Set
The paper and mark scheme
Question paper
Paper 1-style practice paper
80 marks · 1 h 30 min · 10 pages
10 multiple-choice questions and structured questions with answer lines. Higher content across all six topic areas, non-calculator: surds and indices, algebraic manipulation and functions, quadratics, circle theorems, set notation and Venn diagrams, exact trigonometry, sequences and Higher probability.
Mark scheme
PROPaper 1-style practice paper — mark scheme
Answers · Marking points · 5 pages
Model answers with a mark for each creditworthy point — for marking at home or in class.
Coverage
Chapters in this paper
- 1Number
- 2Fractions, decimals & percentages
- 3Indices, surds & standard form
- 4Estimation & bounds
- 5Algebraic manipulation
- 6Formulae, functions & proof
- 7Linear equations & graphs
- 8Quadratic equations & graphs
- 9Simultaneous & inequalities
- 10Sequences & nth term
- 11Graphs of functions
- 12Ratio & scale
- 13Proportion & rates
- 14Angles & constructions
- 15Congruence & transforms
- 16Pythagoras & trig
- 17Mensuration
- 18Circle theorems
- 19Probability
- 20Statistics
How to use
Work through it like the real exam
- 1Print the paper, or open the PDF and write your answers on paper.
- 2Set a timer and work without notes — the real thing is timed and closed-book.
- 3Mark your work with the mark scheme, one marking point at a time, including M marks for method.
- 4Redo every question you lost marks on, then revise that chapter.
Preview
The opening questions
Section A: Multiple-choice questions[10 marks]
Choose one answer for each question. Every correct answer scores one mark.
- 1( )
√50 simplifies to
- A2√5
- B25√2
- C10√5
- D5√2
- 2( )
(2x²)³ equals
- A2x⁶
- B8x⁶
- C6x⁶
- D8x⁵
- 3( )
The exact value of sin 30° is
- A√3⁄2
- B√2⁄2
- C½
- D1
- 4( )
Solve x² − 5x + 6 = 0.
- Ax = 2 or x = 3
- Bx = −2 or x = −3
- Cx = 1 or x = 6
- Dx = −1 or x = −6
Revision
Before you sit the paper
- Revise every chapter this paper covers, using the free notes pages.
- Do the quick quiz on each chapter and note where you lose marks.
- Practise the topical questions with the mark schemes.
- On calculator papers, give non-exact answers to 3 significant figures (angles to 1 d.p.) unless told otherwise; on the non-calculator paper, leave exact fractions and surds.
Tips
Exam tips
Method marks are real marks
- Show every line of working — M marks are awarded for correct method even with a slip in the arithmetic.
- Keep unrounded values in your calculator and round only the final answer.
- Give answers the accuracy asked for: 3 s.f., or 1 d.p. for angles in degrees.
- There is no formula sheet on GCSE papers — learn the memorised formulae list on each chapter page.
Questions
About the Paper 1-style (Higher)
Which real exam is this paper modelled on?
The Higher non-calculator paper: AQA 8300/1H, Edexcel 1MA1/1H and OCR J560 Paper 4, each 80 marks in 1 hour 30 minutes. Every question here is original QuizQuip material — no past-paper or specimen questions are reproduced, and QuizQuip is not affiliated with any awarding body.
What does “give exact answers” mean on a non-calculator paper?
Leave fractions as simplified fractions, keep surds in surd form (2√3, not 3.46), and leave multiples of π unmultiplied (6π, not 18.8). A decimal such as 0.666… loses the accuracy mark that 2⁄3 keeps.
Which Higher topics appear most on non-calculator papers?
Surds and indices, algebraic fractions and factorising, completing the square, functions and inverses, circle theorems, set notation, exact trigonometry values and without-replacement probability. This set practices all of them.