CSSE-style Mathematics Mock 2 - Essex 11+. SECTION A: MATHEMATICS (60 minutes - this is the only section in the paper). Write your answers, with full working, in the space provided; method marks (M1) are awarded for correct working even where the final answer is wrong. Calculators are NOT allowed. You have 60 minutes to attempt all 30 questions, worth 84 marks in total. This is a different set of questions from Mock 1 (EP.T4). The questions get harder as the paper goes on - the final five are designed to stretch even strong candidates, so keep an eye on the clock and do not spend too long on any one question.
1
SECTION A: MATHEMATICS (60 minutes - this paper has one section). This is a different set of questions from Mock 1. Work out 5462 + 3768.
(Total for Question 1 is 1 mark)
2
Write the number six thousand and forty-eight in figures.
(Total for Question 2 is 1 mark)
3
Round 3482 to the nearest hundred.
(Total for Question 3 is 1 mark)
4
Work out 900 - 468.
(Total for Question 4 is 2 marks)
5
Work out 34 x 6.
(Total for Question 5 is 2 marks)
6
Work out 138 / 6.
(Total for Question 6 is 2 marks)
7
Work out 3/8 + 1/4. Give your answer as a fraction in its simplest form.
(Total for Question 7 is 2 marks)
8
A piece of wood is 7.2 m long. Aiden cuts off a piece measuring 3.65 m. How much wood is left?
(Total for Question 8 is 2 marks)
9
A jug at a Chelmsford school fete contains 1.35 litres of squash. A second jug contains 2.6 litres of squash. Work out the total amount of squash in both jugs.
(Total for Question 9 is 2 marks)
10
A coat in a Colchester shop costs £260. In a sale it is reduced by 15%.
(a)Work out 15% of £260.(2)
(b)Work out the sale price of the coat.(1)
(Total for Question 10 is 3 marks)
11
Simplify the ratio 18 : 24 fully.
(Total for Question 11 is 2 marks)
12
Amelia and Noah share £84 in the ratio 3 : 4. Work out how much each person receives.
(Total for Question 12 is 3 marks)
13
Work out 72 - 42.
(Total for Question 13 is 2 marks)
14
Solve the equation 3x + 7 = 25 to find the value of x.
(Total for Question 14 is 3 marks)
15
In a triangle, two of the angles are 52 degrees and 68 degrees. Work out the size of the third angle, and state whether the triangle is acute-angled, right-angled or obtuse-angled.
(Total for Question 15 is 3 marks)
16
A rectangle has length 12 cm and width 7 cm. Work out its perimeter.
(Total for Question 16 is 2 marks)
17
A rectangular lawn in Brentwood measures 9 m by 5 m. A square flower bed of side 3 m is dug out of the lawn.
(a)Work out the area of the lawn before the flower bed is dug out.(1)
(b)Work out the area of grass that remains after the flower bed has been dug out.(2)
(Total for Question 17 is 3 marks)
18
A train leaves Colchester at 09:47 and arrives in London at 10:32.
(a)How long, in minutes, does the journey take?(2)
(b)If the same train is delayed by 18 minutes, at what time does it now arrive?(1)
(Total for Question 18 is 3 marks)
19
Priya buys 3 notebooks at £1.35 each from a stationers in Billericay, and a pen for 89p. Work out the total cost.
(Total for Question 19 is 2 marks)
20
Here are the first four terms of a sequence: 4, 9, 14, 19, ...
(a)Write down the next two terms of the sequence.(1)
(b)Find an expression, in terms of n, for the nth term of the sequence.(2)
(Total for Question 20 is 3 marks)
21
Find all the prime factors of 84.
(Total for Question 21 is 3 marks)
22
A school minibus can carry 16 passengers. A school trip to Colchester Zoo needs to transport 138 pupils and 9 adults. Work out the least number of minibuses needed to transport everyone.
(Total for Question 22 is 4 marks)
23
Three angles lie on a straight line. One of the angles is 90 degrees. Of the other two angles, the larger is twice the size of the smaller. Work out the sizes of the two unknown angles.
(Total for Question 23 is 3 marks)
24
Ahmed opens a savings account in Maldon with £450. The account pays simple interest of 4% per year. Work out the total amount in the account after 3 years, assuming no further deposits or withdrawals are made.
(Total for Question 24 is 4 marks)
25
A football team's goals scored in 5 matches were: 2, 0, 3, 1, 4. Find the mean number of goals scored per match.
(Total for Question 25 is 3 marks)
26
Three friends, Freya, Oliver and Zara, have 45 marbles between them. Oliver has twice as many marbles as Freya. Zara has 5 more marbles than Oliver. How many marbles does each friend have?
(Total for Question 26 is 4 marks)
27
A two-digit number has a digit sum of 11. When the digits are reversed, the new two-digit number is 45 more than the original number. Find the original number.
