GCSE Mathematics (Higher)

Edexcel 1MA1, Higher tier

195 of 199 skills covered

✓ covered · ◐ partial · ○ not yet · — excluded

Foundation and Higher common content

	skill	lessons
1	Order integers, decimals, fractions	Ordering Negative Numbers, Comparing Decimals, Ordering Fractions	✓ covered
2	Symbols =, ≠, <, >, ≤, ≥	More and Fewer, Inequalities, Integer Solutions of Inequalities	✓ covered
3	Four operations on integers incl. negatives, written methods	Carrying, Borrowing, Two Digits by Two Digits, Long Division, Adding and Subtracting Across Zero, Multiplying and Dividing Negative Numbers	✓ covered
4	Four operations on decimals, written methods	Adding in Columns, Subtracting in Columns, Counting the Decimals, Dividing a Decimal, Dividing by a Decimal	✓ covered
5	Four operations on fractions and mixed numbers	Adding Fractions with Unlike Denominators, Subtracting Fractions, Multiplying Fractions, Dividing a Fraction by a Fraction, Mixed Numbers and Improper Fractions	✓ covered
6	Place value incl. very large/small numbers	Tens and Ones, Hundreds, The Thousand Cube, Numbers to Ten Million, Decimals, Hundredths, Thousandths	✓ covered
7	Inverse operations	Counting Up to Subtract, Halving to Divide, Dividing by Splitting	✓ covered
8	Order of operations incl. brackets, powers, roots, reciprocals	Brackets First, Multiply and Divide Before Adding and Subtracting, Brackets with All Four Operations, Powers in the Order of Operations	✓ covered
9	Primes, factors, multiples vocabulary	Factors, Multiples, The Sieve of Eratosthenes	✓ covered
10	Common factors/multiples, HCF, LCM	Common Factors, The Highest Common Factor, The Lowest Common Multiple, Choosing Between HCF and LCM	✓ covered
11	Product of prime factors, unique factorisation	Prime Factorization	✓ covered
12	Systematic listing strategies	Sample Space, Possibility Diagrams, Adding and Multiplying Choices	✓ covered
13	Integer powers and real roots	Index Notation, Squares and Square Roots, Cubes and Cube Roots	✓ covered
14	Recognise powers of 2, 3, 4, 5	Index Notation, Doubling to Multiply, Squares and Square Roots	✓ covered
15	Calculate with roots and integer indices	Laws of Indices, Zero and Negative Indices, Adding and Multiplying Radicals	✓ covered
16	Calculate exactly with fractions and multiples of π	Circumference and Diameter, Area of a Circle, Arcs and Sectors	✓ covered
17	Calculate in standard form	Standard Form, Calculating in Standard Form	✓ covered
18	Interpret/convert standard form	Standard Form	✓ covered
19	Terminating decimals ↔ fractions	Fractions, Decimals and Percents, 0.5 Is a Half, Why Every Fraction Terminates or Recurs	✓ covered
20	Fractions in ratio problems	Ratio, Fraction, Percent	✓ covered
21	Fractions as operators	A Fraction of an Amount, A Fraction of a Group	✓ covered
22	Percentages as operators	Finding a Percent, Taking a Percent Off	✓ covered
23	Standard units of mass/length/time/money	Meters, Centimeters and Kilometers, Grams and Kilograms, Milliliters and Liters, Time Durations, Money as Decimals	✓ covered
24	Standard compound measures in calculations	Speed, Density, Rates, Rate, Total, Units	✓ covered
25	Estimate answers	Rounding to Estimate, Estimating with One Significant Figure	✓ covered
26	Check calculations by approximation	Rounding to Estimate, Casting Out Nines to Check Arithmetic, Estimating with Units	✓ covered
27	Round to decimal places / significant figures	Rounding to the Nearest Ten, Rounding to the Nearest Hundred and Thousand, Rounding Decimals to One and Two Decimal Places, Significant Figures	✓ covered
28	Error intervals from truncation or rounding	Bounds and Error Intervals	✓ covered
29	Apply and interpret limits of accuracy	Bounds and Error Intervals	✓ covered
30	Algebraic notation (ab, 3y, a², a/b, brackets)	Algebraic Notation, Index Notation	✓ covered
