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GCSE · Number

3.3D Estimating: Fluency and Exam Drill

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 40 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

Round 47 to 1 significant figure.

(Total for Question 1 is 1 mark)

Round 0.083 to 1 significant figure.

(Total for Question 2 is 1 mark)

Round 359 to 1 significant figure.

(Total for Question 3 is 1 mark)

Round 0.0067 to 1 significant figure.

(Total for Question 4 is 1 mark)

Estimate 47 + 86 + 392 by rounding each number to 1 significant figure, then adding.

(Total for Question 5 is 2 marks)

Estimate 12.7 × 3.9 by rounding each number to 1 significant figure, then multiply.

(Total for Question 6 is 2 marks)

Estimate 0.049 ÷ 0.012 to 1 significant figure. Show your rounding and the calculation.

(Total for Question 7 is 2 marks)

A delivery van has load mass 1270 kg. Each parcel has mass about 3.6 kg. Using 1 significant figure for each value, estimate how many parcels the van could carry.

(Total for Question 8 is 3 marks)

A square rug has side length 4.8 m. Estimate the area by rounding the side to 1 significant figure, and state whether your estimate is an over-estimate or an under-estimate of the exact area.

(Total for Question 9 is 2 marks)

A small cylinder has radius 1.4 cm and height 12 cm. Estimate its volume to 1 significant figure for each measurement. Give your estimate (to 3 significant figures where appropriate) and say whether it is an over- or under-estimate.

(Total for Question 10 is 3 marks)

A bakery uses 18.7 g of yeast for each loaf. They bake 320 loaves. Use 1 significant figure to estimate the total mass of yeast used and state whether this estimate is an over-estimate or an under-estimate.

(Total for Question 11 is 3 marks)

The prices of three dishes are £4.95, £12.40 and £23.80. Estimate the total cost by rounding each price to 1 significant figure. Give your estimate and explain whether it is likely to be an over-estimate or an under-estimate.

(Total for Question 12 is 4 marks)

Estimate 246 × 78 by rounding each number to 1 significant figure before multiplying.

(Total for Question 13 is 2 marks)

Estimate 5325 ÷ 18 by rounding each number to 1 significant figure before dividing.

(Total for Question 14 is 2 marks)

A large cylindrical water tank has radius 3.6 m and height 8.4 m. Estimate the volume using 1 significant figure for radius and height. State whether your estimate is an over-estimate or an under-estimate.

(Total for Question 15 is 3 marks)

A model car travels at 14.6 m/s for 3.2 s. Estimate the distance travelled by rounding both values to 1 significant figure. Say whether your estimate is likely to be an over-estimate or an under-estimate.

(Total for Question 16 is 3 marks)

Three wooden boards measure 4.12 m, 6.89 m and 5.47 m. Using 1 significant figure for each length, estimate the total length required and decide how many 5 m rolls of material the builder should buy. Show your working.

(Total for Question 17 is 4 marks)

Round 0.995 to 1 significant figure.

(Total for Question 18 is 1 mark)

Mark scheme · 3.3D Estimating: Fluency and Exam Drill

Question 1

B1 50 cao
Answer: 50 (to 1 s.f.)

Question 2

B1 0.08 cao
Answer: 0.08 (to 1 s.f.)

Question 3

B1 400 cao
Answer: 400 (to 1 s.f.)

Question 4

B1 0.007 cao
Answer: 0.007 (to 1 s.f.)

Question 5

M1 round 47->50, 86->90, 392->400 and set up the addition oe
A1 540 cao
Answer: 540

Question 6

M1 round 12.7->10 and 3.9->4 and multiply oe
A1 40 cao
Answer: 40

Question 7

M1 round 0.049->0.05 and 0.012->0.01 and set up division oe
A1 5 cao
Answer: 5

Question 8

M1 round total mass 1270->1000 to 1 s.f.
M1 round parcel mass 3.6->4 to 1 s.f. and divide 1000/4 oe
A1 250 cao
Answer: 250 parcels

Question 9

M1 round 4.8->5 and calculate area 5 × 5 oe
A1 25 and over-estimate cao
Answer: Estimated area = 25 m²; this is an over-estimate

Question 10

M1 round radius 1.4->1 and height 12->10 to 1 s.f.
M1 use V = π r² h and substitute to give V = π × 1² × 10 = 10pi
A1 31.4 cm³ awrt and under-estimate cao
Answer: Approximately 31.4 cm³ (under-estimate)

Question 11

M1 round 18.7->20 g and 320->300 to 1 s.f.
M1 multiply 20 × 300 = 6000 g
A1 6000 g cao; over-estimate (6000 > exact 5984 g) oe
Answer: 6000 g (6.0 kg), over-estimate

Question 12

M1 round 4.95->5, 12.40->10, 23.80->20 to 1 s.f.
M1 add the rounded values 5 + 10 + 20
M1 state whether under/over with reason, e.g. two numbers were rounded down and one up so total is likely down
A1 35 pounds cao
Answer: £35; under-estimate (net rounding down)

Question 13

M1 round 246->200 and 78->80 to 1 s.f. and multiply oe
A1 16000 cao
Answer: 16000

Question 14

M1 round 5325->5000 and 18->20 to 1 s.f. and divide oe
A1 250 cao
Answer: 250

Question 15

M1 round radius 3.6->4 and height 8.4->8 to 1 s.f.
M1 substitute into V = π r² h to give V = π × 4² × 8 = 128pi
A1 402.1 m³ awrt; over-estimate cao
Answer: Approximately 402.1 m³; over-estimate

Question 16

M1 round 14.6->10 and 3.2->3 to 1 s.f.
M1 multiply 10 × 3 = 30 oe
A1 30 m cao; under-estimate
Answer: 30 m; under-estimate

Question 17

M1 round 4.12->4, 6.89->7, 5.47->5 to 1 s.f.
M1 add rounded lengths 4 + 7 + 5 = 16 m
M1 divide by roll length 16/5 = 3.2 and use correct method to find number of rolls
A1 4 rolls cao
Answer: Estimated total 16 m, so 4 rolls

Question 18

B1 1.0 or 1 cao
Answer: 1.0 (to 1 s.f.), i.e. 1

Estimating: Fluency and Exam Drill - Worksheets, Questions and Revision