Time allowed: 60 minutes. Answer ALL 25 questions. Write your answers in the spaces provided. You are NOT allowed to use a calculator. You must show all your working; marks are available for a correct method as well as for the final answer. The number of marks for each question, or part-question, is shown in brackets. This paper covers the whole Core (Level 2) syllabus: number, fractions/decimals/percentages, ratio, algebra, geometry, measures, coordinates, statistics and probability.
1
Write these numbers in order of size, smallest first: 4708, 4087, 4780, 4078 (1 mark)
(Total for Question 1 is 1 mark)
2
Work out 6003 - 2758 (1 mark)
(Total for Question 2 is 1 mark)
3
Find 1/4 of 92 (1 mark)
(Total for Question 3 is 1 mark)
4
Two angles lie on a straight line. One angle is 118 degrees and the other is x degrees. Work out the size of angle x (1 mark)
(Total for Question 4 is 1 mark)
5
Simplify 5a + 3a - 2a (1 mark)
(Total for Question 5 is 1 mark)
6
One winter morning in Aberdeen, the temperature at 6am was -4 degrees C. By midday the temperature had risen by 11 degrees C. By 9pm it had then fallen by 8 degrees C from its midday value. Work out the temperature at 9pm. (2 marks)
(Total for Question 6 is 2 marks)
7
Convert 7/20 to a percentage. (2 marks)
(Total for Question 7 is 2 marks)
8
Simplify the ratio 48:60 fully. (2 marks)
(Total for Question 8 is 2 marks)
9
Solve 3x + 7 = 25 (2 marks)
(Total for Question 9 is 2 marks)
10
A triangle has a base of 14 cm and a perpendicular height of 9 cm. Work out its area. (2 marks)
(Total for Question 10 is 2 marks)
11
Sunita is baking bread and needs 1.2 kg of flour. She has three bags of flour, each weighing 350 g. Show working to decide whether Sunita has enough flour, and if not, say how much more she needs. (2 marks)
(Total for Question 11 is 2 marks)
12
Point A has coordinates (2, 9) and point B has coordinates (8, 3). Find the coordinates of the midpoint of AB. (2 marks)
(Total for Question 12 is 2 marks)
13
In a school reading challenge, five pupils read the following numbers of books: Freya read 7, Kwame read 11, Aoife read 9, Declan read 14, and Mei read 4. Work out the mean number of books read. (2 marks)
(Total for Question 13 is 2 marks)
14
A bag contains 5 red, 3 blue and 2 green counters. Priya takes one counter out of the bag at random.
(a)Find the probability that the counter is blue. (1 mark)(1)
(b)Find the probability that the counter is NOT green. (1 mark)(1)
(Total for Question 14 is 2 marks)
15
Write down all the factors of 84 that are also prime numbers. (2 marks)
In triangle ABC, angle A = 48 degrees, angle B = (x + 12) degrees and angle C = 2x degrees.
(a)Form an equation in x and solve it. (2 marks)(2)
(b)Work out the size of angle C. (1 mark)(1)
(Total for Question 17 is 3 marks)
18
Amir and Priya share 78 sweets in the ratio 5:8. Work out how many sweets Priya receives. (3 marks)
(Total for Question 18 is 3 marks)
19
Declan wants to buy a games console that costs 240 pounds. In a sale, the price is reduced by 15%. Work out the sale price. (3 marks)
(Total for Question 19 is 3 marks)
20
Mr Whitfield's garden in Harrogate is a rectangle measuring 12 m by 8 m. A rectangular patio measuring 5 m by 3 m has been built in one corner of the garden (the patio is not lawn).
(a)Work out the area of the whole rectangular garden. (1 mark)(1)
(b)Work out the area of the patio. (1 mark)(1)
(c)Work out the area of the garden that is lawn (not patio). (2 marks)(2)
(Total for Question 20 is 4 marks)
21
A pie chart was used to show how 60 students travel to school. It shows that they Walk (angle 150 degrees), come by Car (angle 90 degrees), and cycle by Bicycle (angle 60 degrees). The rest of the students travel by Bus.
(a)Work out the angle for the Bus sector of the pie chart. (2 marks)(2)
(b)Work out how many of the 60 students travel by Bus. (2 marks)(2)
(Total for Question 21 is 4 marks)
22
Chizoba is x years old. Her brother Tobenna is 3 years older than twice Chizoba's age. The sum of their ages is 39.
(a)Write down an equation in x to represent this information. (1 mark)(1)
(b)Solve your equation to find Chizoba's age. (2 marks)(2)
(c)Find Tobenna's age. (1 mark)(1)
(Total for Question 22 is 4 marks)
23
A school shop sells pens for 45p each and pencils for 30p each. Yusuf buys 6 pens and 8 pencils, and pays with a 10 pound note.
(a)Work out the total cost of the pens. (1 mark)(1)
(b)Work out the total cost of the pencils. (1 mark)(1)
(c)Work out how much change Yusuf should receive from his 10 pound note. (3 marks)(3)
(Total for Question 23 is 5 marks)
24
A circular table in a village hall in Ludlow has a diameter of 140 cm. Take π = 22/7.