31	Substitute into formulae and expressions	Substitution	✓ covered
32	Vocabulary: expression/equation/formula/identity/inequality	Algebraic Notation, Algebraic Identities, Forming Equations, Inequalities	✓ covered
33	Collect like terms	Like Terms	✓ covered
34	Multiply single term over a bracket	Expanding Brackets	✓ covered
35	Factorise into a single bracket	Factoring by Common Factor	✓ covered
36	Expand products of two binomials	Expanding Two Brackets	✓ covered
37	Factorise x² + bx + c incl. difference of two squares	Factoring Quadratics, Algebraic Identities	✓ covered
38	Laws of indices in expressions	Laws of Indices, The Power of a Power Rule	✓ covered
39	Simplify surd expressions	Radicals, Adding and Multiplying Radicals	✓ covered
40	Use standard mathematical formulae	Substitution, Writing Formulas from Words	✓ covered
41	Rearrange formulae (change the subject)	Changing the Subject of a Formula, Making a Twice-Appearing Letter the Subject	✓ covered
42	Equation vs identity	Algebraic Identities	✓ covered
43	Argue equivalence of expressions	Algebraic Identities, Deriving the Quadratic Formula	✓ covered
44	Expressions as functions (input/output)	Function Notation	✓ covered
45	Coordinates in all four quadrants	The Coordinate Plane	✓ covered
46	Plot straight-line graphs	y = mx + c	✓ covered
47	y = mx + c to identify parallel lines	Gradients of Parallel and Perpendicular Lines	✓ covered
48	Equation of a line (two points / point + gradient)	The Equation of a Line Through Two Points	✓ covered
49	Gradients and intercepts of linear functions	Coordinate Geometry, Gradient from Two Points, y = mx + c	✓ covered
50	Roots/intercepts/turning points of quadratics graphically	Quadratic Graphs, Completing the Square	✓ covered
51	Deduce roots of quadratics algebraically	Solving by Factoring	✓ covered
52	Linear graphs: recognise, sketch, interpret	y = mx + c	✓ covered
53	Quadratic graphs: recognise, sketch, interpret	Quadratic Graphs, Quadratic and Cubic Graphs	✓ covered
54	Simple cubic graphs	Quadratic and Cubic Graphs	✓ covered
55	Reciprocal graph y = 1/x	Reciprocal Graphs	✓ covered
56	Real-context graphs incl. simple kinematics	Distance-Time Graphs, Speed-Time Graphs, Line Graphs	✓ covered
57	Linear equations incl. unknowns both sides	Solving Linear Equations, Equations with the Unknown on Both Sides, Equations with Brackets, Equations with Fractions	✓ covered
58	Approximate solutions of linear equations by graph	Intersections of Graphs	✓ covered
59	Quadratics by factorising	Solving by Factoring	✓ covered
60	Approximate quadratic solutions by graph	Quadratic Graphs, The Discriminant and the Nature of the Roots	✓ covered
61	Two linear simultaneous equations algebraically	Simultaneous by Substitution, Simultaneous by Elimination, Solving Simultaneous Equations by Scaling	✓ covered
62	Simultaneous equations by graph	Simultaneous Equations, Intersections of Graphs	✓ covered
63	Translate situations into expressions/formulae	Forming Equations, Writing Formulas from Words	✓ covered
64	Derive an equation, solve, interpret	Forming Equations, Forming Quadratic Equations	✓ covered
65	Linear inequalities in one variable	Inequalities, Two-Step Inequalities	✓ covered
66	Represent inequality solution set on a number line	Inequalities	✓ covered
67	Term-to-term rules	Term-to-Term Rules	✓ covered
68	Position-to-term rules	The nth Term	✓ covered
69	Triangular, square, cube number sequences	Sequences Worth Knowing	✓ covered
70	Arithmetic, Fibonacci-type, quadratic, geometric progressions	Sequences Worth Knowing, Quadratic Sequences, Geometric Sequences	✓ covered
71	nth term of a linear sequence	The nth Term	✓ covered
72	Convert between related standard units	Converting Lengths, Converting Units of Area, Grams and Kilograms, Milliliters and Liters	✓ covered
