Is A-level Maths hard? Understanding the step up

Simplify (x² − 9) / (x − 3).

First factorise the numerator: x² − 9 = (x − 3)(x + 3). Cancelling the common factor gives x + 3, provided x ≠ 3 (x is not equal to 3).

The original denominator is zero at x = 3, so the original fraction is undefined there. A common mistake is to write only x + 3 and assume every value of x is allowed. The useful habit is to check where the original expression is defined, even after it looks simpler.

A straight line has one gradient; a curve can have a different gradient at each point. For the curve y = x² + 3x, differentiation gives dy/dx = 2x + 3. Here dy/dx means the rate of change of y with respect to x, or the tangent’s gradient. The differentiation rules used here change x² into 2x and 3x into 3.

At x = 2, the gradient is 2 × 2 + 3 = 7. The point on the curve is (2, 10), because 2² + 3 × 2 = 10. The tangent line therefore satisfies y − 10 = 7(x − 2), or y = 7x − 4.

The gradient is 7 at that point, not everywhere on the curve. Notice how the new calculus step depends on familiar substitution and straight-line equations.

Show that the sum of two consecutive integers is odd. Checking 2 + 3 = 5 and 7 + 8 = 15 gives examples, but does not cover every pair.

Let the first integer be n. The next is n + 1. Their sum is n + (n + 1) = 2n + 1. Since 2n is even for every integer n, adding 1 makes the sum odd. This proves the statement for all consecutive integers, including negative ones.

The key change is from showing that something works in selected cases to explaining why it must work generally.

Try the self-check and part of your school’s bridging work. Record specific sticking points, such as “I forgot to change the sign when expanding a bracket”, rather than “I am bad at algebra”. Choose one or two topics to work on first.

Use Pearson’s free GCSE-to-A-level transition resource for example questions, solution videos and practice in algebra, quadratics, equations, graphs and trigonometry. Attempt an example before viewing the solution, as Pearson suggests. Then complete another question on paper and explain each step. Some resources linked from OCR’s article require a school login; the Pearson page provides a public starting point.

Return to the topics without looking at your previous solution, then mix a few question types. Try the short calculus illustration above as a preview of how algebra and graphs connect. Judge whether the explanation becomes clearer after working through it, rather than expecting to know an untaught method immediately.

Bring one corrected question, one you can now solve independently and one that still stops you. Ask what to practise next, which bridging work to complete and what support is available when the course starts. Pearson cautions that its end-of-chapter exam questions mainly suit students who have completed and consolidated the syllabus; do not treat difficulty with those questions before the course as a verdict on your suitability.