)
THE MAGNA CARTA SCHOOL
, Table of Contents
NUMBER.................................................................................................................................................. 3
Basic Number and Decimals (all tiers) ................................................................................................ 3
Basic Number and Decimals (higher tier only) ................................................................................... 3
Factors and Multiples (all tiers) .......................................................................................................... 4
Accuracy (all tiers) ............................................................................................................................... 5
Accuracy (higher tier only) .................................................................................................................. 6
Fractions (all tiers) .............................................................................................................................. 7
Basic Percentages (all tiers) ................................................................................................................ 8
Calculating with Percentages (all tiers)............................................................................................... 9
Indices (all tiers) ................................................................................................................................ 10
Indices (higher tier only) ................................................................................................................... 10
Standard Form (all tiers) ................................................................................................................... 11
Growth and Decay (all tiers) ............................................................................................................. 12
Growth and Decay (higher tier only) ................................................................................................ 12
RATIO AND PROPORTION ..................................................................................................................... 13
Ratio .................................................................................................................................................. 13
Proportion (all tiers) .......................................................................................................................... 14
Proportion (higher tier only) ............................................................................................................. 14
Compound Measures (all tiers)......................................................................................................... 15
ALGEBRA ............................................................................................................................................... 16
Essential Algebra (all tiers) ................................................................................................................ 16
Sequences (all tiers) .......................................................................................................................... 17
Sequences (higher tier only) ............................................................................................................. 17
Equations and Formulae (all tiers) .................................................................................................... 18
Solving Quadratics by Factorising (all tiers) ...................................................................................... 19
Solving Quadratics by Factorising (higher tier only) ......................................................................... 19
Further Quadratics (all tiers) ............................................................................................................. 20
Further Quadratics (higher tier only) ................................................................................................ 21
Simultaneous Equations (all tiers) .................................................................................................... 22
Simultaneous Equations (higher tier only) ....................................................................................... 23
Inequalities (all tiers) ........................................................................................................................ 24
Inequalities (higher tier only)............................................................................................................ 24
Functions (all tiers)............................................................................................................................ 25
Functions (higher tier only) ............................................................................................................... 25
Algebraic Fractions (higher tier only)................................................................................................ 26
Iteration (higher tier only) ................................................................................................................ 27
1
, Algebraic Proofs (all tiers) ................................................................................................................. 28
Coordinates and linear graphs (all tiers) ........................................................................................... 29
Coordinates and linear graphs (higher tier only) .............................................................................. 30
Real Life Graphs (all tiers) ................................................................................................................. 31
Graphs and Transformations (all tiers) ............................................................................................. 32
Graphs and Transformations (higher tier only) ................................................................................ 33
Area Under a Graph and Gradient of a Curve (higher tier only)....................................................... 34
Equation of a Circle and Tangent (higher tier only) .......................................................................... 36
GEOMETRY ............................................................................................................................................ 37
Perimeter and Area (all tiers)............................................................................................................ 37
Properties of Polygons (all tiers) ....................................................................................................... 38
Volume (all tiers) ............................................................................................................................... 39
2D Representation of 3D Shapes (all tiers) ....................................................................................... 41
Angles (all tiers)................................................................................................................................. 42
Bearings and Scale Diagrams (all tiers) ............................................................................................. 44
Pythagoras Theorem (all tiers) .......................................................................................................... 45
Pythagoras Theorem (higher tier only) ............................................................................................. 45
Right-Angled Trigonometry (all tiers) ............................................................................................... 46
Right-Angled Trigonometry (higher tier only)................................................................................... 46
Circle Theorems (higher tier only) .................................................................................................... 47
Congruence and Similarity (all tiers) ................................................................................................. 49
Shape Transformations (all tiers) ...................................................................................................... 50
Shape Transformations (higher tier only) ......................................................................................... 51
Vectors (all tiers) ............................................................................................................................... 52
Vectors (higher tier only) .................................................................................................................. 53
PROBABILITY ......................................................................................................................................... 54
Basic Probability (all tiers)................................................................................................................. 54
Systematic Listing (all tiers) .............................................................................................................. 56
Systematic Listing (higher tier only).................................................................................................. 56
Probability Trees and Venn Diagrams (all tiers)................................................................................ 57
Probability Trees and Venn Diagrams (higher tier only) ................................................................... 58
STATISTICS............................................................................................................................................. 59
Summarising Data (all tiers) .............................................................................................................. 59
Summarising Data (higher tier only) ................................................................................................. 60
Representing Data (all tiers) ............................................................................................................. 61
Representing Data (higher tier only) ................................................................................................ 62
Histograms and Cumulative Frequency (higher tier only) ................................................................ 63
Scatter Graphs (all tiers) ................................................................................................................... 65
2
, NUMBER
Basic Number and Decimals (all tiers)
Topic/Skill Definition/Tips Example
Integer A whole number that can be positive, negative −3, 0, 92
or zero.