73	Convert between compound units	Converting Compound Units	✓ covered
74	Scale factors, scale diagrams, maps	Scale Factor, Map Scales	✓ covered
75	One quantity as a fraction of another	Ratio, Fraction, Percent, A Fraction of a Group	✓ covered
76	Ratio notation, simplest form	Ratio, Tidying a Ratio	✓ covered
77	Divide a quantity in a given ratio	Part-to-Whole Ratios, The Unitary Method, Bar Models for Ratio	✓ covered
78	Express division of a quantity as a ratio	Ratio	✓ covered
79	Ratio in real contexts	Combining Two Ratios, Three-Part Ratios, Before-and-After Ratio Problems	✓ covered
80	Multiplicative relationship as ratio or fraction	Ratio, Fraction, Percent	✓ covered
81	Proportion as equality of ratios	Direct Proportion, Proportion by Unit Value	✓ covered
82	Relate ratios to fractions and linear functions	Ratio, Fraction, Percent, The Constant of Proportionality	✓ covered
83	Percentage as parts per hundred, multiplicative interpretation	Percentage, Percentage Increase	✓ covered
84	Quantity as % of another; percentages > 100%	Comparing with Percent, Percentage	✓ covered
85	Percentage change incl. reverse percentages	Percentage Change, Reverse Percentages	✓ covered
86	Simple interest	Simple Interest, Simple versus Compound Interest	✓ covered
87	Direct proportion problems	Direct Proportion, Proportion by Unit Value	✓ covered
88	Inverse proportion problems	Inverse Proportion	✓ covered
89	Compound units: speed, pay, pricing, density, pressure	Speed, Comparing Unit Rates, Density, Rates, Pressure	✓ covered
90	Compare lengths/areas/volumes by ratio; similarity	Similar Shapes, Ratio of Areas, Ratio of Volumes	✓ covered
91	Inverse proportion ⇔ proportional to 1/Y	Inverse Proportion, The Constant of Proportionality	✓ covered
92	Gradient of a straight line as rate of change	Coordinate Geometry, Distance-Time Graphs	✓ covered
93	Graphs of direct and inverse proportion	Direct Proportion, Reciprocal Graphs	✓ covered
94	Growth and decay incl. compound interest	Compound Interest, Depreciation, Growth and Decay Problems	✓ covered
95	Geometric terms, notation, symmetry	Angles, Parallel and Perpendicular Lines, Symmetry, Rotational Symmetry, Special Quadrilaterals	✓ covered
96	Ruler-and-compass constructions	Constructing a Perpendicular Bisector, Constructing an Angle Bisector, Constructing a Perpendicular from a Point	✓ covered
97	Constructions for figures and loci	Loci	✓ covered
98	Perpendicular distance is shortest	Constructing a Perpendicular from a Point	✓ covered
99	Angles at a point / on a line / vertically opposite	Angles at a Point, Angles on a Line, Vertically Opposite Angles	✓ covered
100	Alternate and corresponding angles	Angles in Parallel Lines	✓ covered
101	Triangle angle sum; polygon angle sums	Angles in a Triangle, Angles in a Polygon, The Interior Angle of a Regular Polygon	✓ covered
102	Properties of special quadrilaterals and triangles	Special Quadrilaterals, Rhombus and Kite	✓ covered
103	Congruence criteria SSS/SAS/ASA/RHS	Congruence Tests	✓ covered
104	Derive angle/side results, simple proofs	Angles in a Triangle, Proving Pythagoras by Dissection	✓ covered
105	Transformations on coordinate axes incl. fractional enlargement	Reflection, Rotation, Translation of Shapes, Enlargement with a Center	✓ covered
106	Circle definitions and parts	Circumference and Diameter, Chords, Arcs, Sectors and Segments	✓ covered
107	Geometrical problems on coordinate axes	The Coordinate Plane, The Midpoint of a Segment, The Distance Between Two Points	✓ covered
108	Faces/edges/vertices of 3D solids	Nets, Prisms and Cylinders, Pyramids and Cones, Euler’s Formula for Polyhedra	✓ covered
109	Plans and elevations	Plans and Elevations	✓ covered
110	Standard units in mensuration	Meters, Centimeters and Kilometers	✓ covered
