Pearson Edexcel GCSE (9–1) Mathematics
1MA1
Original practice paper written in the style of Edexcel papers — not a Pearson publication. This pack is untiered and can include both Foundation and Higher content.
Name: __________________________________
Class: __________________________________
Answer every question. Show all stages of your working. The total number of marks is 65.
This topic pack mixes calculator and non-calculator practice. Each question states whether a calculator may be used.
1
In a car park there are 24 cars and 15 vans and no other vehicles.
Non-calculator
(a)Write the number of vans as a fraction of the number of cars. Give your fraction in its simplest form.
(1)
(b)Write the number of cars as a fraction of the total number of vehicles. Give your fraction in its simplest form.
(2)
(Total for Question 1 is 3 marks)
2
This question is about writing ratios in their simplest form.
Non-calculator
(a)Write the ratio 45 : 27 in its simplest form.
(1)
(b)Write the ratio 500 g : 2 kg in its simplest form.
(2)
(Total for Question 2 is 3 marks)
3
A tank is being filled with water. The volume of water V litres in the tank after t minutes is shown by a straight-line graph that passes through the origin and the point (5, 40).
Either calculator policy
(a)Work out the gradient of the line.
(2)
(b)Write down what this gradient represents in the context of the tank.
(1)
(Total for Question 3 is 3 marks)
4
The depth of water d cm in a container t seconds after filling begins is shown by a curve. The tangent to the curve at the point where t = 6 passes through the points (2, 10) and (10, 46).
Either calculator policy
Use the tangent to estimate the rate at which the depth of water is increasing at the moment t = 6. State the units of your answer.
(2)
(Total for Question 4 is 2 marks)
5
A train travels 210 km in 1 hour 45 minutes.
Calculator
(a)Work out the average speed of the train in km/h.
(2)
(b)A second train travels at a steady 96 km/h for 15 minutes. Work out the distance it travels.
(1)
(Total for Question 5 is 3 marks)
6
A piece of oak has mass 480 g and density 0.75 g/cm³.
Calculator
Work out the volume of the piece of oak.
(2)
(Total for Question 6 is 2 marks)
7
A jacket normally costs £80. In a sale the price is reduced to £68.
Calculator
(a)Work out the percentage reduction in the price of the jacket.
(2)
(b)After the sale, the £68 price is increased by 25%. Work out the new price.
(1)
(Total for Question 7 is 3 marks)
8
In a sale, all normal prices are reduced by 20%. The sale price of a coat is £72.
Calculator
Work out the normal price of the coat.
(3)
(Total for Question 8 is 3 marks)
9
£4500 is shared between Amy, Ben and Carl in the ratio 2 : 3 : 4.
Either calculator policy
(a)Work out how much money Ben receives.
(2)
(b)Work out how much more money Carl receives than Amy.
(1)
(Total for Question 9 is 3 marks)
10
This question is about converting between units.
Either calculator policy
(a)Change 5.2 metres into centimetres.
(1)
(b)Change a speed of 72 km/h into metres per second.
(2)
(Total for Question 10 is 3 marks)
11
£2000 is invested in an account paying 3% per year compound interest.
Calculator
(a)Work out the value of the investment at the end of 2 years.
(2)
(b)Work out the total interest earned over the 2 years.
(1)
(Total for Question 11 is 3 marks)
12
y is directly proportional to x. When x = 4, y = 20.
Either calculator policy
(a)Find a formula for y in terms of x.
(2)
(b)Work out the value of y when x = 9.
(1)
(c)Work out the value of x when y = 65.
(1)
(Total for Question 12 is 4 marks)
13
Two shops sell the same brand of rice. Shop A sells a 2 kg bag for £3.20. Shop B sells a 5 kg bag for £7.50, marked '20% extra free' (so the bag contains 20% more rice than 5 kg at no extra cost).
Calculator
(a)By comparing the price per kilogram at each shop, determine which shop offers the better value for money. You must show all your working.