Decimal A number with a decimal point in it. Can be 3.7, 0.94, −24.07
positive or negative.
Negative A number that is less than zero. Can be −8, −2.5
Number decimals.
Addition To find the total, or sum, of two or more 3 + 2 + 7 = 12
numbers.
Subtraction To find the difference between two numbers. 10 − 3 = 7
To find out how many are left when some are
taken away.
Multiplication Can be thought of as repeated addition. 3 × 6 = 6 + 6 + 6 = 18
Division Splitting into equal parts or groups. 20 ÷ 4 = 5
The process of calculating the number of
times one number is contained within 20
=5
another one. 4
Remainder The amount ‘left over’ after dividing one The remainder of 20 ÷ 6 is 2, because 6 divides
integer by another. into 20 exactly 3 times, with 2 left over.
BIDMAS An acronym for the order you should do 6 + 3 × 5 = 21, 𝑛𝑜𝑡 45
calculations in.
BIDMAS stands for ‘Brackets, Indices, Division, 52 = 25, where the 2 is the index/power.
Multiplication, Addition and Subtraction’.
Indices are also known as ‘powers’ or ‘orders’.
With strings of division and multiplication, or
strings of addition and subtraction, and no 12 ÷ 4 ÷ 2 = 1.5, 𝑛𝑜𝑡 6
brackets, work from left to right.
Basic Number and Decimals (higher tier only)
Topic/Skill Definition/Tips Example
Recurring A decimal number that has digits that repeat 1
= 0.333 … = 0. 3̇
Decimal forever. 3
The part that repeats is usually shown by 1
= 0.142857142857 … = 0. 1̇42857̇
placing a dot above the digit that repeats, or 7
dots over the first and last digit of the
77
repeating pattern. = 0.128333 … = 0.1283̇
600
3
GCSE MATHS
Years 9-11 (all tiers)
THE MAGNA CARTA SCHOOL
, Table of Contents
NUMBER.................................................................................................................................................. 3
Basic Number and Decimals (all tiers) ................................................................................................ 3
Basic Number and Decimals (higher tier only) ................................................................................... 3
Factors and Multiples (all tiers) .......................................................................................................... 4
Accuracy (all tiers) ............................................................................................................................... 5
Accuracy (higher tier only) .................................................................................................................. 6
Fractions (all tiers) .............................................................................................................................. 7
Basic Percentages (all tiers) ................................................................................................................ 8
Calculating with Percentages (all tiers)............................................................................................... 9
Indices (all tiers) ................................................................................................................................ 10
Indices (higher tier only) ................................................................................................................... 10
Standard Form (all tiers) ................................................................................................................... 11
Growth and Decay (all tiers) ............................................................................................................. 12
Growth and Decay (higher tier only) ................................................................................................ 12
RATIO AND PROPORTION ..................................................................................................................... 13
Ratio .................................................................................................................................................. 13
Proportion (all tiers) .......................................................................................................................... 14
Proportion (higher tier only) ............................................................................................................. 14
Compound Measures (all tiers)......................................................................................................... 15
ALGEBRA ............................................................................................................................................... 16
Essential Algebra (all tiers) ................................................................................................................ 16
Sequences (all tiers) .......................................................................................................................... 17
Sequences (higher tier only) ............................................................................................................. 17
Equations and Formulae (all tiers) .................................................................................................... 18
Solving Quadratics by Factorising (all tiers) ...................................................................................... 19
Solving Quadratics by Factorising (higher tier only) ......................................................................... 19
Further Quadratics (all tiers) ............................................................................................................. 20
Further Quadratics (higher tier only) ................................................................................................ 21
Simultaneous Equations (all tiers) .................................................................................................... 22
Simultaneous Equations (higher tier only) ....................................................................................... 23
Inequalities (all tiers) ........................................................................................................................ 24
Inequalities (higher tier only)............................................................................................................ 24
Functions (all tiers)............................................................................................................................ 25
Functions (higher tier only) ............................................................................................................... 25
Algebraic Fractions (higher tier only)................................................................................................ 26
Iteration (higher tier only) ................................................................................................................ 27
1
, Algebraic Proofs (all tiers) ................................................................................................................. 28
