Predicted Papers with Mark Schemes (written in the board's style; not official papers)

A. AQA GCSE Mathematics (8300), Higher, Paper 1 (Non-calculator), extract set: 40 marks

1. Work out 2⅔ ÷ 1⅗. Give your answer as a mixed number. (3)
2. Write 0.000 0372 in standard form. (1)
3. Expand and simplify (2x − 3)(x + 5). (2)
4. Solve the simultaneous equations 3x + 2y = 16 and x − y = 2. (3)
5. Simplify √50 + √18. (2)
6. A bag holds red and blue counters in the ratio 3 : 5. 12 more red counters are added and the ratio becomes 1 : 1. How many blue counters are there? (3)
7. Evaluate 27^(−2/3). (2)
8. Prove that the sum of any three consecutive integers is a multiple of 3. (3)
9. Factorise fully 6x² − x − 2. (2)
10. Rearrange y = (3x + a)/(x − 2) to make x the subject. (4)
11. The nth term of a sequence is n² + 3n. Show that every term is even. (3)
12. Find the equation of the tangent to the circle x² + y² = 25 at the point (3, 4). (4)
13. Show that sin 60° × tan 30° = ½. (2)
14. Write 0.4̇5̇ as a fraction in its simplest form. (3)
15. f(x) = 2x − 1, g(x) = x². Solve fg(x) = 17. (3)

Mark scheme

1. 8/3 ÷ 8/5 (M1); 8/3 × 5/8 = 5/3 (M1); 1⅔ (A1)
2. 3.72 × 10⁻⁵ (B1)
3. 2x² + 10x − 3x − 15 (M1); 2x² + 7x − 15 (A1)
4. Eliminate a variable, e.g. 3x + 2(x − 2) = 16 (M1); x = 4 (A1); y = 2 (A1)
5. 5√2 or 3√2 (M1); 8√2 (A1)
6. 3k + 12 = 5k (M1); k = 6 (M1); blue = 30 (A1)
7. 1/27^(2/3) or 9 (M1); 1/9 (A1)
8. n + (n+1) + (n+2) (M1); = 3n + 3 (A1); = 3(n + 1), which is a multiple of 3 (A1)
9. (3x − 2)(2x + 1) (B2; B1 if the signs are reversed)
10. y(x − 2) = 3x + a (M1); xy − 2y = 3x + a (M1); x(y − 3) = a + 2y (M1); x = (a + 2y)/(y − 3) (A1)
11. n² + 3n = n(n + 3) (M1); one of n and n + 3 is even (M1); so the product is even (A1)
12. Gradient of radius = 4/3 (M1); tangent gradient = −3/4 (M1); y − 4 = −¾(x − 3) (M1); y = −¾x + 25/4 (A1)
13. (√3/2)(1/√3) (M1); = ½ (A1)
14. 100x − x = 45 (M1); x = 45/99 (M1); 5/11 (A1)
15. fg(x) = 2x² − 1 (M1); 2x² = 18 (M1); x = ±3 (A1)

B. AQA GCSE English Language (8700), Paper 1, Section A (Reading) structure

Unseen extract: about 50 lines of 20th/21st-century prose fiction.

• Q1 List four things about X from lines 1–5. (4)
• Q2 Look in detail at lines 6–15. How does the writer use language to describe the storm? (8)
• Q3 How has the writer structured the text to interest you as a reader? (8)
• Q4 "In the second half, the writer makes the reader feel the character's fear." To what extent do you agree? (20)
• Section B Q5 Write a description suggested by the picture, OR a story about a journey that goes wrong. (40: 24 for content and organisation, 16 for technical accuracy)

Mark scheme summary (levels): Q2/Q3: L4 (7–8) perceptive, detailed analysis with judicious subject terminology; L3 (5–6) clear explanation; L2 (3–4) some understanding; L1 (1–2) simple. Q4: L4 (16–20) critical, perceptive evaluation with judicious references. Q5: content L4 (19–24) compelling and convincing, with extensive and ambitious vocabulary; technical accuracy L4 (13–16) consistently secure sentence demarcation and a wide range of punctuation.

