SATBot — Maths PDF Pack

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Paper 1 (Arithmetic): 25 questions · 30 minutes · 25 marks
Paper 2 (Reasoning): 15 questions · 40 minutes · 25 marks

Do not use a calculator for either paper. Show your working where it may earn method marks.

Instructions
• Read each question carefully before you begin.
• Write your answer in the answer box provided.
• If you make a mistake, cross it out neatly and write your answer again.
• Show all working — even if you make a mistake, you may still earn marks.
• Do not spend too long on any one question.

Score record

Paper 1 score

out of 25

Paper 2 score

out of 25

Total score

out of 50

Work through each question. Write one answer per box. You may NOT use a calculator.

376 + 489 =

1 mark

1,004 − 367 =

1 mark

48 × 7 =

1 mark

364 ÷ 4 =

1 mark

²⁄₅ + ³⁄₅ =

1 mark

3.6 + 4.75 =

1 mark

12.4 − 5.8 =

1 mark

56 × 34 =

1 mark

¾ of 240 =

1 mark

15² =

1 mark

0.4 × 0.3 =

1 mark

7,200 ÷ 9 =

1 mark

³⁄₄ − ¼ =

1 mark

4.8 × 100 =

1 mark

432 ÷ 16 =

1 mark

25% of 360 =

1 mark

1⅓ + 2⅔ =

1 mark

√144 =

1 mark

596 × 8 =

1 mark

4⁵⁄₆ − 1½ =

1 mark

0.35 × 20 =

1 mark

2³ × 5 =

1 mark

3,456 ÷ 12 =

1 mark

60% of 450 =

1 mark

¼ ÷ 2 =

1 mark

Read each question carefully. Show your working — you may earn method marks even if your final answer is wrong.

A cinema has 24 rows of seats. Each row has 32 seats. How many seats are there altogether?

Working

2 marks

Write these fractions in order, starting with the smallest: ³⁄₄ ½ ⁷⁄₈ ⅝

1 mark

A bag of apples weighs 2.4 kg. Sam uses 650 g. How many grams of apples are left?

Working

2 marks

What is the value of the digit 7 in the number 4,738,205?

1 mark

A rectangle has a perimeter of 54 cm. Its length is 17 cm. What is its width?

Working

2 marks

Round 3,847,265 to the nearest million.

1 mark

Pencils cost 35p each. Pens cost £1.20 each. Jake buys 4 pencils and 3 pens. How much does he spend altogether?

Working

2 marks

The temperature at midnight is −8°C. By noon it has risen by 13°C. What is the temperature at noon?

1 mark

A shape has vertices at (2,1), (6,1), (6,4) and (2,4). What is the area of the shape?

Working

2 marks

Express 45 minutes as a fraction of 3 hours. Give your answer in its simplest form.

Working

2 marks

A train departs at 09:47 and arrives at 12:23. How long is the journey?

Working

2 marks

What percentage of 80 is 60?

Working

2 marks

A swimming pool holds 125,000 litres of water. In one day, 18,750 litres evaporate. How many litres remain? Give your answer in thousands.

Working

2 marks

A recipe for 6 people needs 450 g of flour. How much flour is needed for 10 people?

Working

2 marks

The mean of five numbers is 14. Four of the numbers are 11, 16, 9 and 18. What is the fifth number?

Working

2 marks

This answer key is for parent or teacher use. Do not share with the child until after they have completed the paper. Where a question shows method marks (2M), award 1 mark if working is correct but the final answer is wrong.

Paper 1: Arithmetic — Answers

Q	Answer	Marks	Explanation
1	865	1	376+489: add column by column with carries. 6+9=15 (write 5, carry 1); 7+8+1=16 (write 6, carry 1); 3+4+1=8.
2	637	1	1004−367: borrow across zeros. Check: 637+367=1004 ✓
3	336	1	48×7 = (40×7)+(8×7) = 280+56 = 336.
4	91	1	364÷4: 36÷4=9, 4÷4=1. Answer: 91.
5	1	1	²⁄₅ + ³⁄₅ = ⁵⁄₅ = 1.
6	8.35	1	Line up decimals: 3.60+4.75=8.35.
7	6.6	1	12.4−5.8=6.6.
8	1,904	1	56×34 = 56×30+56×4 = 1680+224 = 1904.
9	180	1	¾ of 240: 240÷4=60; 60×3=180.
10	225	1	15²=15×15=225.
11	0.12	1	0.4×0.3: 4×3=12; two decimal places → 0.12.
12	800	1	7200÷9: 72÷9=8; add two zeros → 800.
13	½	1	³⁄₄−¼=²⁄₄=½.
14	480	1	4.8×100: move digits two places left → 480.
15	27	1	432÷16=27. Check: 16×27=432 ✓
16	90	1	25%=¼. 360÷4=90.
17	4	1	1⅓+2⅔=3+⅓+⅔=3+1=4.
18	12	1	√144=12 (12×12=144).
19	4,768	1	596×8=(600×8)−(4×8)=4800−32=4768.
20	3⅓	1	4⁵⁄₆−1³⁄₆=3²⁄₆=3⅓.
21	7	1	0.35×20=0.35×2×10=7.
22	40	1	2³=8; 8×5=40.
23	288	1	3456÷12=288. Check: 12×288=3456 ✓
24	270	1	10% of 450=45; 60%=6×45=270.
25	⅛	1	¼÷2=¼×½=⅛.

Paper 2: Reasoning — Answers

Q	Answer	Marks	Explanation / Method marks
1	768	2	24×32=24×30+24×2=720+48=768. Award 1M for correct method with arithmetic error.
2	½, ⅝, ¾, ⅞	1	Convert to eighths: ½=⁴⁄₈, ⅝=⁵⁄₈, ¾=⁶⁄₈, ⅞=⁷⁄₈.
3	1,750 g	2	2.4 kg=2400 g; 2400−650=1750 g. Award 1M for correct conversion to grams.
4	700,000	1	7 is in the hundred-thousands column; value=700,000.
5	10 cm	2	54=2×(17+w); 27=17+w; w=10. Award 1M for correct formula used.
6	4,000,000	1	847 thousands rounds up (≥500 thousands) → 4,000,000.
7	£5.00	2	4×35p=£1.40; 3×£1.20=£3.60; total=£5.00. Award 1M for correct partial working.
8	5°C	1	−8+13=5°C.
9	12 sq units	2	Width=4, Height=3; Area=12. Award 1M for correct dimensions identified.
10	¼	2	45/180=1/4. Award 1M for 45/180 unsimplified.
11	2 hours 36 minutes	2	09:47→12:23. Award 1M for correct method (e.g. counting on).
12	75%	2	60÷80×100=75%. Award 1M for 60/80 or 0.75 seen.
13	106.25 thousand litres	2	125,000−18,750=106,250=106.25 thousand. Award 1M for correct subtraction.
14	750 g	2	450÷6=75 g per person; 75×10=750 g. Award 1M for correct unit rate.
15	16	2	Total=14×5=70; 11+16+9+18=54; 70−54=16. Award 1M for total=70 seen.