Mathematics

Key Facts

• Last-minute priority: rounding, standard form, and percentage change.
• Estimate first to catch silly errors.
• A number in standard form looks like A × 10^n where 1 ≤ A < 10.
• Use place value columns when rounding.

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Key Facts

• Know 1/2, 1/4, 1/5, 1/8, 3/8 as decimals.
• Last-minute priority: percentage increase/decrease questions.
• Use multipliers to avoid rounding errors.
• Percent means “out of 100”.

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Key Facts

• Ratios compare parts of the same unit.
• Unitary method: find 1 part, then scale.
• Direct proportion keeps the ratio constant.
• Simplify before doing any calculations.

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• Last-minute priority: solve, expand, factorise quickly.
• Substitute values carefully.

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Key Facts

• Use y = mx + c to identify gradient and intercept.
• Graphs show relationships between variables.

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• Interior angles of polygon = (n-2) × 180°.
• Exterior angles sum to 360°.

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• Circle area = πr^2
• Trapezium area = 0.5(a+b)h
• Perimeter is the total boundary.

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• If P(A) = 0.3 then P(not A) = 0.7.
• Mutual exclusive outcomes add.

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• Range = highest - lowest.
• Median is robust to outliers.

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• Enlargement uses a scale factor.
• Rotation angles are in degrees.

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• nth term helps you jump to any term quickly.
• Second differences signal a quadratic sequence.

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Key Facts

• Roots solve ax^2 + bx + c = 0.
• Discriminant shows number of roots.

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Key Facts

• Only works in right-angled triangles.
• Check the hypotenuse is the longest side.

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Key Facts

• Pythagoras is your backup if two sides are known.
• Only use trig in right-angled triangles unless otherwise stated.

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Key Facts

• Opposite angles in a cyclic quadrilateral sum to 180°.
• Centre angle is twice the circumference angle.

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Key Facts

• a^(m) × a^(n) = a^(m+n)
• a^(-n) = 1/a^n

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• Parallel vectors are scalar multiples.
• Use column vectors for 2D coordinates.

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• Elimination removes a variable.
• Substitution replaces a variable.

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• Composite functions combine two rules.
• Inverse functions undo each other.

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