111	Measure segments/angles; maps and scale drawings	Reading a Ruler, Reading Scales, Map Scales, Angles	✓ covered
112	Bearings	The Eight-Point Compass, Three-Figure Bearings, Back Bearings	✓ covered
113	Area of triangle, parallelogram, trapezium	Area of a Triangle, Area of a Parallelogram, Area of a Trapezium	✓ covered
114	Volume of cuboids, prisms, cylinders	Volume of a Cuboid, Prisms and Cylinders	✓ covered
115	Circumference and area of a circle	Circumference and Diameter, Area of a Circle	✓ covered
116	Perimeters and areas incl. composite shapes	Area and Perimeter, Area of Composite Shapes	✓ covered
117	Surface area and volume of spheres/pyramids/cones/composites	Spheres, Pyramids and Cones, Surface Area of a Cuboid, Surface Area of a Cylinder, Cones and Spheres	✓ covered
118	Arc lengths, sector angles and areas	Arcs and Sectors	✓ covered
119	Congruence and similarity in length problems	Similar Shapes, Similarity Conditions	✓ covered
120	Pythagoras' theorem in 2D	Pythagoras’ Theorem, Finding a Shorter Side with Pythagoras’ Theorem, Proving Pythagoras by Dissection	✓ covered
121	Trig ratios in right-angled triangles	Sine, Cosine and Tangent, Solving Right Triangles, Finding an Angle from a Ratio, Elevation and Depression	✓ covered
122	Exact trig values 0°–90°	Exact Sine, Cosine and Tangent at 30, 45 and 60°	✓ covered
123	Translations as 2D vectors	Translation of Shapes, Column Vectors	✓ covered
124	Vector add/subtract/scalar multiply; representations	Adding Vectors, Subtracting Vectors, Scalar Multiplication	✓ covered
125	Frequency of outcomes: tables and frequency trees	Tally and Frequency Tables, Experimental Probability, Frequency Trees	✓ covered
126	Expected outcomes from randomness/fairness	Expected Counts from a Chance	✓ covered
127	Relative frequency vs theoretical; 0–1 scale	The Probability Scale, Experimental Probability	✓ covered
128	Exhaustive outcomes sum to one	Complementary Events, Probability Distributions	✓ covered
129	Mutually exclusive events sum to one	Mutually Exclusive Events, Complementary Events	✓ covered
130	Empirical samples tend to theoretical distribution	The Law of Large Numbers	✓ covered
131	Enumerate sets: tables, grids, Venn, tree diagrams	Venn Diagrams, Two-Way Tables, Possibility Diagrams, Tree Diagrams	✓ covered
132	Sample spaces for single and combined experiments	Sample Space, Possibility Diagrams	✓ covered
133	Independent combined events, tree diagrams	Independent Events, Tree Diagrams	✓ covered
134	Dependent events without replacement	Without Replacement, Multiplying Along a Tree Without Replacement	✓ covered
135	Infer population properties from a sample	Populations and Samples, Sampling Methods, Capture and Recapture	✓ covered
136	Frequency tables, bar charts, pie charts, pictograms	Tally and Frequency Tables, Bar Charts, Pie Charts, Reading Pictograms	✓ covered
137	Vertical line charts for ungrouped discrete data	Vertical Line Charts	✓ covered
138	Tables and line graphs for time series	Reading Tables, Line Graphs, Time Series	✓ covered
139	Compare distributions via graphical representations	Comparing Data Sets, Stem and Leaf, Histograms, Dot Diagrams	✓ covered
140	Central tendency: median, mean, mode, modal class	The Mean, Median and Mode, Measures of Central Tendency, Averages from a Frequency Table, Mean of Grouped Data	✓ covered
141	Spread: range, incl. consideration of outliers	Range and IQR	✓ covered
142	Apply statistics to describe a population	Comparing Data Sets, Sampling Methods	✓ covered
143	Scatter graphs of bivariate data	Scatter Plots	✓ covered
144	Correlation ≠ causation	Correlation, Correlation Is Not Causation	✓ covered
145	Lines of best fit and predictions	Line of Best Fit	✓ covered
146	Interpolation/extrapolation and their dangers	Interpolation and Extrapolation	✓ covered

