Daily Dumplings
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- 168 topics, ten questions at random each time
- Marked as you answer, with the working shown after each question
- Mix up to ten topics, from one year or several
- A free account keeps your scores so you can see what has stuck
Year 7
Algebraic expressions
Substituting, collecting like terms and a first look at expanding brackets.
Algebra · 100 questionsYear 7Equations
One- and two-step equations, brackets and simple word problems.
Algebra · 102 questionsYear 7Number plane and patterns
Quadrants, coordinates and finding the rule for a pattern.
Algebra · 102 questionsYear 7Angle relationships
Straight lines, triangles, parallel lines and angles at a point.
Geometry · 95 questionsYear 7Triangles and quadrilaterals
Classifying triangles and quadrilaterals, diagonals and angle sums.
Geometry · 103 questionsYear 7Length, area and volume
Metric units, perimeter, area of key shapes and volume of prisms.
Measurement · 100 questionsYear 7Decimals and percentages
Decimal sums, converting to percentages and finding a percentage.
Number · 106 questionsYear 7Divisibility and remainders
Divisibility tests, remainders and clock arithmetic puzzles.
Number · 102 questionsYear 7Fractions
Fractions of amounts, adding, simplifying and comparing, with numbers small enough to do in your head.
Number · 100 questionsYear 7Integers
Ten quick questions on adding, subtracting, multiplying and dividing with negative numbers.
Number · 98 questionsYear 7Matrices
Extension: matrix order, adding, scaling and multiplying, written [a b; c d].
Number · 106 questionsYear 7Primes, powers and square roots
Factors, primes, index notation, square roots, HCF and LCM.
Number · 104 questionsYear 7Recurring decimals to fractions
Extension: terminating and recurring decimals, and turning them into fractions.
Number · 118 questionsYear 7Probability
Sample spaces, chance, complements and relative frequency.
Probability · 101 questionsYear 7Data and graphs
Types of data, choosing graphs, and mean, median, mode and range.
Statistics · 101 questionsYear 8
Equations
One-step, two-step and both-sides equations with whole-number working.
Algebra · 93 questionsYear 8Expanding and factorising
Using the distributive law and taking out the highest common factor.
Algebra · 101 questionsYear 8Formulas and inequalities
Substituting into and rearranging formulas, and simple inequalities.
Algebra · 105 questionsYear 8Indices
Index laws with whole-number and zero indices, for numbers and pronumerals.
Algebra · 109 questionsYear 8Linear relationships
Tables of values, points on a line, intercepts and reading a rule.
Algebra · 102 questionsYear 8Non-linear relationships
Spotting parabolas and other curves from rules and tables.
Algebra · 100 questionsYear 8Similar figures and scale
Enlargements, scale factors, similar shapes and map scales.
Geometry · 100 questionsYear 8Transformations and congruence
Translations, reflections, rotations and the tests for congruent triangles.
Geometry · 104 questionsYear 8Circles
Circle parts, circumference, area, semicircles, quadrants and sectors.
Measurement · 103 questionsYear 8Pythagoras and area
Pythagorean triads and the area formulas for common shapes.
Measurement · 100 questionsYear 8Surface area and volume
Volume of prisms and cylinders, capacity, and simple surface area.
Measurement · 101 questionsYear 8Fractions, decimals and percentages
Eight questions on the three ways of writing the same amount.
Number · 99 questionsYear 8Percentages
Finding a percentage, discounts, increases and working backwards, without a calculator.
Number · 99 questionsYear 8Ratios and rates
Simplifying and sharing in a ratio, speed, unit rates and map scales.
Number · 96 questionsYear 8Surds
Simplifying, adding, multiplying and rationalising simple surds.
Number · 100 questionsYear 8Probability
Sample spaces, complements, relative frequency and simple two-step outcomes.
Probability · 101 questionsYear 8Data and summary statistics
Samples, bias, mean, median, mode, range and choosing a display.
Statistics · 100 questionsYear 8Spread and box plots
Stem-and-leaf and dot plots, quartiles, IQR and five-number summaries.
Statistics · 101 questionsYear 9
Algebraic fractions
Simplifying, multiplying, adding and solving with algebraic fractions.
Algebra · 100 questionsYear 9Direct and inverse variation
Direct and inverse variation, finding the constant, and squares and roots.
Algebra · 97 questionsYear 9Equations and inequalities
Solving equations and inequalities, formulas and worded problems.