Coordinates and linear graphs (all tiers) ........................................................................................... 29
Coordinates and linear graphs (higher tier only) .............................................................................. 30
Real Life Graphs (all tiers) ................................................................................................................. 31
Graphs and Transformations (all tiers) ............................................................................................. 32
Graphs and Transformations (higher tier only) ................................................................................ 33
Area Under a Graph and Gradient of a Curve (higher tier only)....................................................... 34
Equation of a Circle and Tangent (higher tier only) .......................................................................... 36
GEOMETRY ............................................................................................................................................ 37
Perimeter and Area (all tiers)............................................................................................................ 37
Properties of Polygons (all tiers) ....................................................................................................... 38
Volume (all tiers) ............................................................................................................................... 39
2D Representation of 3D Shapes (all tiers) ....................................................................................... 41
Angles (all tiers)................................................................................................................................. 42
Bearings and Scale Diagrams (all tiers) ............................................................................................. 44
Pythagoras Theorem (all tiers) .......................................................................................................... 45
Pythagoras Theorem (higher tier only) ............................................................................................. 45
Right-Angled Trigonometry (all tiers) ............................................................................................... 46
Right-Angled Trigonometry (higher tier only)................................................................................... 46
Circle Theorems (higher tier only) .................................................................................................... 47
Congruence and Similarity (all tiers) ................................................................................................. 49
Shape Transformations (all tiers) ...................................................................................................... 50
Shape Transformations (higher tier only) ......................................................................................... 51
Vectors (all tiers) ............................................................................................................................... 52
Vectors (higher tier only) .................................................................................................................. 53
PROBABILITY ......................................................................................................................................... 54
Basic Probability (all tiers)................................................................................................................. 54
Systematic Listing (all tiers) .............................................................................................................. 56
Systematic Listing (higher tier only).................................................................................................. 56
Probability Trees and Venn Diagrams (all tiers)................................................................................ 57
Probability Trees and Venn Diagrams (higher tier only) ................................................................... 58
STATISTICS............................................................................................................................................. 59
Summarising Data (all tiers) .............................................................................................................. 59
Summarising Data (higher tier only) ................................................................................................. 60
Representing Data (all tiers) ............................................................................................................. 61
Representing Data (higher tier only) ................................................................................................ 62
Histograms and Cumulative Frequency (higher tier only) ................................................................ 63
Scatter Graphs (all tiers) ................................................................................................................... 65
2
, NUMBER
Basic Number and Decimals (all tiers)
Topic/Skill Definition/Tips Example
Integer A whole number that can be positive, negative −3, 0, 92
or zero.
Decimal A number with a decimal point in it. Can be 3.7, 0.94, −24.07
positive or negative.
Negative A number that is less than zero. Can be −8, −2.5
Number decimals.
Addition To find the total, or sum, of two or more 3 + 2 + 7 = 12
numbers.
Subtraction To find the difference between two numbers. 10 − 3 = 7
To find out how many are left when some are
taken away.
Multiplication Can be thought of as repeated addition. 3 × 6 = 6 + 6 + 6 = 18
Division Splitting into equal parts or groups. 20 ÷ 4 = 5
The process of calculating the number of
times one number is contained within 20
=5
another one. 4
Remainder The amount ‘left over’ after dividing one The remainder of 20 ÷ 6 is 2, because 6 divides
integer by another. into 20 exactly 3 times, with 2 left over.
BIDMAS An acronym for the order you should do 6 + 3 × 5 = 21, 𝑛𝑜𝑡 45
calculations in.
BIDMAS stands for ‘Brackets, Indices, Division, 52 = 25, where the 2 is the index/power.
Multiplication, Addition and Subtraction’.
Indices are also known as ‘powers’ or ‘orders’.
With strings of division and multiplication, or
strings of addition and subtraction, and no 12 ÷ 4 ÷ 2 = 1.5, 𝑛𝑜𝑡 6
brackets, work from left to right.
Basic Number and Decimals (higher tier only)
Topic/Skill Definition/Tips Example
Recurring A decimal number that has digits that repeat 1
= 0.333 … = 0. 3̇
Decimal forever. 3
The part that repeats is usually shown by 1
= 0.142857142857 … = 0. 1̇42857̇
placing a dot above the digit that repeats, or 7
dots over the first and last digit of the
77
repeating pattern. = 0.128333 … = 0.1283̇
600
3