Higher-only content

	skill	lessons
1	Product rule for counting	Adding and Multiplying Choices	✓ covered
2	Estimate powers and roots	Squares and Square Roots	✓ covered
3	Fractional indices	Fractional Indices	✓ covered
4	Calculate exactly with surds	Radicals, Adding and Multiplying Radicals	✓ covered
5	Simplify surds (√12 = 2√3)	Adding and Multiplying Radicals	✓ covered
6	Rationalise denominators	Rationalizing the Denominator	✓ covered
7	Recurring decimals ↔ fractions	Turning Recurring Decimals into Fractions, Why Every Fraction Terminates or Recurs	✓ covered
8	Upper/lower bounds in calculationsbounds-and-error-intervals — bounds of a single value covered; propagation missing — planned as the exam-item lesson "Propagating Upper and Lower Bounds" (2026-08-25 spec)	Bounds and Error Intervals	◐ partial
9	Simplify and manipulate algebraic fractions	Algebraic Fractions, Adding and Multiplying Algebraic Fractions	✓ covered
10	Expand products of more than two binomialsbinomial-theorem covers (a+b)^n; three distinct binomials — planned as the exam-item lesson "Expanding Three Binomials" (2026-08-25 spec)	The Binomial Theorem	◐ partial
11	Factorise ax² + bx + c	Factoring Quadratics with a Leading Coefficient	✓ covered
12	Formal algebraic proof	Direct Proof, Proof by Exhaustion	✓ covered
13	Inverse functions (formal notation)	Inverse Functions	✓ covered
14	Composite functions (formal notation)	Composite Functions	✓ covered
15	Perpendicular lines m₁m₂ = −1	Gradients of Parallel and Perpendicular Lines	✓ covered
16	Turning points by completing the square	Completing the Square	✓ covered
17	Exponential graphs y = kˣ	Exponential Growth, Exponential Decay, Exponentials and Logarithms	✓ covered
18	Graphs of sin, cos, tan (any angle, degrees)	Sine and Cosine of Angles Past 90 Degrees, The Graphs of Sine and Cosine, The Graph of Tangent	✓ covered
19	Graph translations and reflections f(x)+a, f(x+a), −f(x), f(−x)	Transforming Graphs	✓ covered
20	Exponential graphs in real contexts	Growth and Decay Problems	✓ covered
21	Estimate gradients of curves (no calculus)	The Gradient of a Curve	✓ covered
22	Estimate areas under graphs; velocity-time distance	Speed-Time Graphs, Area Under a Curve	✓ covered
23	Equation of a circle x² + y² = r²	The Equation of a Circle	✓ covered
24	Tangent to a circle at a point	The Tangent to a Circle at a Point	✓ covered
25	Quadratics requiring rearrangement first	Fractional Equations, Forming Quadratic Equations	✓ covered
26	Solve quadratics by completing the square	Completing the Square, Deriving the Quadratic Formula	✓ covered
27	Solve quadratics by the formula	The Quadratic Formula	✓ covered
28	Simultaneous equations: one linear, one quadratic	A Linear Equation Paired with a Quadratic, Where a Line Meets a Circle	✓ covered
29	Approximate solutions by iteration	Solving Equations by Iteration	✓ covered
30	Linear inequalities in two variables (graphical)	Forming an Inequality in Two Variables, Graphing an Inequality in Two Variables, The Overlap of Two Inequality Regions	✓ covered
31	Quadratic inequalities in one variable	Solving a Quadratic Inequality	✓ covered
32	Inequality solution sets in set notationset-notation exists but is never applied to inequality solutions — planned as the exam-item lesson "Solution Sets of Inequalities" (2026-08-25 spec)	Set Notation	◐ partial
33	Geometric sequences with surd ratiogeometric-sequences — rational ratios only; surd ratios never exercised	Geometric Sequences	◐ partial
34	Other non-standard sequences	Sequences Worth Knowing, Continued Fractions	✓ covered
35	nth term of a quadratic sequence	Quadratic Sequences	✓ covered
36	Construct direct/inverse proportion equations	The Constant of Proportionality	✓ covered
37	Gradient at a point = instantaneous rate	The Gradient of a Curve	✓ covered
38	Average vs instantaneous rates (chords/tangents)	The Gradient of a Curve, From First Principles	✓ covered
39	General iterative growth/decay processes	Compound Interest, Depreciation, Recurrence Relations	✓ covered
40	Enlargement with negative scale factors	Enlargement with a Center	✓ covered
41	Combinations of transformations; invariance	Combined Transformations	✓ covered
42	Circle theorems: apply and prove	Angle in a Semicircle, Angle at the Center, Angles in the Same Segment, Cyclic Quadrilaterals, Tangent Properties, The Alternate Segment Theorem, Chords and the Center	✓ covered
43	Similar figures: area k², volume k³	Ratio of Areas, Ratio of Volumes, Scaling Area and Volume	✓ covered
44	Pythagoras and trig in 3D	Trigonometry in Three Dimensions, The Slant Height of a Cone	✓ covered
45	Sine rule	The Sine Rule, Finding Angles with the Sine Rule	✓ covered
46	Cosine rule	The Cosine Rule, Finding Angles with the Cosine Rule	✓ covered
47	Area = ½ab sin C	Area with Sine	✓ covered
48	Vector geometric arguments and proofs	Vector Proofs with Midpoints, Collinear Vectors	✓ covered
49	Conditional probability via tables/trees/Venn	Conditional Probability, Conditional Probability from Tables, Reversing a Tree: the Base-Rate Answer	✓ covered
50	Histograms incl. frequency density	Histograms, Frequency Density	✓ covered
51	Cumulative frequency graphs	Cumulative Frequency, Quartiles from the Curve	✓ covered
52	Box plots	Box and Whisker	✓ covered
53	Quartiles and IQR	Range and IQR, Quartiles from the Curve	✓ covered

Practice these in the app

Other syllabuses: Singapore PSLE Mathematics · Singapore O-Level Mathematics · SAT Math · Singapore A-Level H2 Mathematics