1.
Write 480 as a product of prime factors. [2]
JD SCIENCE
Number
Answer all questions. Show working. Answers are in a separate file on the Worksheets page — do not look at them until you have finished.
2.
Find the HCF and LCM of 40 and 54. [3]
3.
Work out (4 × 10⁵) + (5 × 10⁴). Give your answer in standard form. [3]
4.
Work out (4 × 10⁴) × (5 × 10⁻³). Give your answer in standard form. [2]
5.
Convert 0.2929... to a fraction in its simplest form. [3]
6.
6.6000000000000005 cm has been rounded to 1 decimal place. Write the error interval. [2]
7.
A rectangle is measured as 12.4 cm by 5.2 cm, each to 1 d.p. Work out the upper bound of the area. [3]
8.
A jacket is reduced by 20% in a sale and now costs £52. Work out the original price. [3]
9.
Grace invests £280 at 5% compound interest for 3 years. Work out the value of the investment. [3]
10.
The same £280 is invested at 5% simple interest for 3 years. Work out the interest earned. [2]
11.
A car worth £8400 depreciates by 15% a year for 2 years. Find its value after 2 years. [3]
12.
Work out 2 3/4 + 1 5/6. Give your answer as a mixed number. [3]
13.
Work out 3 1/5 ÷ 2/3. [3]
14.
Write down the reciprocal of 0.2 [1]
15.
Simplify √88. [2]
16.
Rationalise the denominator of 6 / √18. [3]
17.
Work out 3⁷ ÷ 3⁴. [1]
18.
Work out 5⁻². [2]
19.
Work out 27^(2/3). [2]
20.
Estimate (39.6 × 19) ÷ 7.9 by rounding each number to 1 significant figure. [2]
21.
Write 7/8 as a decimal and as a percentage. [2]
22.
Share £220 in the ratio 2 : 3 : 5. [3]
23.
Round 0.04682 to 2 significant figures. [1]
24.
Work out (2.5 × 10⁷) ÷ (5 × 10³) in standard form. [2]
25.
A shop buys a lamp for £24 and sells it for £32. Work out the percentage profit. [2]
26.
Simplify (√12 + √2)(√12 − √2). [3]
27.
Grace writes 4.7 × 10ⁿ = 0.00047.
(a) Find n. [1]
(b) Write 470 000 in standard form. [2]
28.
A number x is given as 90 to the nearest 10. Find the lower bound of 1000 / x. [3]
29.
Explain the difference between a terminating decimal and a recurring decimal. Give an example of each. [3]
30.
Work out 1 1/2 × 2 2/3. [3]
31.
Here is a number machine: input → × 4 → − 7 → output.
(a) Find the output when the input is 5. [1]
(b) The output is 29. Find the input. [2]
32.
In a OCR 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]