Shortcut and Mashup problems

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Problem	Topics (click for search box)	Type & Difficulty	Other key words
Swaps	Addition, subtraction, multiplication, division reciprocals, inverses	Shortcut ★	N2a - Adding and subtracting positive integers N2b - Multiplying positive integers N2d - Applying the four operations to decimals subtracting multiplying times product minus take away difference N2f - Applying the four operations to fractions N3a - Relationships between operations, including inverse operations N2e - Applying the four operations to negative numbers
How wrong?	Subtraction, Multiplication, decimals	Shortcut ★	N2d - Applying the four operations to decimals subtracting multiplying times product minus take away difference distributive law property distributivity
Multiplication primetime	Multiplication, prime factorisation, time	Shortcut ★	N2b N4c G14d numbers Multiplying positive integers, multiply, times, remainders, divide, division, residue, modular arithmetic, modulo, clock, am, pm. hours, days, minutes, unique prime factors, factorization, factorise, factorize, factoring, money, £, pounds, and relationships, fundamental theorem of arithmetic, composite
A tricky slope?	Gradient, coordinates, decimals, fractions	Shortcut ★	A9a A9c A10a Plotting straight-line graphs, Finding the equation of a line through two given points or through one point with a given gradient (e.g. parallel or perpendicular to another line), gradient, Identifying and interpreting gradients and intercepts of linear functions graphically and algebraically, slope, intercept, y=mx+c, adding and subtracting fractions and decimals, addition, subtraction
Pedestrian pair power	Speed, prime factorisation, indices, inequalities	Shortcut ★	N4c N7a A4i R11a A22a Solving linear inequalities in one variable Using compound units, Prime numbers, Calculating with positive and negative integer indices, Index laws and solving equations involving indices, distance time Root, prime factors, factorize, factorise, factorization, factorisation, speed, metres second, hour, minutes time, composite, indices, index laws, powers, base rebase, changing base, inequality, less greater more than
Tutti frutti 🔒	Scaling, simultaneous equations, money	Shortcut ★	A19a G14c, Solving two linear simultaneous equations algebraically by elimination, simultaneous equations, scale
Change 🔒	Money, symmetry	Shortcut ★	G14c Money, coins, change
Complementary cards 🔒	Systematic listing strategies, symmetry	Shortcut ★	N5a Systematic listing strategies and the product rule for counting
Similar rectangles 🔒	Similar shapes, enlargement	Shortcut ★	G19a Lengths, areas and volumes in similar shapes G7e Enlargement Dilation R12a Ratios and similar shapes; scale, area and volume factors
Parallelogram 🔒	Straight line graphs, Area of parallelogram	Shortcut ★	A9a Plotting straight-line graphs A9b Identifying parallel and perpendicular lines G16b Area of parallelograms
Six-digit numbers 🔒	Systematic lisiting strategies, probability	Shortcut ★	Structure, N5a - Systematic listing strategies and the product rule for counting P2a Theoretical probability
Products of primes 🔒	Properties of multiplication, products of primes	Shortcut ★	N2b - Multiplying positive integers N4c - Prime numbers and prime factorisation factors numbers
Cube 🔒	3D geometry definitions, percentages	Mashup ★	G13a Plans and elevations of 3D shapes G12a Properties of 3D shapes with GeoGebra applets G1b 3D geometry terms R9a - Converting between fractions and percentages
Perimeter, pi, and fractions 🔒	Area, perimeter, fractions	Mashup ★	G17a - Perimeter of polygons, G17b - Circumference of a circle, G16a - Area of rectangles, G17c - Area of a circle, N12a - Interpreting fractions and percentages as operators, R3a - Expressing one quantity as a fraction of another
Prism density 🔒	Density, prisms	Mashup ★	G13a Plans and elevations of 3D shapes, R11a - Using compound units, R1a - Changing between standard units and compound units in numerical and algebraic contexts
Fractions and simultaneous equations 🔒	Adding fractions, simultaneous equations	Mashup ★	N2f Applying the four operations to fraction A19a Solving two linear simultaneous equations algebraically by elimination