Algebra · 100 questionsYear 9Expanding and factorising
Single brackets, binomial products, perfect squares and common factors.
Algebra · 100 questionsYear 9Index laws
Multiplying, dividing and raising powers, plus zero and negative indices.
Algebra · 100 questionsYear 9Linear relationships
Solving for x, gradients and intercepts: the backbone of senior algebra.
Algebra · 99 questionsYear 9Quadratic equations
Null factor law, factorising, completing the square and word problems.
Algebra · 101 questionsYear 9Simultaneous equations
Substitution, elimination, where lines meet and worded problems.
Algebra · 99 questionsYear 9Earning money and interest
Wages, overtime, commission, tax, and simple and compound interest.
Financial mathematics · 102 questionsYear 9Exponential growth and decay
Doubling, halving, growth factors and repeated percentage change.
Functions · 101 questionsYear 9Parabolas and non-linear graphs
Graphs of y = ax² + c, and telling parabolas, hyperbolas and circles apart.
Functions · 106 questionsYear 9Angles and polygons
Angle facts, parallel lines, and the angles of triangles and polygons.
Geometry · 98 questionsYear 9Congruent triangles
Congruence tests, matching sides and angles, and congruence in quadrilaterals.
Geometry · 100 questionsYear 9Similar figures and scale
Scale factors, similarity tests, scale drawings, and area and volume ratios.
Geometry · 99 questionsYear 9Errors and accuracy in measurement
Precision, limits of accuracy, and absolute and percentage error.
Measurement · 100 questionsYear 9Perimeter, area and circles
Composite shapes, sectors and annuli in terms of π, and working backwards.
Measurement · 101 questionsYear 9Pythagoras' theorem
Exact surd answers, triads, the converse, 3D boxes and distances.
Measurement · 105 questionsYear 9Surface area and volume
Area, surface area and volume of prisms, cylinders and other solids, with unit conversions.
Measurement · 99 questionsYear 9Trigonometric ratios
Sine, cosine and tangent in right-angled triangles with whole-number sides.
Measurement · 98 questionsYear 9Percentages, profit and discount
Percentages of amounts, increases and discounts, GST, profit and reverse percentages.
Number · 104 questionsYear 9Rational and irrational numbers
Classifying real numbers, recurring decimals as fractions and surds.
Number · 114 questionsYear 9Ratios and rates
Simplifying and sharing in ratios, rates, speed and unit conversions.
Number · 100 questionsYear 9Scientific notation and rounding
Writing and calculating in scientific notation, comparing sizes, rounding and limits of accuracy.
Number · 100 questionsYear 9Surds and fractional indices
Simplifying surds, operations with surds and fractional indices.
Number · 99 questionsYear 9Probability
Multistage events, with and without replacement, two-way tables and Venn ideas.
Probability · 103 questionsYear 9Bivariate data and scatter plots
Variables, association, lines of best fit, prediction and causation.
Statistics · 100 questionsYear 9Statistics and data displays
Histograms, frequency tables, shape, outliers and comparing spread.
Statistics · 100 questionsYear 10
Coordinate geometry
Distance, midpoint, gradient and the equation of a line.
Algebra · 101 questionsYear 10Logarithms
Reading a logarithm as a power, and the three log laws.
Algebra · 96 questionsYear 10Non-linear simultaneous equations
Where lines meet parabolas, circles and hyperbolas.
Algebra · 99 questionsYear 10Non-monic quadratics and algebraic fractions
Factorising ax² + bx + c and simplifying algebraic fractions.
Algebra · 102 questionsYear 10Quadratics
Factorising, the null factor law, and reading a parabola.
Algebra · 99 questionsYear 10Simultaneous equations
Elimination, substitution and where two lines meet.
Algebra · 100 questionsYear 10The quadratic formula
Using the formula, the discriminant and choosing a method.
Algebra · 102 questionsYear 10Loans, credit and investments
Compound interest, depreciation, loans and credit cards.
Financial mathematics · 100 questionsYear 10Exponential and logarithmic graphs
Graphs of y = aˣ and y = logₐ x: intercepts, asymptotes and inverses.
Functions · 98 questionsYear 10Functions and relations
Function notation, domain and range, and linear inequalities.
Functions · 101 questionsYear 10Non-linear relationships
Hyperbolas, circles, exponentials and cubics from their equations.