(a)Work out the radius of the table. (1 mark)(1)
(b)Work out the circumference of the table. (2 marks)(2)
(c)A tablecloth needs to hang over the edge of the table by 20 cm all the way round. Work out the diameter of the tablecloth needed. (2 marks)(2)
(Total for Question 24 is 5 marks)
25
At a school fete, a profit of 480 pounds is shared between the Year 8 charity fund and the PTA in the ratio 3:5.
(a)Work out how much money the Year 8 charity fund receives. (2 marks)(2)
(b)The charity fund then donates 25% of its share to a local animal shelter. Work out how much money is donated to the animal shelter. (2 marks)(2)
(c)Work out how much money the charity fund has left after the donation. (2 marks)(2)
(Total for Question 25 is 6 marks)
Mark scheme · CE.M13 Maths: Full Practice Paper (Core, Non-Calculator)
Question 1
B1 4078, 4087, 4708, 4780 all in correct order
Answer: 4078, 4087, 4708, 4780
Question 2
B1 3245 cao
Answer: 3245
Question 3
B1 23 cao
Answer: 23
Question 4
B1 62 (degrees) cao
Answer: 62 degrees
Question 5
B1 6a cao
Answer: 6a
Question 6
M1 -4 + 11 (= 7), the midday temperature
A1 -1 (degrees C) cao
Answer: -1 degrees C
Question 7
M1 7/20 = 35/100 or equivalent complete method
A1 35% cao
Answer: 35%
Question 8
M1 divides both parts by a common factor (e.g. by 4, by 6 or by 12)
A1 4:5 cao (fully simplified)
Answer: 4:5
Question 9
M1 3x = 18 (subtracts 7 from both sides)
A1 x = 6 cao
Answer: x = 6
Question 10
M1 0.5 x 14 x 9 or equivalent complete method
A1 63 cm2 cao
Answer: 63 cm2
Question 11
M1 3 x 350 = 1050 g (or 1.05 kg)
A1 No, she does not have enough; she is 150 g (0.15 kg) short
Answer: No, she is 150 g (0.15 kg) short of the flour she needs
Question 12
M1 ((2+8)/2 , (9+3)/2) or equivalent complete method
A1 (5, 6) cao
Answer: (5, 6)
Question 13
M1 7+11+9+14+4 (= 45)
A1 9 (books) cao
Answer: 9 books
Question 14
(a) B1 3/10 oe cao
(a) Answer: 3/10
(b) B1 4/5 oe cao
(b) Answer: 4/5
Question 15
M1 a correct list, or attempt at a list, of the factors of 84
A1 2, 3, 7 (all three, no extras) cao
Answer: 2, 3, 7
Question 16
M1 6x + 15 (correct first expansion)
M1 -2x + 8 (correct second expansion, signs handled correctly)
A1 4x + 23 cao
Answer: 4x + 23
Question 17
(a) M1 48 + (x+12) + 2x = 180 oe
(a) A1 x = 40 cao
(a) Answer: x = 40
(b) B1 80 (degrees), follow through 2 x their x
(b) Answer: 80 degrees
Question 18
M1 identifies 13 total parts (5 + 8)
M1 78 / 13 (= 6), the value of one part
A1 48 (sweets) cao
Answer: 48 sweets
Question 19
M1 finds 15% of 240 (e.g. 10% = 24 and 5% = 12, so 15% = 36)
M1 240 - 36 (subtracts the discount from the original price)
A1 204 pounds cao
Answer: 204 pounds
Question 20
(a) B1 96 m2 cao
(a) Answer: 96 m2
(b) B1 15 m2 cao
(b) Answer: 15 m2
(c) M1 96 - 15 (follow through their (a) and (b))
(c) A1 81 m2 cao
(c) Answer: 81 m2
Question 21
(a) M1 360 - (150 + 90 + 60)
(a) A1 60 (degrees) cao
(a) Answer: 60 degrees
(b) M1 (their (a) / 360) x 60
(b) A1 10 (students) cao
(b) Answer: 10 students
Question 22
(a) B1 x + (2x + 3) = 39 oe
(a) Answer: x + (2x + 3) = 39
(b) M1 3x + 3 = 39 leading to 3x = 36
(b) A1 x = 12 cao
(b) Answer: 12 years old
(c) B1 27 (follow through 2 x their x + 3)
(c) Answer: 27 years old
Question 23
(a) B1 2.70 pounds (270p) cao
(a) Answer: 2.70 pounds
(b) B1 2.40 pounds (240p) cao
(b) Answer: 2.40 pounds
(c) M1 2.70 + 2.40 (follow through their (a) and (b)), the total cost
(c) M1 10.00 - their total cost
(c) A1 4.90 pounds cao
(c) Answer: 4.90 pounds
Question 24
(a) B1 70 cm cao
(a) Answer: 70 cm
(b) M1 22/7 x 140 (or 2 x 22/7 x 70)
(b) A1 440 cm cao
(b) Answer: 440 cm
(c) M1 140 + 2 x 20 (adds the overhang to both sides of the diameter)
(c) A1 180 cm cao
(c) Answer: 180 cm
Question 25
(a) M1 480 / 8 (= 60), the value of one part (8 total parts)