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EARLY ACCESS JMaths is in active development — new content added regularly

Topic 1: Number & Algebra

232 questions
1.1

Standard Form

16
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1.2

Arithmetic Sequences & Series

7
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1.3

Geometric Sequences & Series

9
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1.4

Financial Applications (compound interest, annual depreciation)

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1.5

Exponents & Logarithms

34
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1.6

Approximation & Percentage Error

14
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1.7

Amortization & Annuities

26
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1.8

Systems of Linear Equations (up to 3 variables, polynomial equations, GDC)

20
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1.9

Laws of Logarithms

11
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1.10

Rational Exponents

9
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1.11

Infinite Geometric Series

12
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1.12

Complex Numbers (Cartesian) (modulus, argument, conjugate, complex plane, quadratic roots)

13
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1.13

Complex Numbers (Polar & Euler) (cis form, exponential form, sinusoidal addition)

10
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1.14

Matrices (multiplication, determinants, inverses, solving systems Ax=b)

23
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1.15

Eigenvalues & Eigenvectors (characteristic polynomial, diagonalization, matrix powers)

28
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Topic 2: Functions

233 questions
2.1

Equation of a Straight Line

20
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2.2

Functions: Domain, Range & Graph (function notation, inverse concept)

4
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2.3

Graph of a Function

13
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2.4

Key Features of Graphs (intersections, asymptotes, maxima, minima)

6
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2.5

Modelling with Functions (linear, quadratic, exponential, cubic, sinusoidal, direct/inverse variation)

85
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2.6

Modelling Skills (fitting models, choosing parameters, testing reasonableness)

7
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2.7

Composite & Inverse Functions

29
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2.8

Transformations of Graphs (translations, reflections, stretches, composite transformations)

57
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2.9

Advanced Modelling (half-life, natural log models, logistic models, piecewise functions)

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2.10

Scaling with Logarithms (linearizing data, log-log graphs, semi-log graphs)

12
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Topic 3: Geometry & Trigonometry

322 questions
3.1

3D Geometry, Volume & Surface Area (pyramid, cone, sphere, hemisphere, angle between line and plane)

54
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3.2

Trig Ratios, Sine & Cosine Rules (area of triangle, right-angled triangles)

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3.3

Applications of Trigonometry (elevation, depression, bearings, labelled diagrams)

19
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3.4

Arc Length & Sector Area

13
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3.5

Perpendicular Bisectors

13
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3.6

Voronoi Diagrams (sites, vertices, edges, cells, nearest neighbour interpolation, toxic waste problem)

13
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3.7

Radians

7
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3.8

Unit Circle & Trig Identities (Pythagorean identity, tan definition, ambiguous case)

40
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3.9

Matrix Transformations (reflections, stretches, rotations, determinant interpretation)

26
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3.10

Vectors (unit vectors, position vectors, column representation, magnitude)

11
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3.11

Vector Equation of a Line

55
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3.12

Vector Kinematics (constant velocity, variable velocity, displacement in 2D/3D)

12
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3.13

Scalar & Vector Products (dot product, cross product, area of parallelogram, angle between vectors)

20
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3.14

Graph Theory Basics (vertices, edges, degree, simple/complete/weighted/directed graphs, trees)

15
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3.15

Adjacency Matrices & Walks (k-length walks, weighted tables, transition matrices)

12
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3.16

Graph Algorithms (Eulerian trails, Hamiltonian cycles, Kruskal, Prim, Chinese postman, TSP)

12
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Topic 4: Statistics & Probability

363 questions
4.1

Population, Sample & Data Types

16
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4.2

Frequency Distributions & Histograms (cumulative frequency, box plots, quartiles, percentiles)

15
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4.3

Central Tendency & Dispersion (mean, median, mode, standard deviation, variance, grouped data)

21
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4.4

Linear Correlation & Regression (Pearson's r, scatter diagrams, line of best fit, prediction)

14
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4.5

Probability Concepts (sample space, complementary events, expected occurrences)

24
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4.6

Venn Diagrams, Trees & Tables (conditional probability, combined events, independence)

61
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4.7

Discrete Random Variables

21
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4.8

Binomial Distribution

6
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4.9

Normal Distribution

27
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4.10

Spearman's Rank Correlation

13
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4.11

Hypothesis Testing (chi-squared, t-test, goodness of fit, p-values, significance levels)

43
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4.12

Data Collection Methods (surveys, reliability, validity, categorizing data)

7
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4.13

Non-linear Regression (least squares curves, sum of square residuals, R-squared)

12
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4.14

Linear Combinations of Random Variables (E(X), Var(X), unbiased estimates of mean and variance)

7
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4.15

Normal Combinations (distribution of sample mean, central limit theorem)

18
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4.16

Confidence Intervals

17
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4.17

Poisson Distribution

23
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4.18

Critical Values & Regions (test for mean, proportion, Poisson mean, Type I/II errors)

11
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4.19

Transition Matrices & Markov Chains (steady state, long-term probabilities, regular chains)

7
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Topic 5: Calculus

294 questions
5.1

Introduction to Limits

19
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5.2

Increasing & Decreasing Functions

13
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5.3

Derivative of x^n

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5.4

Tangents & Normals

20
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5.5

Integration as Anti-differentiation (boundary conditions, definite integrals, area under curve)

12
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5.6

Stationary Points

12
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5.7

Optimisation

11
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5.8

Trapezoidal Rule

13
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5.9

Derivatives of Trig, Exp & Log Functions (chain rule, product rule, quotient rule, related rates)

26
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5.10

Second Derivative

37
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5.11

Definite & Indefinite Integration (trig, exp, 1/x, integration by inspection/substitution)

57
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5.12

Area Under & Between Curves (volumes of revolution about x and y axes)

38
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5.13

Kinematics

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5.14

Differential Equations (modelling from context, separation of variables)

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Questions for 5.14 are coming soon!

5.15

Slope Fields

6
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5.16

Euler's Method (first order DEs, coupled systems)

6
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5.17

Coupled Differential Equations (phase portraits, equilibrium points, eigenvalue analysis)

12
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5.18

Second Order DEs (Euler's method for second order)

12
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