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 third Core (Level 2) paper covers the same breadth as Papers 1 and 2: number, fractions/decimals/percentages, ratio, algebra, geometry, measures, coordinates, statistics and probability, with entirely different questions.
1
Write the number four hundred and seven thousand and sixteen in figures. (1 mark)
(Total for Question 1 is 1 mark)
2
Work out 7004 - 4867 (1 mark)
(Total for Question 2 is 1 mark)
3
Find 5/6 of 132 (1 mark)
(Total for Question 3 is 1 mark)
4
Two angles lie on a straight line. One angle is 127 degrees and the other is z degrees. Work out the size of angle z (1 mark)
(Total for Question 4 is 1 mark)
5
Simplify 9m + 2n - 4m + 5n (1 mark)
(Total for Question 5 is 1 mark)
6
At a ski resort in the Alps, the temperature at dawn was -7 degrees C. By midday it had risen by 19 degrees C. Work out the temperature at midday. (2 marks)
(Total for Question 6 is 2 marks)
7
Convert 11/20 to a percentage. (2 marks)
(Total for Question 7 is 2 marks)
8
Simplify the ratio 63:81 fully. (2 marks)
(Total for Question 8 is 2 marks)
9
Solve 6x - 11 = 37 (2 marks)
(Total for Question 9 is 2 marks)
10
A cuboid-shaped storage box has length 8 cm, width 5 cm and height 3 cm. Work out its volume. (2 marks)
(Total for Question 10 is 2 marks)
11
Aisha is making a fruit punch and needs 750 ml of orange juice. She has two cartons of orange juice, each containing 320 ml. Show working to decide whether she has enough orange juice, and if not, say how much more she needs. (2 marks)
(Total for Question 11 is 2 marks)
12
Point E has coordinates (4, 11) and point F has coordinates (12, 3). Find the coordinates of the midpoint of EF. (2 marks)
(Total for Question 12 is 2 marks)
13
In a fundraising bake sale, six form groups raised the following amounts of money in pounds: 42, 55, 38, 61, 47, 45. Work out the mean amount raised. (2 marks)
(Total for Question 13 is 2 marks)
14
A jar contains 7 blue sweets, 5 yellow sweets and 8 green sweets. Noah takes one sweet from the jar at random.
(a)Find the probability that it is yellow. (1 mark)(1)
(b)Find the probability that it is NOT green. (1 mark)(1)
(Total for Question 14 is 2 marks)
15
Write down all the factors of 66 that are also prime numbers. (2 marks)
In triangle DEF, angle D = 45 degrees, angle E = (4x + 9) degrees and angle F = 2x degrees.
(a)Form an equation in x and solve it. (2 marks)(2)
(b)Work out the size of angle F. (1 mark)(1)
(Total for Question 17 is 3 marks)
18
Grace and Idris share 108 stickers in the ratio 5:7. Work out how many stickers Idris receives. (3 marks)
(Total for Question 18 is 3 marks)
19
A bicycle costs 350 pounds. In a sale, the price is reduced by 12%. Work out the sale price. (3 marks)
(Total for Question 19 is 3 marks)
20
Mrs Patel's garden in Norwich is a rectangle measuring 15 m by 9 m. A rectangular pond measuring 4 m by 4 m has been dug in one corner of the garden (the pond is not lawn).
(a)Work out the area of the whole rectangular garden. (1 mark)(1)
(b)Work out the area of the pond. (1 mark)(1)
(c)Work out the area of the garden that is lawn (not pond). (2 marks)(2)
(Total for Question 20 is 4 marks)
21
A pie chart was used to show how 90 students travel to a summer fair. It shows that they go by Walking (angle 110 degrees), by Bus (angle 95 degrees), and by Cycling (angle 75 degrees). The rest go by Car.
(a)Work out the angle for the Car sector of the pie chart. (2 marks)(2)
(b)Work out how many of the 90 students go by Car. (2 marks)(2)
(Total for Question 21 is 4 marks)
22
Femi is x years old. His aunt Adaeze is 7 years older than four times Femi's age. The sum of their ages is 57.
(a)Write down an equation in x to represent this information. (1 mark)(1)
(b)Solve your equation to find Femi's age. (2 marks)(2)
(c)Find Adaeze's age. (1 mark)(1)
(Total for Question 22 is 4 marks)
23
A stationery shop sells notebooks for 65p each and rulers for 40p each. Simone buys 7 notebooks and 5 rulers, and pays with a 10 pound note.
(a)Work out the total cost of the notebooks. (1 mark)(1)
(b)Work out the total cost of the rulers. (1 mark)(1)
(c)Work out how much change Simone should receive from her 10 pound note. (3 marks)(3)
(Total for Question 23 is 5 marks)
24
A circular fountain base in a park in Bath has a diameter of 98 cm. Take π = 22/7.
