The five Math question types that decide a 700+ score

1. Systems with a condition on the number of solutions

These ask for the value of a constant that gives no solution, exactly one solution, or infinitely many. The whole question is the discriminant for quadratics, or parallel versus identical lines for linear systems.

Recognise it by the phrase 'exactly one solution' or 'no solution' together with a letter constant. Set the discriminant to zero, or match the slopes, and you are done.

2. Quadratic and exponential modelling in words

A word problem describes growth, decay, projectile height, or revenue, and asks for a maximum, a zero, or a rate. The difficulty is almost never the algebra. It is translating the sentence into the right form.

Write down what each variable means in words before you write any equation. Half the errors at this level are solving the right equation for the wrong quantity.

3. Circles and completing the square

Given an expanded circle equation, find the centre or radius. You can complete the square, or you can graph it and read the centre off the screen. Learn both and use whichever your brain reaches for first under pressure.

4. Right triangles, similarity and trigonometry

The hard versions stack two triangles and give you one shared angle or one shared side. Draw the figure even when one is provided, mark every known value on your drawing, and look for the shared piece. The relationship sine of an angle equals cosine of its complement appears often enough to be worth memorising outright.

5. Statistics: what a change to the data set does

Adding a value, removing an outlier, or shifting every value changes mean, median, range and standard deviation differently. These questions need no computation at all if you know the behaviour of each measure.

• Adding a constant to every value shifts mean and median, leaves range and standard deviation unchanged.
• Removing an extreme value moves the mean much more than the median.
• Spreading values out raises standard deviation; clustering them lowers it.

How to practise these

Do them in themed blocks of ten, not mixed in. You are trying to build recognition, and recognition needs repetition of the same pattern in a row. Once you can name the type within five seconds of reading the question, move them back into mixed practice.