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 fourth Core (Level 2) paper covers the same breadth as Papers 1, 2 and 3: number, fractions/decimals/percentages, ratio, algebra, geometry, measures, coordinates, statistics and probability, with entirely different questions.
1
Write the number eight hundred and thirteen thousand and forty-two in figures. (1 mark)
(Total for Question 1 is 1 mark)
2
Work out 8005 - 4728 (1 mark)
(Total for Question 2 is 1 mark)
3
Find 5/8 of 96 (1 mark)
(Total for Question 3 is 1 mark)
4
Two angles lie on a straight line. One angle is 134 degrees and the other is w degrees. Work out the size of angle w (1 mark)
(Total for Question 4 is 1 mark)
5
Simplify 8h + 3k - 5h + 6k (1 mark)
(Total for Question 5 is 1 mark)
6
One evening in Fort William, the temperature was -5 degrees C. Overnight it fell by 8 degrees C. Work out the temperature after it fell. (2 marks)
(Total for Question 6 is 2 marks)
7
Convert 17/25 to a percentage. (2 marks)
(Total for Question 7 is 2 marks)
8
Simplify the ratio 72:96 fully. (2 marks)
(Total for Question 8 is 2 marks)
9
Solve 4x - 9 = 23 (2 marks)
(Total for Question 9 is 2 marks)
10
A triangle has a base of 16 cm and a perpendicular height of 11 cm. Work out its area. (2 marks)
(Total for Question 10 is 2 marks)
11
Bilal is making a smoothie and needs 900 ml of milk. He has three cartons of milk, each containing 250 ml. Show working to decide whether he has enough milk, and if not, say how much more he needs. (2 marks)
(Total for Question 11 is 2 marks)
12
Point G has coordinates (5, 12) and point H has coordinates (13, 4). Find the coordinates of the midpoint of GH. (2 marks)
(Total for Question 12 is 2 marks)
13
In a charity quiz, five teams scored the following points: 34, 41, 29, 38, 33. Work out the mean score. (2 marks)
(Total for Question 13 is 2 marks)
14
A box contains 6 red pens, 4 blue pens and 10 black pens. Freya takes one pen from the box at random.
(a)Find the probability that it is blue. (1 mark)(1)
(b)Find the probability that it is NOT black. (1 mark)(1)
(Total for Question 14 is 2 marks)
15
Write down all the factors of 105 that are also prime numbers. (2 marks)
In triangle XYZ, angle X = 41 degrees, angle Y = (4x + 13) degrees and angle Z = 3x degrees.
(a)Form an equation in x and solve it. (2 marks)(2)
(b)Work out the size of angle Z. (1 mark)(1)
(Total for Question 17 is 3 marks)
18
Priya and Callum share 117 conkers in the ratio 4:9. Work out how many conkers Callum receives. (3 marks)
(Total for Question 18 is 3 marks)
19
A tablet computer costs 320 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 Kowalski's garden in Preston is a rectangle measuring 18 m by 11 m. A rectangular patio measuring 5 m by 4 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 108 students travel to a school open evening. It shows that they go by Walking (angle 120 degrees), by Car (angle 90 degrees), and by Bicycle (angle 70 degrees). The rest go 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 108 students go by Bus. (2 marks)(2)
(Total for Question 21 is 4 marks)
22
Tunde is x years old. His grandmother Ngozi is 6 years older than five times Tunde's age. The sum of their ages is 78.
(a)Write down an equation in x to represent this information. (1 mark)(1)
(b)Solve your equation to find Tunde's age. (2 marks)(2)
(c)Find Ngozi's age. (1 mark)(1)
(Total for Question 22 is 4 marks)
23
A craft shop sells buttons for 55p each and ribbons for 85p each. Grace buys 6 buttons and 4 ribbons, and pays with a 10 pound note.
(a)Work out the total cost of the buttons. (1 mark)(1)
(b)Work out the total cost of the ribbons. (1 mark)(1)
(c)Work out how much change Grace should receive from her 10 pound note. (3 marks)(3)
(Total for Question 23 is 5 marks)
24
A circular flower bed in a park in Durham has a diameter of 112 cm. Take π = 22/7.
(a)Work out the radius of the flower bed. (1 mark)(1)
(b)Work out the circumference of the flower bed. (2 marks)(2)
(c)A low edging strip needs to sit 9 cm out from the edge of the flower bed all the way round. Work out the diameter of the circle that the edging forms. (2 marks)(2)
(Total for Question 24 is 5 marks)
25
At a summer fete, a profit of 720 pounds is shared between the PTA fund and the school trip fund in the ratio 5:7.
