*Shortcut* and *Mashup* problems

*Shortcut*problems?

*Shortcut* problems can be solved with very little working if students have a good understanding of the relevant concepts. It is often possible to solve these *without* such an understanding, but students will find it far more laborious. Here is an example of a *Shortcut* resource:

*Mashup*problems?

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:

You can filter these resources by topic, BossMaths lesson code (e.g. G20a for Pythagoras’ Theorem) or any relevant key word:

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Problem | Topics (click for search box) | Type & Difficulty | Other key words |
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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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |

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 |