Core and extended routes are both covered. Agree your tier with your teacher before drilling the harder topics.
Syllabus code 0580 · checked against the board on 2026-09-13 · 15 questions available on this subject's topics (27 marks)
Simplify (2x³y)² × 3x⁻²y⁴ ÷ 6xy², leaving your answer in terms of x and y.
2 marks · Simplify · Powers, roots and index laws
Answer: 2x³y⁴
Work in three lines — bracket, multiply, divide. Learners who try to do it in one line lose the index of x more often than any other single mark in the paper.
Work out 8^(2/3).
1 mark · Work out · Powers, roots and index laws
Answer: 4
Read a fractional index as "root, then power". Root first is easier arithmetic, and it keeps the numbers small enough to do without a calculator.
A jacket is marked at P1,250. In a sale the price falls by 20%. The sale price is later increased by 20% to become the new normal price. Show that the new normal price is P1,200.
2 marks · Show that · Percentage change, including repeated change over time
Answer: P1,250 × 0.80 = P1,000; P1,000 × 1.20 = P1,200
This is the 20%-up-is-not-20%-down trap. Both marks belong to the two calculations; the answer is already printed, so quoting it earns nothing.
Expand and simplify (2x − 3)(x + 5).
1 mark · Expand and simplify · Simplifying, expanding and factorising
Answer: 2x² + 7x − 15
Write all four products before collecting. Skipping a term is the single most common error in this question type, and it costs the whole mark rather than part of it.
Solve 3(2x − 1) = 2(x + 4) + 5.
3 marks · Solve · Linear and simultaneous equations
Answer: x = 4
Expand both sides first, then collect. Collecting before expanding is where sign errors are born.
Find the nth term of the sequence 5, 8, 11, 14, …
1 mark · Find · Sequences and the nth term
Answer: 3n + 2
One mark, five seconds of checking: substitute n = 1 and n = 2 into your own rule. It is the cheapest verification in the whole paper.
Each exterior angle of a regular polygon is 24°. How many sides does the polygon have?
1 mark · Find · Angles, polygons and parallel lines
Answer: 15
The exterior angle fact does all the work in polygon questions. Interior angles total 180(n − 2), which is slower and easier to get wrong.
A, B, C and D lie on a circle in that order. Angle ABC = 74°. Find angle ADC, giving a reason for your answer.
3 marks · Find, giving a reason · Circle theorems
Answer: 106°, because opposite angles of a cyclic quadrilateral add to 180°.
Circle theorem questions carry a reason mark. A correct number with no theorem named typically loses one third of the marks available.
In a right-angled triangle the hypotenuse is 9.6 m. One of the sides next to an angle is 7.2 m. Work out that angle, giving your answer to one decimal place.
3 marks · Work out · Pythagoras and right-angled trigonometry
Answer: 41.4°
Label opposite, adjacent and hypotenuse on the diagram before choosing a ratio. Most marks lost here are lost to using sine because it was written first on the formula sheet.
Find the median of 4, 7, 2, 9, 5, 7, 3.
1 mark · Find · Averages from lists and frequency tables
Answer: 5
Order first, always. With an even count, take the mean of the two middle values — that is where 5.5 style answers come from.
A bag contains 5 red counters and 3 blue counters. Two counters are taken at random without replacement. Find the probability that both counters are red, giving your answer as a fraction in its lowest terms.
3 marks · Find · Probability, with and without replacement
Answer: 5/14
Without replacement changes the second fraction on both the top and the bottom. Write the second fraction separately — it is usually a mark of its own.
A straight line passes through the points (2, 5) and (6, 13). Find the equation of the line in the form y = mx + c.
3 marks · Find · Graphs, gradients and curve sketching
Answer: y = 2x + 1
One mark for the gradient, one for substituting a point, one for the finished equation. Show each of the three lines — a bare correct equation can score one mark, not three.
Showing 12 of 15. Open the bank to filter by topic, format or assessment objective.