(a)Work out how much money the PTA fund receives. (2 marks)(2)
(b)The PTA fund then spends 25% of its share on new equipment. Work out how much money is spent on equipment. (2 marks)(2)
(c)Work out how much money the PTA fund has left after this spending. (2 marks)(2)
(Total for Question 25 is 6 marks)
Mark scheme · CE.M31 Maths: Full Practice Paper (Core, Non-Calculator, Set 4)
Question 1
B1 813042 cao
Answer: 813042
Question 2
B1 3277 cao
Answer: 3277
Question 3
B1 60 cao
Answer: 60
Question 4
B1 46 (degrees) cao
Answer: 46 degrees
Question 5
B1 3h + 9k cao
Answer: 3h + 9k
Question 6
M1 -5 - 8 (correct method)
A1 -13 (degrees C) cao
Answer: -13 degrees C
Question 7
M1 17/25 = 68/100 or equivalent complete method
A1 68% cao
Answer: 68%
Question 8
M1 divides both parts by a common factor (e.g. by 8 or by 12)
A1 3:4 cao (fully simplified)
Answer: 3:4
Question 9
M1 4x = 32 (adds 9 to both sides)
A1 x = 8 cao
Answer: x = 8
Question 10
M1 1/2 x 16 x 11 or equivalent complete method
A1 88 cm2 cao
Answer: 88 cm2
Question 11
M1 3 x 250 = 750 ml
A1 No, he does not have enough; he is 150 ml short
Answer: No, he is 150 ml short of the milk he needs
Question 12
M1 ((5+13)/2 , (12+4)/2) or equivalent complete method
A1 (9, 8) cao
Answer: (9, 8)
Question 13
M1 34+41+29+38+33 (= 175)
A1 35 (points) cao
Answer: 35 points
Question 14
(a) B1 1/5 oe cao
(a) Answer: 1/5
(b) B1 1/2 oe cao
(b) Answer: 1/2
Question 15
M1 a correct list, or attempt at a list, of the factors of 105
A1 3, 5, 7 (all three, no extras) cao
Answer: 3, 5, 7
Question 16
M1 18x + 24 (correct first expansion)
M1 -5x + 15 (correct second expansion, signs handled correctly)
A1 13x + 39 cao
Answer: 13x + 39
Question 17
(a) M1 41 + (4x+13) + 3x = 180 oe
(a) A1 x = 18 cao
(a) Answer: x = 18
(b) B1 54 (degrees), follow through 3 x their x
(b) Answer: 54 degrees
Question 18
M1 identifies 13 total parts (4 + 9)
M1 117 / 13 (= 9), the value of one part
A1 81 (conkers) cao
Answer: 81 conkers
Question 19
M1 finds 15% of 320 (e.g. 10% = 32 and 5% = 16, so 15% = 48)
M1 320 - 48 (subtracts the discount from the original price)
A1 272 pounds cao
Answer: 272 pounds
Question 20
(a) B1 198 m2 cao
(a) Answer: 198 m2
(b) B1 20 m2 cao
(b) Answer: 20 m2
(c) M1 198 - 20 (follow through their (a) and (b))
(c) A1 178 m2 cao
(c) Answer: 178 m2
Question 21
(a) M1 360 - (120 + 90 + 70)
(a) A1 80 (degrees) cao
(a) Answer: 80 degrees
(b) M1 (their (a) / 360) x 108
(b) A1 24 (students) cao
(b) Answer: 24 students
Question 22
(a) B1 x + (5x + 6) = 78 oe
(a) Answer: x + (5x + 6) = 78
(b) M1 6x + 6 = 78 leading to 6x = 72
(b) A1 x = 12 cao
(b) Answer: 12 years old
(c) B1 66 (follow through 5 x their x + 6)
(c) Answer: 66 years old
Question 23
(a) B1 3.30 pounds (330p) cao
(a) Answer: 3.30 pounds
(b) B1 3.40 pounds (340p) cao
(b) Answer: 3.40 pounds
(c) M1 3.30 + 3.40 (follow through their (a) and (b)), the total cost
(c) M1 10.00 - their total cost
(c) A1 3.30 pounds cao
(c) Answer: 3.30 pounds
Question 24
(a) B1 56 cm cao
(a) Answer: 56 cm
(b) M1 22/7 x 112 (or 2 x 22/7 x 56)
(b) A1 352 cm cao
(b) Answer: 352 cm
(c) M1 112 + 2 x 9 (adds the overhang to both sides of the diameter)
(c) A1 130 cm cao
(c) Answer: 130 cm
Question 25
(a) M1 720 / 12 (= 60), the value of one part (12 total parts)