Functions · 107 questionsYear 10Quadratic functions
Turning point form, completing the square and features of parabolas.
Functions · 110 questionsYear 10Rates of change
Average rates, constant and variable rates, and reading rate graphs.
Functions · 99 questionsYear 10Transformations of graphs
Translating, reflecting and dilating familiar graphs.
Functions · 102 questionsYear 10Circle geometry
Angle, chord and tangent theorems, one step at a time.
Geometry · 100 questionsYear 10Geometry reasoning
Congruence, similarity and quadrilateral facts, one reason at a time.
Geometry · 101 questionsYear 10Introduction to networks
Degrees, trails, circuits, Euler trails and planar graphs.
Geometry · 100 questionsYear 10Locus
Extension: describing loci in words and simple locus equations.
Geometry · 100 questionsYear 10Sufficiency conditions and proof
Properties versus sufficient conditions for special quadrilaterals.
Geometry · 106 questionsYear 10Surface area and volume
Pyramids, cones, spheres and composite solids, in terms of π.
Measurement · 116 questionsYear 10Surds
Simplifying, adding, multiplying and rationalising square roots.
Number · 98 questionsYear 10Polynomials
Degree, P(a), the remainder and factor theorems, and roots.
Polynomials · 102 questionsYear 10Probability
Single events, two-step experiments, with and without replacement.
Probability · 97 questionsYear 10Bivariate statistics
Trends, interpolation vs extrapolation, gradient and intercept in context.
Statistics · 100 questionsYear 10Spread and comparing data
Quartiles, IQR, outliers, box plots, skew and standard deviation.
Statistics · 102 questionsYear 10The normal distribution
A bridge to senior maths: bell curves, the 68-95-99.7 rule and z-scores.
Statistics · 101 questionsYear 103D trigonometry and bearings
True and compass bearings, back bearings and simple 3D right triangles.
Trigonometry · 106 questionsYear 10Sine and cosine rules
Choosing the sine, cosine or area rule, and the ambiguous case.
Trigonometry · 101 questionsYear 10Trig functions and the unit circle
Angles of any size, ASTC, exact values, graphs and simple equations.
Trigonometry · 112 questionsYear 11 Standard
Formulas and equations
Substituting into formulas, solving equations and changing the subject.
Algebra · 100 questionsYear 11 StandardLinear relationships
Gradient, intercepts, y = mx + c, direct variation and linear models.
Algebra · 107 questionsYear 11 StandardEarning and managing money
Wages, salaries, overtime, commission, deductions and GST.
Financial mathematics · 102 questionsYear 11 StandardNetworks, paths and trees
Network terms, degree, shortest paths and minimum spanning trees.
Geometry · 101 questionsYear 11 StandardMeasurement and time
Unit conversions, 24-hour time, time zones and measurement error.
Measurement · 100 questionsYear 11 StandardPerimeter and area
Composite shapes, circles, sectors and the trapezoidal rule.
Measurement · 101 questionsYear 11 StandardSurface area and volume
Prisms, cylinders, cones, spheres, composite solids and capacity.
Measurement · 101 questionsYear 11 StandardTime and location
Latitude, longitude, time zones, UTC, daylight saving and elapsed time.
Measurement · 102 questionsYear 11 StandardUnits, accuracy and errors
Metric units, prefixes, scientific notation, significant figures and error.
Measurement · 106 questionsYear 11 StandardData analysis
Mean, median, mode, range, interquartile range and types of data.
Statistics · 101 questionsYear 11 Advanced
Differentiation rules and tangents
Product, quotient and chain rules, gradients, tangents and normals.
Calculus · 100 questionsYear 11 AdvancedIntroduction to differentiation
The power rule, chain rule and product rule, one question at a time.
Calculus · 100 questionsYear 11 AdvancedExponentials and logarithms
The number e, natural logs and the log laws.
Functions · 100 questionsYear 11 AdvancedFunctions
Function notation, domain and range, composites, gradients and absolute values.
Functions · 99 questionsYear 11 AdvancedGraph transformations
Translations, dilations and reflections of graphs, and circles.
Functions · 100 questionsYear 11 AdvancedLinear functions and coordinate geometry
Gradient, intercepts, forms of a line, distance, midpoint and linear models.
Functions · 106 questionsYear 11 AdvancedPiecewise, absolute value and composite functions
Even and odd functions, f(g(x)), piecewise rules, |x| and semicircles.
