Home / iGCSE Mathematics (0580) C9.4 Calculate the mean, median, mode and range Paper 3

iGCSE Mathematics (0580) C9.4 Calculate the mean, median, mode and range Paper 3

IGCSE Mathematics(0580) Practice Questions Paper 3 - All Chapters
Question

Heidi records the colour of each of 500 cars crossing a bridge.
The pie chart shows some of this information.

(a) How many cars are red?

(b) 35 cars are grey.

Show, by calculation, that the sector angle for grey is 25.2°.

(c) 175 cars are white and 150 cars are black.

Complete the pie chart to show this information.

(d) Find the probability that a car chosen at random is not grey.

Give your answer as a fraction in its simplest form.

(e) Another 320 cars cross the bridge.

How many of these 320 cars are expected to be white?

(f) Heidi also records the number of people in each car crossing the bridge for one hour.

Number of peopleFrequency
120
26
30
415
58
612

Calculate the mean.

▶️ Answer/Explanation
Solution

(a) Ans: 125

From the pie chart, the red sector represents 25% of 500 cars.

Number of red cars = 25% × 500 = 125.

(b) Ans: 25.2°

Total cars = 500. Sector angle = (Number of grey cars/Total cars) × 360°.

Calculation: (35/500) × 360° = 25.2°.

(c) Ans: Completed pie chart

White cars angle: (175/500) × 360° = 126°.

Black cars angle: (150/500) × 360° = 108°.

(d) Ans: 93/100

Probability = (Total cars – Grey cars)/Total cars.

Calculation: (500-35)/500 = 465/500 = 93/100 simplified.

(e) Ans: 112

Expected white cars = (White cars/Total cars) × New cars.

Calculation: (175/500) × 320 = 112.

(f) Ans: 3.34

Mean = Total people/Total cars.

Total people = (1×20)+(2×6)+(4×15)+(5×8)+(6×12) = 204.

Total cars = 20+6+15+8+12 = 61. Mean = 204/61 ≈ 3.34.

Question

(a) A company makes glass using silica, soda, lime and magnesia.

The table gives information about the proportions used.

(i) Complete the table.

(ii) Complete the pie chart to show this information.

(iii) The masses of lime and magnesia used are in the ratio

lime : magnesia = 3 : 2

Find the percentage of the total mass of glass that is magnesia.

(iv) The company uses 8.25 kg of soda to make some glass.

Work out how many kilograms of silica they use.

(b) The company uses the formula M = 2.5 × A × T to find the mass of a sheet of glass.

M is the mass in kilograms.
A is the area in square metres.
T is the thickness in millimetres.

Use the formula to calculate the mass of a rectangular sheet of glass that is 1.9 m long, 0.6 m wide and 8 mm thick.

(c) In one year, 130,000,000 tonnes of glass were produced worldwide.

Write this number in standard form.

(d) The company sets targets to recycle its waste materials.
The bar chart shows the target rate and the actual rate for some of its recycling.

(i) The target rate for recycling glass was 55%.
The actual rate for recycling glass was 70%.

Complete the bar chart.

(ii) Which materials did the company recycle at more than double their target rate?

▶️ Answer/Explanation
Solution

(a)(i) Soda: 54°, Lime and magnesia: 36°

For soda: 15% of 360° = 54°. For lime and magnesia: 10% of 360° = 36°.

(a)(ii) Pie chart completed with sectors: Silica 270°, Soda 54°, Lime and magnesia 36°.

(a)(iii) 4%

Magnesia is 2 parts of the 5-part ratio (3:2). 10% total × 2/5 = 4%.

(a)(iv) 41.25 kg

Silica is 75% when soda is 15%. So (8.25 kg ÷ 15) × 75 = 41.25 kg.

(b) 22.8 kg

Area = 1.9 × 0.6 = 1.14 m². Mass = 2.5 × 1.14 × 8 = 22.8 kg.

(c) 1.3 × 108

Standard form for 130,000,000 is 1.3 × 108.

(d)(i) Bar chart shows glass target at 55% and actual at 70%.

(d)(ii) Plastic and Wood

Plastic (actual 60% vs target 20%) and Wood (actual 90% vs target 40%) both exceed double their targets.

More IGCSE Mathematics(0580) Practice Questions Paper 3 ........
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