1.
Write 432 as a product of prime factors.
[2 marks]
- Use a factor tree / repeated division
- Final answer: 2 × 2 × 2 × 2 × 3 × 3 × 3
JD SCIENCE
Number
Indicative marking points. Award marks for equivalent scientific or mathematical wording. Do not issue this sheet with the student worksheet.
2.
Find the HCF and LCM of 36 and 48.
[3 marks]
- HCF from common primes; LCM from all primes to highest power
- Final answer: HCF = 12, LCM = 144
3.
Work out (3.6 × 10⁵) + (4.8 × 10⁴). Give your answer in standard form.
[3 marks]
- Convert to the same power of 10, then add
- Final answer: 4.08 × 10^5
4.
Work out (3.6 × 10⁴) × (4.8 × 10⁻³). Give your answer in standard form.
[2 marks]
- Multiply numbers and add indices
- Final answer: 17.3 × 10^1
5.
Convert 0.2727... to a fraction in its simplest form.
[3 marks]
- Let x = recurring decimal, 100x − x = integer
- Final answer: 3/11
6.
6.4 cm has been rounded to 1 decimal place. Write the error interval.
[2 marks]
- 6.3500000000000005 ≤ actual value < 6.45
7.
A rectangle is measured as 12.0 cm by 5.0 cm, each to 1 d.p. Work out the upper bound of the area.
[3 marks]
- Upper length × upper width
- Final answer: 60.852 cm²
8.
A jacket is reduced by 20% in a sale and now costs £48. Work out the original price.
[3 marks]
- Reverse percentage: sale price ÷ 0.8
- Final answer: £60.00
9.
Amira invests £240 at 4% compound interest for 3 years. Work out the value of the investment.
[3 marks]
- 240 × (1 + 4/100)^3
- Final answer: £269.97
10.
The same £240 is invested at 4% simple interest for 3 years. Work out the interest earned.
[2 marks]
- I = PRT/100
- Final answer: £28.80
11.
A car worth £8000 depreciates by 15% a year for 2 years. Find its value after 2 years.
[3 marks]
- Multiply by 0.85 twice
- Final answer: £5780.00
12.
Work out 2 3/4 + 1 5/6. Give your answer as a mixed number.
[3 marks]
- Convert to improper fractions, LCD 12
- Final answer: 4 7/12
13.
Work out 3 1/5 ÷ 2/3.
[3 marks]
- 16/5 × 3/2 = 48/10 = 24/5
- Final answer: 4 4/5
14.
Write down the reciprocal of 0.2
[1 mark]
- 5
15.
Simplify √72.
[2 marks]
- Write as a product with a square factor
- Final answer: 6√2
16.
Rationalise the denominator of 6 / √12.
[3 marks]
- Multiply numerator and denominator by the surd
- Final answer: 6 / √12 = 6√12 / 12, then simplify if possible (2√3)
17.
Work out 3⁷ ÷ 3⁴.
[1 mark]
- Subtract indices
- Final answer: 3³ or 27
18.
Work out 5⁻².
[2 marks]
- Negative index means reciprocal
- Final answer: 1/25
19.
Work out 27^(2/3).
[2 marks]
- Cube root of 27 is 3, then square
- Final answer: 9
20.
Estimate (39.6 × 18.2) ÷ 7.9 by rounding each number to 1 significant figure.
[2 marks]
- 40 × rounded value ÷ 8
- Final answer: 90
21.
Write 7/8 as a decimal and as a percentage.
[2 marks]
- 0.875
- 87.5%
22.
Share £180 in the ratio 2 : 3 : 5.
[3 marks]
- Total parts = 10
- Final answer: £36.00 : £54.00 : £90.00
23.
Round 0.04682 to 2 significant figures.
[1 mark]
- 2nd sf is 6, next digit 8 so round up
- Final answer: 0.047
24.
Work out (2.5 × 10⁷) ÷ (5 × 10³) in standard form.
[2 marks]
- Divide numbers, subtract indices
- Final answer: 5 × 10³
25.
A shop buys a lamp for £20 and sells it for £28. Work out the percentage profit.
[2 marks]
- Profit ÷ cost × 100
- Final answer: 40%
26.
Simplify (√8 + √2)(√8 − √2).
[3 marks]
- Difference of two squares
- Final answer: 6
27.
Amira writes 4.7 × 10ⁿ = 0.00047.
(a) [1 mark]
- n = −4
(b) [2 marks]
- 4.7 × 10⁵
28.
A number x is given as 80 to the nearest 10. Find the lower bound of 1000 / x.
[3 marks]
- To minimise 1000/x use the upper bound of x
- Final answer: 11.765
29.
Explain the difference between a terminating decimal and a recurring decimal. Give an example of each.
[3 marks]
- Terminating stops, e.g. 0.25
- Recurring repeats, e.g. 1/3 = 0.333...
30.
Work out 1 1/2 × 2 2/3.
[3 marks]
- 3/2 × 8/3 = 4
- Final answer: 4
31.
Here is a number machine: input → × 4 → − 7 → output.
(a) [1 mark]
- 13
(b) [2 marks]
- (29 + 7) ÷ 4 = 9
32.
In a AQA calculator paper, a student writes 3.6 × 10⁴ + 2.1 × 10³ = 5.7 × 10⁷. Explain the mistake and give the correct answer in standard form.
[3 marks]
- Powers of 10 were added incorrectly / numbers not converted to the same power
- Correct: 3.81 × 10⁴