Functions · 101 questionsYear 11 AdvancedQuadratic and cubic functions
Parabolas and cubics: roots, vertex, axis of symmetry and the discriminant.
Functions · 101 questionsYear 11 AdvancedProbability
Addition and product rules, conditional probability, independence and Venn diagrams.
Probability · 99 questionsYear 11 AdvancedData and relative frequency
Random variables, frequency tables, relative and expected frequency.
Statistics · 100 questionsYear 11 AdvancedRadians and exact values
Converting between degrees and radians, exact trig values and arc length.
Trigonometry · 100 questionsYear 11 AdvancedSine, cosine and area rules
Sine, cosine and area rules, bearings, arcs and sectors in radians.
Trigonometry · 100 questionsYear 11 AdvancedTrig identities and equations
Reciprocal ratios, Pythagorean identities, ASTC and solving trig equations.
Trigonometry · 116 questionsYear 11 Extension 1
Further inequalities
Quadratic, rational and absolute value inequalities.
Algebra · 101 questionsYear 11 Extension 1Related rates and further rates of change
Related rates, cooling and limited growth, and repeated roots.
Calculus · 100 questionsYear 11 Extension 1Binomial theorem
Pascal's triangle, binomial coefficients and picking out one term of an expansion.
Combinatorics · 97 questionsYear 11 Extension 1Permutations and combinations
Factorials, permutations, combinations, arrangements with repeats and the pigeonhole principle.
Combinatorics · 97 questionsYear 11 Extension 1Further work with functions
Reciprocal, sum, product and square root graphs, and y² = f(x), in words.
Functions · 100 questionsYear 11 Extension 1Inverse functions and parametric form
Finding inverses, restricting domains and converting parametric equations.
Functions · 100 questionsYear 11 Extension 1Polynomials
Degree, the remainder and factor theorems, and sums and products of roots.
Polynomials · 97 questionsYear 11 Extension 1Roots and coefficients
Sums and products of roots, forming polynomials and symmetric expressions.
Polynomials · 109 questionsYear 11 Extension 1Auxiliary angles
Writing a sin x + b cos x as one wave, max and min values and equations.
Trigonometry · 100 questionsYear 11 Extension 1Further trigonometry
Compound-angle and double-angle formulas, used forwards and backwards.
Trigonometry · 105 questionsYear 11 Extension 1Three-dimensional trigonometry
Box diagonals, angles with a plane, elevation from two points and bearings.
Trigonometry · 100 questionsYear 12 Standard
Linear models and variation
Reading gradients and intercepts in context, break-even points and variation.
Algebra · 100 questionsYear 12 StandardAnnuities
Future and present value annuities using a given factor (Standard 2).
Financial mathematics · 100 questionsYear 12 StandardDepreciation, loans and credit cards
Straight-line and declining-balance depreciation, loans and credit cards.
Financial mathematics · 100 questionsYear 12 StandardInvestments and interest
Simple and compound interest, compounding periods, inflation and share dividends.
Financial mathematics · 99 questionsYear 12 StandardCritical path analysis
Activity tables, start times, float and the critical path (Standard 2).
Geometry · 100 questionsYear 12 StandardNetwork flow
Capacities, cuts and maximum flow equals minimum cut (Standard 2).
Geometry · 100 questionsYear 12 StandardRates and ratios
Fuel use, heart rate, energy, scale drawings and mixing ratios.
Measurement · 100 questionsYear 12 StandardRelative frequency and probability
Relative frequency, tree diagrams, expected frequency and complements.
Probability · 100 questionsYear 12 StandardBivariate data analysis
Scatter plots, correlation, lines of best fit and making predictions.
Statistics · 102 questionsYear 12 StandardNormal distribution
z-scores and the 68, 95, 99.7 rule. Standard 2 content.
Statistics · 100 questionsYear 12 StandardNon-right-angled trigonometry
Sine rule, cosine rule, triangle area and radial surveys (Standard 2).
Trigonometry · 100 questionsYear 12 StandardRight-angled trigonometry and bearings
Sin, cos and tan, angles of elevation and depression, and bearings.
Trigonometry · 101 questionsYear 12 Advanced
Curve sketching
Increasing and decreasing, stationary points, concavity and inflections.
Calculus · 104 questionsYear 12 AdvancedDifferentiation
Derivatives of trig, exponential and log functions, the second derivative and stationary points.