(a)Work out the radius of the fountain base. (1 mark)(1)
(b)Work out the circumference of the fountain base. (2 marks)(2)
(c)A low rail needs to sit 15 cm out from the edge of the fountain base all the way round. Work out the diameter of the circle that the rail forms. (2 marks)(2)
(Total for Question 24 is 5 marks)
25
At a summer concert, a profit of 540 pounds is shared between the music department and the drama department in the ratio 4:5.
(a)Work out how much money the music department receives. (2 marks)(2)
(b)The music department then spends 30% of its share on new sheet music. Work out how much money is spent on sheet music. (2 marks)(2)
(c)Work out how much money the music department has left after this spending. (2 marks)(2)
(Total for Question 25 is 6 marks)
Mark scheme · CE.M25 Maths: Full Practice Paper (Core, Non-Calculator, Set 3)
Question 1
B1 407016 cao
Answer: 407016
Question 2
B1 2137 cao
Answer: 2137
Question 3
B1 110 cao
Answer: 110
Question 4
B1 53 (degrees) cao
Answer: 53 degrees
Question 5
B1 5m + 7n cao
Answer: 5m + 7n
Question 6
M1 -7 + 19 (correct method)
A1 12 (degrees C) cao
Answer: 12 degrees C
Question 7
M1 11/20 = 55/100 or equivalent complete method
A1 55% cao
Answer: 55%
Question 8
M1 divides both parts by a common factor (e.g. by 3 or by 9)
A1 7:9 cao (fully simplified)
Answer: 7:9
Question 9
M1 6x = 48 (adds 11 to both sides)
A1 x = 8 cao
Answer: x = 8
Question 10
M1 8 x 5 x 3 or equivalent complete method
A1 120 cm3 cao
Answer: 120 cm3
Question 11
M1 2 x 320 = 640 ml
A1 No, she does not have enough; she is 110 ml short
Answer: No, she is 110 ml short of the orange juice she needs
Question 12
M1 ((4+12)/2 , (11+3)/2) or equivalent complete method
A1 (8, 7) cao
Answer: (8, 7)
Question 13
M1 42+55+38+61+47+45 (= 288)
A1 48 (pounds) cao
Answer: 48 pounds
Question 14
(a) B1 1/4 oe cao
(a) Answer: 1/4
(b) B1 3/5 oe cao
(b) Answer: 3/5
Question 15
M1 a correct list, or attempt at a list, of the factors of 66
A1 2, 3, 11 (all three, no extras) cao
Answer: 2, 3, 11
Question 16
M1 10x + 15 (correct first expansion)
M1 -4x + 8 (correct second expansion, signs handled correctly)
A1 6x + 23 cao
Answer: 6x + 23
Question 17
(a) M1 45 + (4x+9) + 2x = 180 oe
(a) A1 x = 21 cao
(a) Answer: x = 21
(b) B1 42 (degrees), follow through 2 x their x
(b) Answer: 42 degrees
Question 18
M1 identifies 12 total parts (5 + 7)
M1 108 / 12 (= 9), the value of one part
A1 63 (stickers) cao
Answer: 63 stickers
Question 19
M1 finds 12% of 350 (e.g. 10% = 35 and 2% = 7, so 12% = 42)
M1 350 - 42 (subtracts the discount from the original price)
A1 308 pounds cao
Answer: 308 pounds
Question 20
(a) B1 135 m2 cao
(a) Answer: 135 m2
(b) B1 16 m2 cao
(b) Answer: 16 m2
(c) M1 135 - 16 (follow through their (a) and (b))
(c) A1 119 m2 cao
(c) Answer: 119 m2
Question 21
(a) M1 360 - (110 + 95 + 75)
(a) A1 80 (degrees) cao
(a) Answer: 80 degrees
(b) M1 (their (a) / 360) x 90
(b) A1 20 (students) cao
(b) Answer: 20 students
Question 22
(a) B1 x + (4x + 7) = 57 oe
(a) Answer: x + (4x + 7) = 57
(b) M1 5x + 7 = 57 leading to 5x = 50
(b) A1 x = 10 cao
(b) Answer: 10 years old
(c) B1 47 (follow through 4 x their x + 7)
(c) Answer: 47 years old
Question 23
(a) B1 4.55 pounds (455p) cao
(a) Answer: 4.55 pounds
(b) B1 2.00 pounds (200p) cao
(b) Answer: 2.00 pounds
(c) M1 4.55 + 2.00 (follow through their (a) and (b)), the total cost
(c) M1 10.00 - their total cost
(c) A1 3.45 pounds cao
(c) Answer: 3.45 pounds
Question 24
(a) B1 49 cm cao
(a) Answer: 49 cm
(b) M1 22/7 x 98 (or 2 x 22/7 x 49)
(b) A1 308 cm cao
(b) Answer: 308 cm
(c) M1 98 + 2 x 15 (adds the overhang to both sides of the diameter)
(c) A1 128 cm cao
(c) Answer: 128 cm
Question 25
(a) M1 540 / 9 (= 60), the value of one part (9 total parts)