C. OCR GCSE Computer Science (J277), Paper 2: 25-mark extract

1. State the output of this algorithm when n = 5. (2)

total = 0
for i = 1 to n
    if i MOD 2 == 1 then total = total + i endif
next i
print(total)

2. Describe how a binary search finds 23 in [3, 8, 11, 15, 23, 30, 42]. (4)
3. Complete the truth table for P = NOT(A AND B) OR C, for all 8 input combinations. (4)
4. Write an algorithm that asks for a password until the user enters one at least 8 characters long, then prints "Accepted". (5)
5. Explain two differences between a compiler and an interpreter. (4)
6. Identify three types of test data for an input age 0–120, with an example of each. (6)

Mark scheme: 1) 9 (1+3+5), with 1 mark for working. 2) Middle item = 15 (1); 23 > 15 so discard the left half (1); new middle of [23, 30, 42] = 30 (1); 23 < 30, so check 23 and it is found (1). 3) P = 0 only when A=1, B=1, C=0; all other rows give 1 (4 marks for all correct, −1 per error). 4) Input (1); loop condition (1); len() check (1); re-input inside the loop (1); output after the loop (1). 5) e.g. a compiler translates all the code at once and an interpreter translates line by line (2); a compiler produces an executable and an interpreter needs the translator each time it runs (2). 6) Normal: e.g. 35 (2); boundary: 0 or 120 (2); invalid/erroneous: e.g. 150 or "abc" (2).

D. Edexcel GCSE Combined Science (1SC0), Biology Paper 1 Higher: 20-mark extract

1. Describe how to investigate the effect of pH on the rate of amylase activity (Core Practical). (6)
2. Calculate the magnification if an image is 25 mm long and the real cell is 50 µm long. (2)
3. Explain why active transport is needed for root hair cells to absorb mineral ions. (3)
4. Explain how vaccination provides immunity. (4)
5. Evaluate the use of stem cells in medicine. (5)

Mark scheme: 1) Levels-marked (6 marks): buffers at a range of pH values, water bath at 35 °C, starch + amylase, sample every 30 s into iodine, record the time until there is no blue-black colour, control the volumes, repeat. 2) 25 mm = 25,000 µm (1); ×500 (1). 3) The concentration of ions is lower in the soil than in the cell (1); so they move against the concentration gradient (1); which needs energy from respiration (1). 4) Inactive or dead pathogen/antigen injected (1); white blood cells/lymphocytes produce antibodies (1); memory cells are formed (1); a faster, larger secondary response (1). 5) For: can treat diabetes and paralysis, therapeutic cloning avoids rejection. Against: ethical concerns over embryos, risk of viral transfer or cancer. Plus a justified conclusion (levels marked).

E. SQA Higher Mathematics, Paper 1 (non-calculator): extract

1. Find the equation of the line through A(−2, 5) perpendicular to 3y = x + 4. (3)
2. Differentiate f(x) = 4√x − 3/x². (3)
3. Find ∫(6x² − 4x + 1) dx. (2)
4. Show that (x − 2) is a factor of x³ − 3x² − 4x + 12 and hence factorise fully. (4)
5. Solve log₂(x + 3) + log₂(x − 3) = 4. (4)

Marking (SQA style, one mark per process): 1) Gradient 1/3 (•1); perpendicular gradient −3 (•2); y − 5 = −3(x + 2) (•3). 2) Write as 4x^(1/2) − 3x^(−2) (•1); 2x^(−1/2) (•2); +6x^(−3) (•3). 3) 2x³ − 2x² (•1); + x + c (•2). 4) Synthetic division shows remainder 0 (•1), so it is a factor (•2); quotient x² − x − 6 (•3); (x − 2)(x − 3)(x + 2) (•4). 5) log₂(x² − 9) (•1); x² − 9 = 16 (•2); x = ±5 (•3); reject −5, so x = 5 (•4).

Building more papers with this template

For each board and subject: (1) download the specimen and recent papers from the board's site; (2) match the number of questions, mark tariffs and command words; (3) list the topics tested in the last 3 series and give more weight to ones that haven't come up; (4) write the mark scheme in the board's own format (AQA/Edexcel M1/A1/B1; SQA •1 process marks; levels-based for extended responses).