Calculus · 100 questionsYear 12 AdvancedIntegration
Standard integrals, definite integrals and simple areas.
Calculus · 100 questionsYear 12 AdvancedMotion and rates of change
Displacement, velocity, acceleration, rates and exponential growth.
Calculus · 100 questionsYear 12 AdvancedOptimisation
Maximum and minimum problems, and global versus local extrema.
Calculus · 100 questionsYear 12 AdvancedFinancial mathematics
Compound interest, annuities and reducing-balance loans.
Financial mathematics · 104 questionsYear 12 AdvancedTrig graphs and transformations
Amplitude, period and shifts of trig graphs, and periodic models.
Functions · 108 questionsYear 12 AdvancedSequences and series
Arithmetic and geometric terms, sums and limiting sums.
Sequences and series · 100 questionsYear 12 AdvancedContinuous random variables
PDFs, CDFs, medians, uniform distributions, mean and variance.
Statistics · 100 questionsYear 12 AdvancedRandom variables
Discrete distributions, expected value, and a first look at continuous random variables.
Statistics · 100 questionsYear 12 AdvancedThe normal distribution
Normal curves, the empirical rule and z-scores.
Statistics · 100 questionsYear 12 Extension 1
Areas and volumes of revolution
Volumes about the x- and y-axes, cones, spheres and areas between curves.
Calculus · 101 questionsYear 12 Extension 1Differential equations
Checking solutions, slope fields, separable equations and logistic growth.
Calculus · 101 questionsYear 12 Extension 1Further calculus
Integrals that give inverse trig functions, substitution and integrating sin² and cos².
Calculus · 100 questionsYear 12 Extension 1Proof by induction
Base cases, inductive steps, sums, divisibility and spotting flawed proofs.
Proof · 100 questionsYear 12 Extension 1Binomial distribution
Mean and variance, small binomial probabilities and recognising a binomial situation.
Statistics · 100 questionsYear 12 Extension 1Sampling distribution of the mean
Sample means, their spread, the central limit theorem and the empirical rule.
Statistics · 100 questionsYear 12 Extension 1Inverse trigonometric functions
Exact values, domains and ranges, and the derivatives of the inverse trig functions.
Trigonometry · 124 questionsYear 12 Extension 1Projectile motion
Velocity components, time of flight, greatest height and range.
Vectors · 100 questionsYear 12 Extension 1Vectors
Magnitude, adding and scaling, the dot product, perpendicular vectors and components.
Vectors · 100 questionsYear 12 Extension 2
Integration by parts
Choosing u and dv, one-step examples, repeated parts and recurrences.
Calculus · 100 questionsYear 12 Extension 2Partial fractions and substitutions
Partial fractions, the t-results, completing the square and substitutions.
Calculus · 101 questionsYear 12 Extension 2Projectiles
Equations of motion, time of flight, greatest height, range and the path.
Calculus · 101 questionsYear 12 Extension 2Resisted motion
Resistance proportional to v or v², setting up equations and terminal velocity.
Calculus · 100 questionsYear 12 Extension 2Simple harmonic motion
Period, amplitude, centre of motion, maximum speed and v² in terms of x.
Calculus · 102 questionsYear 12 Extension 2Complex numbers
Powers of i, adding and multiplying, conjugates and the modulus.
Complex numbers · 100 questionsYear 12 Extension 2Geometry of complex numbers
Distance, rotation by i, and loci and regions on the Argand diagram.
Complex numbers · 100 questionsYear 12 Extension 2Polar form and De Moivre
Modulus and argument, multiplying in polar form, powers and roots of unity.
Complex numbers · 100 questionsYear 12 Extension 2Roots of unity and complex polynomials
Cube roots of unity, conjugate roots and factorising over the complex numbers.
Complex numbers · 100 questionsYear 12 Extension 2Further proof by induction
Induction for inequalities, recursive sequences and nth derivatives.
Proof · 98 questionsYear 12 Extension 2Proof
Converse, contrapositive, negation, quantifiers and counterexamples.
Proof · 100 questionsYear 12 Extension 2Proving inequalities
Squares are non-negative, AM-GM with two terms and spotting faulty steps.
Proof · 100 questionsYear 12 Extension 2Vectors in three dimensions
Magnitude, dot product, lines and spheres in three dimensions.
Vectors · 100 questionsWant a full paper? Read a free paper for your year, or download the writing booklet.
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