(4)
(b)Priya needs at least 30 kg of rice, bought as cheaply as possible using bags from the better-value shop only. Work out the least amount she pays.
(2)
(Total for Question 13 is 6 marks)
14
£650 is invested in an account paying 4% simple interest per year.
Calculator
(a)Work out the interest earned in one year.
(2)
(b)Work out the total interest earned after 3 years.
(1)
(Total for Question 14 is 3 marks)
15
To make a shade of green paint, blue paint and yellow paint are mixed in the ratio 5 : 3. To make some green paint, 40 litres of blue paint is used.
Non-calculator
(a)Work out the number of litres of yellow paint needed.
(2)
(b)Work out the total number of litres of green paint made.
(1)
(Total for Question 15 is 3 marks)
16
A 750 g box of cereal costs £2.40. A 1.2 kg box of the same cereal costs £3.60.
Calculator
By working out the price per kilogram for each box, determine which box is the better value for money. You must show all your working.
(3)
(Total for Question 16 is 3 marks)
17
Here are the ingredients needed to make 8 flapjacks: 200 g oats, 120 g butter, 3 tablespoons of syrup.
Either calculator policy
(a)Work out the mass of oats needed to make 12 flapjacks.
(2)
(b)Work out the mass of butter needed to make 20 flapjacks.
(1)
(Total for Question 17 is 3 marks)
18
A map is drawn to a scale of 1 : 25000.
Calculator
(a)Two towns are 8 cm apart on the map. Work out the real distance between the towns, in kilometres.
(2)
(b)A road is 5 km long in real life. Work out its length on the map, in centimetres.
(2)
(Total for Question 18 is 4 marks)
19
A shop buys a bicycle for £120 and later sells it for £150.
Calculator
(a)Work out the percentage profit the shop makes on the bicycle.
(2)
(b)In a later sale, the £150 selling price is reduced by 15%. Work out the sale price of the bicycle.
(2)
(Total for Question 19 is 4 marks)
20
The numbers of visitors to a museum in six consecutive months were: January 120, February 135, March 150, April 145, May 170, June 185.
Calculator
(a)Describe the trend in the number of visitors.
(2)
(b)Work out the percentage increase from January to June. Give your answer to 1 decimal place.
(2)
(Total for Question 20 is 4 marks)
Pearson Edexcel GCSE (9–1) Mathematics
1
(a)
Answer: 5/8
B1 for 5/8 (from 15/24 simplified).
(b)
Answer: 8/13
M1 for 24/39 (cars over total). A1 for 8/13.
3 marks
2
(a)
Answer: 5 : 3
B1 for 5 : 3.
(b)
Answer: 1 : 4
M1 for converting to common units, e.g. 500 : 2000. A1 for 1 : 4.
3 marks
3
(a)
Answer: 8
M1 for 40 ÷ 5. A1 for 8.
(b)
Answer: The rate at which the tank is filling, i.e. 8 litres per minute.
B1 for the rate of filling / 8 litres per minute (accept flow rate in litres per minute).
3 marks
4
Answer: 4.5 cm/s
M1 for (46 − 10) ÷ (10 − 2) using the two given tangent points. A1 for 4.5 cm/s (accept 4.5 cm per second).
2 marks
5
(a)
Answer: 120 km/h
M1 for 210 ÷ 1.75 (converting 1 h 45 min to 1.75 h). A1 for 120.
(b)
Answer: 24 km
B1 for 24 (from 96 × 0.25 or 96 ÷ 4).
3 marks
6
Answer: 640 cm³
M1 for 480 ÷ 0.75 (volume = mass ÷ density). A1 for 640.
2 marks
7
(a)
Answer: 15%
M1 for 12/80 × 100 (or (80 − 68)/80 × 100). A1 for 15.
(b)
Answer: £85
B1 for 85 (from 68 × 1.25 or 68 + 25% of 68).
3 marks
8
Answer: £90
M1 for recognising £72 represents 80% of the normal price. M1 for 72 ÷ 0.8 (or 72 ÷ 80 × 100). A1 for 90.
