Hiroshima Entrance Math cheat sheet

Use the three standard identities for squares and difference of squares.

Take out a common factor before trying other factorisations.

Convert surds to like radicals before adding or subtracting.

Rationalise any denominator containing a root.

Check signs carefully when subtracting a bracket.

Elimination and substitution must both produce the same pair.

In y=ax+b, a is the gradient and b is the y-intercept.

An intersection point satisfies both equations simultaneously.

Parallel lines have identical gradients.

Always substitute back to check a simultaneous solution.

The sign of a controls whether the parabola opens up or down.

The discriminant b²−4ac determines the number of real roots.

Intersections with a line come from solving a quadratic equation.

Never divide by a variable that could be zero.

Check intersection coordinates in both original equations.

Parallel lines give equal alternate and corresponding angles.

A triangle's angles sum to 180°; an exterior angle equals the two remote interior angles.

Polygon interior sum is (n−2)×180° and exterior sum is 360°.

The central angle is twice the inscribed angle on the same arc.

A tangent meets the radius at 90°.

SAS requires the equal angle to be included between the equal sides.

AA is usually the quickest similarity test.

Lengths scale by k, areas by k², and volumes by k³.

A parallel line inside a triangle creates proportional segments.

Match corresponding vertices before writing any ratio.

Sort the data before finding the median.

Mean uses the sum of all values; range uses only the largest and smallest.

Probability is favourable outcomes over equally likely outcomes.

Without replacement, update both numerator and denominator after each draw.

Expected frequency equals probability multiplied by the number of trials.