1.23 Estimating answers
9 exam questions worth 22 marks. Write your answer, open the mark scheme, then give yourself the marks you earned. Your answers are saved on this device.
0 / 22
Which is the best estimate for 4.87 \times 21.3?
Choose one answer.
Correct Not quite: the answer is 100
Mark scheme
B: 100
Model answer
100 (B). 5 × 20 = 100.
Work out an estimate for \dfrac{6.82 \times 3.14}{0.21}.
Mark scheme
B1: 7, 3 and 0.2 (1 s.f. values); M1: 7 × 3 ÷ 0.2; A1: 105
Model answer
7 × 3 ÷ 0.2 = 21 ÷ 0.2 = 105.
Work out an estimate for \dfrac{38.6 + 11.2}{2.1 \times 4.9}.
Mark scheme
B1: 40, 10, 2 and 5; M1: (40 + 10) ÷ (2 × 5); A1: 5
Model answer
(40 + 10) ÷ (2 × 5) = 50 ÷ 10 = 5.
Write each number correct to 1 significant figure. (a) 0.0486 (b) 4952 (c) 0.52
Mark scheme
B1: 0.05; B1: 5000; B1: 0.5
Model answer
(a) 0.05 (b) 5000 (c) 0.5.
Work out an estimate for \dfrac{7.8 \times 19.6}{0.039}.
Mark scheme
B1: 8, 20 and 0.04; M1: 8 × 20 ÷ 0.04; A1: 4000
Model answer
8 × 20 ÷ 0.04 = 160 ÷ 0.04 = 4000.
Work out an estimate for \sqrt{82.5}.
Mark scheme
M1: uses 81 = 9²; A1: 9
Model answer
The nearest square number to 82.5 is 81 = 9², so √82.5 is about 9.
48.7 \div 0.52 is estimated as 50 \div 0.5 = 100. Is the estimate bigger or smaller than the exact answer? Give a reason.
Mark scheme
B1: bigger; B1: the top was rounded up and the bottom was rounded down, both of which make the answer larger
Model answer
It is bigger. 48.7 was rounded up to 50 and 0.52 was rounded down to 0.5, and both changes increase the value of the fraction.
Ali's calculator shows 0.49 \times 810 = 3969. Use an estimate to show that this answer is wrong.
Mark scheme
M1: 0.5 × 800; A1: 400, which is much smaller than 3969
Model answer
0.5 × 800 = 400, which is about ten times smaller than 3969, so the answer is wrong (it should be 396.9).
Tickets cost £11.95 each. Estimate the total cost of 38 tickets. Show your working and say whether your estimate is bigger or smaller than the exact cost.
Mark scheme
M1: 40 and 12 (rounded values); A1: 40 × 12 = £480; B1: bigger (both numbers were rounded up)
Model answer
40 × 12 = £480. Both 38 and £11.95 were rounded up, so the estimate is bigger than the exact cost (£454.10).
Found a mistake?