3 marks
9
(a)
Answer: £1500
M1 for 4500 ÷ 9 (= 500 for one part). A1 for 1500 (3 parts).
(b)
Answer: £1000
B1 for 1000 (Carl £2000 − Amy £1000; ft their one-part value).
3 marks
10
(a)
Answer: 520 cm
B1 for 520.
(b)
Answer: 20 m/s
M1 for 72 × 1000 ÷ 3600 (or 72000 m per 3600 s). A1 for 20.
3 marks
11
(a)
Answer: £2121.80
M1 for 2000 × 1.03² (or two successive 3% increases). A1 for 2121.80.
(b)
Answer: £121.80
B1 for 121.80 (their value from (a) − 2000).
3 marks
12
(a)
Answer: y = 5x
M1 for y = kx with k = 20/4. A1 for y = 5x.
(b)
Answer: 45
B1 for 45 (ft their formula).
(c)
Answer: 13
B1 for 13 (ft their formula).
4 marks
13
(a)
Answer: Shop A: £3.20 ÷ 2 = £1.60 per kg. Shop B: 20% extra free means 5 × 1.2 = 6 kg for £7.50, so £7.50 ÷ 6 = £1.25 per kg. Since £1.25 < £1.60, Shop B offers the better value for money.
M1 for Shop A price per kg: 3.20 ÷ 2 = 1.60. M1 for Shop B mass: 5 × 1.2 = 6 kg (or 20% of 5 = 1 kg extra → 6 kg). M1 for Shop B price per kg: 7.50 ÷ 6 = 1.25. A1 for a correct conclusion that Shop B is better value, supported by both prices per kg (1.60 and 1.25).
(b)
Answer: £37.50
M1 for 30 ÷ 6 = 5 bags (of 6 kg from Shop B). A1 for 5 × 7.50 = £37.50.
6 marks
14
(a)
Answer: £26
M1 for 0.04 × 650 (or 4/100 × 650). A1 for 26.
(b)
Answer: £78
B1 for 78 (their one-year interest × 3).
3 marks
15
(a)
Answer: 24 litres
M1 for 40 ÷ 5 × 3 (= one part is 8 litres, then × 3). A1 for 24.
(b)
Answer: 64 litres
B1 for 64 (40 + their 24).
3 marks
16
Answer: Small box: £2.40 ÷ 0.75 kg = £3.20 per kg. Large box: £3.60 ÷ 1.2 kg = £3.00 per kg. Since £3.00 < £3.20, the 1.2 kg box is the better value for money.
M1 for the price per kg of the 750 g box: 2.40 ÷ 0.75 = 3.20. M1 for the price per kg of the 1.2 kg box: 3.60 ÷ 1.2 = 3.00. A1 for a correct conclusion that the 1.2 kg box is better value, supported by both figures (3.20 and 3.00 per kg).
3 marks
17
(a)
Answer: 300 g
M1 for a correct proportion method, e.g. 200 ÷ 8 × 12 (or 200 ÷ 8 = 25 per flapjack). A1 for 300.
(b)
Answer: 300 g
B1 for 300 (from 120 ÷ 8 × 20).
3 marks
18
(a)
Answer: 2 km
M1 for 8 × 25000 = 200000 cm (or a correct conversion method). A1 for 2 (km).
(b)
Answer: 20 cm
M1 for 5 km = 500000 cm then ÷ 25000. A1 for 20 (cm).
4 marks
19
(a)
Answer: 25%
M1 for (150 − 120) ÷ 120 × 100 (= 30 ÷ 120 × 100). A1 for 25.
(b)
Answer: £127.50
M1 for 150 × 0.85 (or 150 − 15% of 150). A1 for 127.50.
4 marks
20
(a)
Answer: The number of visitors generally increases, with a small decrease from March to April.
B1 for a generally increasing trend. B1 for identifying the decrease from March to April.
(b)
Answer: 54.2%
M1 for (185 - 120)/120 × 100. A1 for 54.2% to 1 decimal place.
4 marks