Step 1: Multiply 3,847 × 6 = 23,082
Step 2: Multiply 3,847 × 20 = 76,940
Step 3: Add the two results: 23,082 + 76,940 = 100,022
Free SATs Arithmetic Practice — Paper 1
The arithmetic paper is pure calculation — no word problems, no diagrams, no context. Just numbers. If your child knows the methods, this paper is full of marks waiting to be picked up.
What the Arithmetic Paper Covers
Paper 1 has 36 questions and lasts 30 minutes. No calculator is allowed. The questions progress from simpler calculations at the start to more challenging ones at the end. Each correct answer is worth 1 mark, except for two long multiplication and two long division questions which are worth 2 marks each (1 for method, 1 for answer).
The paper tests pure numerical fluency. Your child needs to be confident with written methods for all four operations, comfortable with fractions and decimals, and quick enough to finish within the time limit. There is no reading comprehension involved — every question is a straightforward calculation.
Topic Breakdown
Here is what typically appears on the arithmetic paper, roughly in order of difficulty:
Addition & Subtraction
Column addition and subtraction with numbers up to 7 digits. Expect carrying and borrowing across multiple columns. These questions appear early in the paper and are great confidence builders — make sure your child sets out their working neatly in columns.
Multiplication & Division
Times tables facts, short multiplication, long multiplication (up to 4 digits by 2 digits), short division, and long division (up to 4 digits by 2 digits). The long methods are worth 2 marks each, so showing clear working is essential.
Fractions
Adding, subtracting, multiplying, and dividing fractions. Finding fractions of amounts. Converting between mixed numbers and improper fractions. Simplifying answers. Fractions typically make up a quarter of the paper.
Decimals & Percentages
Adding and subtracting decimals, multiplying and dividing by 10, 100, 1000. Finding percentages of amounts (typically 10%, 25%, 50%, and combinations). These often appear in the second half of the paper.
Order of Operations (BODMAS)
Questions that mix operations and require your child to apply the correct order: Brackets, Orders, Division/Multiplication, Addition/Subtraction. Usually 1–2 questions near the end of the paper.
5 Worked Examples
Here are five typical arithmetic paper questions with step-by-step solutions:
Example 1: Long Multiplication
Calculate 3,847 × 26
Worth 2 marks: 1 for correct method, 1 for correct answer.
Example 2: Adding Fractions
¾ + ⅖ = ?
Step 1: Find a common denominator — LCM of 4 and 5 is 20
Step 2: Convert: ¾ = 15/20 and ⅖ = 8/20
Step 3: Add numerators: 15 + 8 = 23
Answer: 23/20 = 1 3/20
Example 3: Long Division
Calculate 7,524 ÷ 36
Step 1: 36 goes into 75 twice (72), remainder 3 → bring down 2 → 32
Step 2: 36 goes into 32 zero times, remainder 32 → bring down 4 → 324
Step 3: 36 goes into 324 nine times (324), remainder 0
Answer: 209
Worth 2 marks: show the bus stop method clearly.
Example 4: Percentage of an Amount
Find 35% of 480
Step 1: 10% of 480 = 48
Step 2: 30% = 48 × 3 = 144
Step 3: 5% = 48 ÷ 2 = 24
Step 4: 35% = 144 + 24 = 168
Example 5: Order of Operations
Calculate 6 + 4 × 3 − 2
Step 1: Multiplication first — 4 × 3 = 12
Step 2: Then left to right — 6 + 12 − 2
Step 3: 6 + 12 = 18, then 18 − 2 = 16
Common mistake: doing 6 + 4 first to get 10. BODMAS means multiply before adding.
Top Tips for the Arithmetic Paper
- Work through the paper in order. The questions get harder as you go. Pick up the early marks quickly and save time for the trickier questions at the end.
- Show your working clearly. For long multiplication and long division (2-mark questions), you get 1 mark for correct method even if the final answer is wrong. Neat columns matter.
- Check with inverse operations. Finished a subtraction? Add your answer back to check. Finished a division? Multiply to verify. This catches silly mistakes.
- Know your times tables cold. Nearly every question on this paper relies on quick recall of multiplication facts up to 12 × 12. If your child hesitates on 7 × 8 or 6 × 9, that adds up to a lot of lost time.
- Practise fractions separately. Fractions make up roughly a quarter of the paper. Being fluent with common denominators, simplifying, and converting between mixed numbers and improper fractions is essential. See our fractions guide for a full breakdown.
- Use the full 30 minutes. If your child finishes early, go back and check every answer. Careless errors cost more marks than not knowing the method.
Time Management
With 36 questions in 30 minutes, your child has roughly 50 seconds per question on average. But the early questions (simple addition, subtraction, times tables) should take 15–20 seconds each, banking time for the harder fraction and BODMAS questions at the end.
A good rule of thumb: aim to reach question 20 within 12–13 minutes. That leaves plenty of time for the trickier second half and a final check. Practising under timed conditions — even at home — builds this sense of pacing.
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