Pattern product proof 🔒	Multiplication, division, rearranging, spotting patterns	Shortcut ★★	A5a A17a N2c Dividing with positive integers, N3a Relationships between operations, including inverse operations, Pattern-spotting, proofs, rearranging, rearrange, multiply and divide relationships, rewrite
Solutions required? 🔒	Substitution, completing the square, index laws	Shortcut ★★	Powers, indices, base, rebasing rebase, substitute substituting A2a A11b A4i A17a A18a A18b Solving quadratic equations by factorising Solving quadratic equations by completing the square N7a Calculating with positive and negative integer indices
Easy expanding 🔒	Expanding brackets, symmetry	Shortcut ★★	A4d Multiplying two or more brackets, symmetric
Generating simultaneous equations 🔒	Simultaneous equations, substitution	Shortcut ★★	A2a Substituting numerical values into formulae and expressions A19a - Solving two linear simultaneous equations algebraically by elimination A19b - Solving two linear simultaneous equations graphically or algebraically by substitution
Simultaneous symmetry 🔒	Simultaneous equations, symmetry	Shortcut ★★	A19a - Solving two linear simultaneous equations algebraically by elimination A19b - Solving two linear simultaneous equations graphically or algebraically by substitution
Prime calculations 🔒	Prime factorisation, indices, sums, products, differences	Shortcut ★★	N4c A4c Subtraction, Addition, Multiplication, multiplying, adding, subtracting, finding a differences, minus, plus, times, take away, Prime numbers and prime factorisation, distributive law distributivity property factorising factorizing factoring factorise factorize
Rhombi 🔒	Angles on parallel lines, Special quadrilaterals	Shortcut ★★	G4a Properties of special quadrilaterals, Rhombuses, G3b Alternate angles on parallel lines
Two out of three ain't bad 🔒	Simultaneous equations, symmetry	Shortcut ★★	A19a - Solving two linear simultaneous equations algebraically by elimination
Don't expand	Quadratic equations,	Shortcut ★★	N4c Prime numbers and prime factorisationA18a Solving quadratic equations by factorising
Exterior equations	Exterior angles and solving equations	Mashup ★★	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
Gradients	Gradients of straight lines, surds, rearranging	Mashup ★★	A5a Rearranging formulas to change the subject N8b Surds A10a Identifying and interpreting gradients and intercepts of linear functions graphically and algebraically slope standard
Not one in a million 🔒	Standard form, multiples, probability	Mashup ★★	N4b, N9c Adding and subtracting in standard form, P2a Theoretical probability, inequalities, integers, inequality, probabilities
Not standard form 🔒	Standard form, Indices	Mashup ★★	N9b Multiplying and dividing in standard form, A4i Index laws, powers, abases
Subprime 🔒	Prime factorisation, algebraic fractions, index laws	Mashup ★★	N4c Prime numbers and prime factorisation, A4f Simplifying, multiplying and dividing algebraic fractions, A4i Index laws and solving equations involving indices, Prime factors, factorize, factorise, factorization, factorisation, factoring, powers, indices, simplifying, lowest terms, substitute, substitution, substituting, cancelling
Prime terms 🔒	Arithmetic, quadratic, and Fibonacci-type sequences, prime numbers	Mashup ★★	N4c Prime numbers and prime factorisation, A24b - Recognising and using arithmetic, geometric and quadratic sequences, A24c - Recognising and using Fibonacci type sequences
Transforming sequences 🔒	Arithmetic and quadratic sequences, squaring, finding square roots, expanding, factorising	Mashup ★★	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
Don't be a surd 🔒	Surds, geometric sequences	Mashup ★★	N8b Surds simplifying rationalising denominators, rationalizing, rationalise, rationalize
Irrational stats 🔒	Surds, median, mode, range	Mashup ★★	N8b Surds simplifying. rationalising denominators, rationalizing, rationalise, rationalize, Statistics, S4a S4b S4c S4d
Points 🔒	Sequences, coordinates	Mashup ★★	A25a - Finding the nth term of a linear sequence G7a - Coordinates
Symmetry and probability 🔒	Lines of symmetry, probability	Mashup ★★	G1c - Reflection symmetry, probability, P7a - Constructing theoretical possibility spaces for combined experiments with equally likely outcomes and use these to calculate theoretical probabilities, sample
Tiles 🔒	Area, perimeter, simultaneous equations	Mashup ★★	G16a G16b G16c Area of rectangles triangles parallelograms G17a Perimeter of polygons composite shapes made up of G17d
