Become a Maths Boss: 25 Problems with Solutions

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A24b - Recognising and using arithmetic, geometric and quadratic sequences, A24c - Recognising and using Fibonacci type sequences A25a - Finding the nth term of a linear sequence A25b - Finding the nth term of a quadratic sequence additions, adding to, subtractions from, subtracting, take away, totals, sums, differences, wholes numbers, four operations, A17a, A17b Solving linear equations in one unknown algebraically where the unknown is on both sides of the equation,G3c The sum of angles in a triangle and the angle properties of polygons, polygons, exterior, sides, edges, writing setting up solve linear Indices, powers, indexes, bases, power, exponents, solving, solutions, equations, rewriting different bases, rebasing, rebase G10a circle theorems angle in a semicircle 90º degrees G20a Pythagoras' theorem Pythagorean G11a Solve geometrical problems on coordinate axes Surds

Greater, less, than, equal to, solves, unknowns, graphs, graphically, regions, shaded shades, shading by, inequality

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edges, vertex, vertices, faces, corners, sides, surfaces, nets, polyhedra, polyhedrons, curved shapes, 3-d three dimensions dimensional Equivalent, Equivalence, algebraic expressions, Equations, identities, argument, constructing, proofs, constructions, show that, prove, proving with Our Mashup problems interweave different topics within a single question, and generally require a significant amount of written working. Here is an example of a Mashup problem, requiring knowledge of circle theorems, ratios, and trigonometry:

Start typing in the search box to instantly filter by exam board, year, tier and month/season of sitting—e.g. OCR summer 2017 higher instantly brings up links to the relevant papers. G19a Lengths, areas and volumes in similar shapes G7e Enlargement Dilation R12a Ratios and similar shapes; scale, area and volume factorsconstructions, isometric, 3-d, hexagonal, hexagons, triangles, triangular, dotty, side view, overhead view, birdseye bird's eye top perspectives Primes, Unique, factorizes, factorizations, factorising, factorizing,HCFs, LCMs, highest, lowest, common, multiples, factorises, factors, decompose, decomposition, decomposing, fundamental theorem of arithmetic In the table below you find class and cohort versions of each QLA. The class QLAs (typically around 1 MB) can take data for up to 40 students while the cohort QLAs (typically around 5 MB) can take data for up to 300 students. The QLAs are otherwise identical. Because of the formulas in the spreadsheets, older computers may struggle to load or run the cohort QLAs, but should be fine with the class QLAs. Past papers, mark schemes, grade boundaries, and QLA links N8b Surds simplifying. rationalising denominators, rationalizing, rationalise, rationalize, Statistics, S4a S4b S4c S4d

Right angled triangles, Pythagoras's, Pythagorean, 90º, degrees, triple, a positives, negatives, directed numbers, adding, additions to, subtracting, subtractions from, multiplying by, multiplications, dividing, divisions Use the grey <> tool to move the line horizontally, keeping it to the left of the semicircle. Once you’ve decided where you’d like the line, do not move it again. Keep it fixed. Estimating, approximating, rounding, calculators, calculating, technology, estimates, estimations, figures, significanttruncate, truncation, Decimals places, significant figures, place values Rounding numbers and measures to an appropriate degree of accuracy, 1 2 3 4 5 dp d.p. sf s.f. sigfig N4c Prime numbers and prime factorisation, A24b - Recognising and using arithmetic, geometric and quadratic sequences, A24c - Recognising and using Fibonacci type sequences A21b Deriving and solving an equation or simultaneous equations to describe a situation, S4a S4b R9c Finding percentages and percentage changes multiplicatively using decimals, Average, spread, increase decrease percentage change