3.6H Proportion: Higher Tier Practice

EDEXCEL Edexcel 1MA1 · Calculator allowed · about 75 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

Answer ALL questions. Show all your working.

A car uses fuel at a rate directly proportional to distance travelled. If the car uses 8.4 litres of fuel for 60 km, work out how many litres it uses for 225 km.

(Total for Question 1 is 2 marks)

A recipe for a sauce uses ingredients in the ratio tomato:oil:vinegar = 6:1:0.5 by mass. Ava wants to make 1.2 kg of the sauce. Calculate the mass of oil she should use, giving your answer in grams.

(Total for Question 2 is 2 marks)

Quantities A and B are inversely proportional. When A = 12, B = 5. Work out the value of B when A = 18.

(Total for Question 3 is 3 marks)

A map uses a scale of 1 cm to 7.5 km. A cyclist plans a route that is proportional to the straight-line distance. On the map the route would be 28 cm. Calculate the real distance and then the time taken if the cyclist rides at an average speed of 18 km/h. Give the time in hours and minutes, correct to the nearest minute.

(Total for Question 4 is 4 marks)

A retailer sells two sizes of detergent. A 1.8 litre bottle costs 5.58 pounds and a 3.6 litre bottle costs 10.26 pounds. Which size is better value per litre? Show your working and justify your answer.

(Total for Question 5 is 4 marks)

A metal rod is stretched so that its length increases in direct proportion to the temperature increase. At 20 degrees C the rod is 1.25 m long. At 80 degrees C the rod is 1.253 m long. Assuming linear proportional change, find an expression for the length L (in metres) as a function of temperature t in degrees C, of the form L = m t + c. Give m and c to 6 decimal places.

(Total for Question 6 is 5 marks)

An alloy is made by mixing metals X and Y in the ratio X:Y = 7:3 by mass. A manufacturer needs 560 kg of alloy. However, metal X costs 12.40 pounds per kg and metal Y costs 7.10 pounds per kg. Calculate the minimum total cost to make 560 kg of alloy. Show clear working.

(Total for Question 7 is 6 marks)

Mark scheme · 3.6H Proportion: Higher Tier Practice

Question 1

M1 use of direct proportion method, e.g. unit rate or ratio: 8.4/60 * 225 or equivalent
A1 31.5 litres cao
Answer: 31.5 litres (cao). Working: unit rate = 8.4/60 = 0.14 L/km; 0.14 * 225 = 31.5 L. Check: 225/60 = 3.75; 3.75 * 8.4 = 31.5.

Question 2

M1 find fraction for oil: total parts = 6 + 1 + 0.5 = 7.5, so oil = 1/7.5 of total or equivalent
A1 160 g cao
Answer: 160 g. Working: total = 1.2 kg = 1200 g; oil = 1/7.5 * 1200 g = 160 g. Check: 1200/7.5 = 160.

Question 3

M1 use product k = A * B = 12 * 5 = 60
M1 use B = k / A to find B = 60 / 18
A1 10/3 or 3.333... cao
Answer: 10/3 (or 3.333... ) cao. Working: k = 12 * 5 = 60 so B = 60/18 = 10/3.

Question 4

M1 convert map length to real distance: distance = 28 * 7.5 km
A1 210 km cao
M1 use time = distance / speed: 210 / 18 hours
A1 11 hours 40 minutes cao
Answer: 210 km and 11 hours 40 minutes. Working: distance = 28 * 7.5 = 210 km. Time = 210 / 18 = 11.666... hours = 11 hours + 0.666...*60 = 11 hours 40 minutes. Check: 18 * 11.666... = 210.

Question 5

M1 calculate unit prices: 5.58/1.8 and 10.26/3.6
M1 correct numerical comparison of the two unit prices
A1 state both unit prices correctly, e.g. 5.58/1.8 = 3.10 (to 2 dp) and 10.26/3.6 = 2.85 (to 2 dp) cao
A1 conclude 3.6 litre bottle is better value cao
Answer: 3.6 litre bottle is better value. Working: 5.58/1.8 = 3.10 pounds per litre; 10.26/3.6 = 2.85 pounds per litre. Since 2.85 < 3.10 the 3.6 L bottle is cheaper per litre. Check: 1.8 * 3.10 = 5.58 and 3.6 * 2.85 = 10.26.

Question 6

M1 use two points to find gradient m = (1.253 - 1.25) / (80 - 20)
A1 m = 0.000050 cao to 6 dp
M1 substitute one point to find c using L = m t + c
A1 c = 1.249000 cao to 6 dp
A1 final correct expression L = 0.000050 t + 1.249000 cao
Answer: L = 0.000050 t + 1.249000. Working: m = (1.253 - 1.25)/(80 - 20) = 0.003/60 = 0.00005 = 0.000050 to 6 dp. Then c = 1.25 - 0.00005*20 = 1.25 - 0.001 = 1.249000. Check: at t = 80, L = 0.00005*80 + 1.249 = 0.004 + 1.249 = 1.253.

Question 7

M1 find masses from ratio: total parts = 7 + 3 = 10, X = 7/10 * 560 kg, Y = 3/10 * 560 kg
M1 calculate mass of X: 7/10 * 560 = 392 kg
M1 calculate mass of Y: 3/10 * 560 = 168 kg
M1 calculate cost of X: 392 * 12.40 = 4860.80 pounds
A1 calculate cost of Y: 168 * 7.10 = 1192.80 pounds cao
A1 total cost = 4860.80 + 1192.80 = 6053.60 pounds cao
Answer: 6053.60 pounds. Working: total parts 10 so X = 7/10 * 560 = 392 kg, Y = 168 kg. Cost X = 392 * 12.40 = 4860.80 pounds. Cost Y = 168 * 7.10 = 1192.80 pounds. Total = 4860.80 + 1192.80 = 6053.60 pounds. Check: 392*12 = 4704; 392*0.4 = 156.8; sum 4860.8. 168*7 = 1176; 168*0.1 = 16.8; sum 1192.8. Total 6053.6.

Proportion: Higher Tier Practice - Worksheets, Questions and Revision