Rounding and inequalities 🔒	Rounding, error intervals, inequalities	Mashup ★★	N15a - Rounding and truncating N15b - Using inequality notation to specify simple error intervals A22a - Solving linear inequalities in one variable
Investments 🔒	Compound interest, non-calculator skills	Shortcut ★★★	R16a Growth and decay problems
Powerplay 🔒	Index laws, simultaneous equations	Shortcut ★★★	Powers, indices, A19a Solving two linear simultaneous equations algebraically by elimination A19b Solving two linear simultaneous equations graphically or algebraically by substitution A4i Index laws and solving equations involving indices
Round a rectangle 🔒	Perimeter, circumference, circle theorems, Pythagoras' Theorem	Shortcut ★★★	G10a, N8a, G20a, A21b, A18a, Solving quadratic by factorising Deriving and solving an equation or simultaneous equations to describe a situation, Perimeter, circumference, circle theorems, obling, rectangles, diagonals, pi, exact values, cyclic quadrilateral, angles in a semicircle 90º degrees, factorize, factorise, factorization, factorisation
Factorised fun 🔒	Quadratic curves, roots, turning points, factorisation	Shortcut ★★★	A18a A18b A18c Solving quadratic equations formula, A11b Identifying turning points of quadratic functions, A4e Factorising quadratics, Quadratic factors, factorize, factorise, factorization, factorisation, factorizing, solve solving equations completed completing the square form, turning minimum point maximum curve coordinates, parabolas
Not quite congruent 🔒	Congruent triangles, sine rule	Shortcut ★★★	G5a Congruence criteria for triangles (SSS, SAS, ASA, RHS), trigonometry, G22a The sine rule
Fib 🔒	Fibonacci sequences, estimation	Shortcut ★★★	A24c - Recognising and using Fibonacci type sequences, golden ratio, section, phi, N14a - Estimating answers and checking calculations
A quadratic sequence 🔒	Quadratic sequences, quadratic equations	Shortcut ★★★	A25b - Finding the nth term of a quadratic sequence, A18a - Solving quadratic equations by factorising A18b A18c completing the square using the quadratic formula
Widening range 🔒	Mean, range, percentages	Mashup ★★★	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
Square 🔒	Area, coordinates, Pythagoras, surds, midpoints, circle theorems	Mashup ★★★	G10a circle theorems angle in a semicircle 90º degrees G20a Pythagoras' theorem Pythagorean G11a Solve geometrical problems on coordinate axes Surds
In a spin 🔒	Rotation, gradient	Mashup ★★★	Perpendicular lines segments rotate rotating angle centre of
Perimeter bounds 🔒	Perimeter, bounds, arithmetic sequences	Mashup ★★★	Squares, rectangles, linear sequences, nth term, upper bounds, lower bounds, and, error intervals N15b Using inequality notation to specify simple error intervals N16a Applying and interpreting limits of accuracy, including upper and lower bounds G17a Perimeter of polygons A25a Finding the nth term of a linear sequence A23a A24b
A triangle and a circle 🔒	Trigonometry, circle theorems	Mashup ★★★	G10a circle theorems Segment angles G20b G20c inverse trigonometric functions right-angled triangles
Probability pi 🔒	Trigonometry, circle theorems, probability	Mashup ★★★	G10a circle theorems Segment angles G22b G23a cosine rule area of triangle using sine 1/2 absinC probability fraction P2a
Congruent chords 🔒	Circle theorems, congruence, symmetry	Mashup ★★★	G10a circle theorems Segment angles G5a G7a reflection rotation G1c G1d
From radius to angles to area	Circle theorems, ratios, trigonometry	Mashup ★★★	G10a R5a Dividing a ratio in a given quantity, G23a area of triangle using sine ratio, radius, shaded area, triangle, sine 1/2 ab sinC 1/2absinc
Frusta 🔒	Quadratic sequences, volume of a cone	Mashup ★★★	G17g - Volume of spheres, pyramids, and cones A25b - Finding the nth term of a quadratic sequence A24b - Recognising and using arithmetic, geometric and quadratic sequences, frustums
Square and semicircle 🔒	Circle theorems, Pythagoras, prime factors	Mashup ★★★	G10a Circle theorems, G20a Pythagoras' theorem, N4c Prime numbers and prime factorisation, product decomposition Pythagorean
Intervowen area (dynamic)	Area of triangles, multiplying decimals, fractions, surds, algebraic expressions	Mashup ★★★	N2b Multiplying positive integers N2f Applying the four operations to fractions N8b Surds A4b Multiplying a single term over a bracket A4d Multiplying two or more brackets G16c Area of triangles