(Total for Question 27 is 4 marks)
28
Isla pays exactly £3.40 for a magazine using only 20p coins and 50p coins. She uses more 20p coins than 50p coins, and she uses the smallest possible total number of coins while doing this. How many 20p coins and how many 50p coins does she use?
(Total for Question 28 is 5 marks)
29
Look at an ordinary analogue clock face, with an hour hand and a minute hand moving at constant speeds.
(a)At exactly 4 o'clock, work out the size of the smaller angle between the hour hand and the minute hand.(2)
(b)At exactly 20 minutes past 4, work out the size of the smaller angle between the hour hand and the minute hand.(3)
(Total for Question 29 is 5 marks)
30
A number, x, is chosen so that when it is doubled and 9 is added, the result is the same as when 60 is subtracted from three times the number.
(a)Form an equation in x from this information and solve it to find the value of x.(3)
(b)Determine, with reasoning, whether x is a prime number.(2)
(Total for Question 30 is 5 marks)
Mark scheme · EP.T15 CSSE-Style Maths Mock 2 (Essex)
Question 1
B1 9230 cao
Answer: 9230
Question 2
B1 6048 cao
Answer: 6048
Question 3
B1 3500 cao
Answer: 3500
Question 4
M1 Correct method shown, e.g. borrowing across the columns
A1 432 cao
Answer: 432
Question 5
M1 30 x 6 = 180 and 4 x 6 = 24 (or an equivalent method)
A1 204 cao
Answer: 204
Question 6
M1 Correct division method shown, e.g. 6 x 20 = 120, then 138 - 120 = 18
A1 23 cao
Answer: 23
Question 7
M1 Converts 1/4 to 2/8 (or another equivalent common denominator)
A1 5/8 oe
Answer: 5/8
Question 8
M1 Correctly lines up the decimal points and subtracts, e.g. 7.20 - 3.65
A1 3.55 m cao
Answer: 3.55 m
Question 9
M1 Correctly lines up the decimal points and adds, e.g. 1.35 + 2.60
A1 3.95 litres cao
Answer: 3.95 litres
Question 10
(a) M1 Finds 10% of £260 = £26 (or another valid method)
(a) A1 £39 cao
(a) Answer: £39
(b) B1 £221 ft (£260 minus the candidate's answer to part a)
(b) Answer: £221
Question 11
M1 Divides both parts by a common factor, e.g. 18:24 = 9:12
A1 3 : 4 oe
Answer: 3 : 4
Question 12
M1 3 + 4 = 7 parts, £84 / 7 = £12 per part
M1 Amelia = 3 x £12, Noah = 4 x £12
A1 Amelia = £36 and Noah = £48 cao
Answer: Amelia = £36, Noah = £48
Question 13
M1 72 = 49 and 42 = 16
A1 33 cao
Answer: 33
Question 14
M1 Subtracts 7 from both sides: 3x = 18
M1 Divides both sides by 3
A1 x = 6 cao
Answer: x = 6
Question 15
M1 180 - 52 - 68
A1 60 degrees cao
B1 Acute-angled triangle, since 52, 68 and 60 degrees are all less than 90 degrees
Answer: 60 degrees; acute-angled triangle
Question 16
M1 2 x (12 + 7)
A1 38 cm cao
Answer: 38 cm
Question 17
(a) B1 45 m2 cao
(a) Answer: 45 m2
(b) M1 Area of flower bed = 32 = 9 m2
(b) A1 36 m2 ft (the candidate's part a answer minus 9 m2)
(b) Answer: 36 m2
Question 18
(a) M1 09:47 to 10:00 = 13 minutes, 10:00 to 10:32 = 32 minutes
(a) A1 45 minutes cao
(a) Answer: 45 minutes
(b) B1 10:50 ft (the original arrival time plus 18 minutes)
(b) Answer: 10:50
Question 19
M1 3 x £1.35 = £4.05
A1 £4.94 cao
Answer: £4.94
Question 20
(a) B1 24, 29 cao
(a) Answer: 24, 29
(b) M1 Uses the common difference of 5 to start the expression 5n
(b) A1 5n - 1 oe
(b) Answer: 5n - 1
Question 21
M1 Splits 84 into a factor pair, e.g. 84 = 2 x 42
M1 Continues to fully factorise, e.g. 84 = 2 x 2 x 3 x 7
A1 2, 3 and 7 cao
Answer: 2, 3 and 7
Question 22
M1 Total people = 138 + 9 = 147
M1 147 / 16 = 9.1875 (or awrt 9.19)
dM1 Recognises that 9 minibuses is not enough (9 x 16 = 144, leaving 3 people), so rounds up; dependent on the previous method mark
A1 10 cao
Answer: 10 minibuses
Question 23
M1 180 - 90 = 90 for the two unknown angles combined
M1 Sets up x + 2x = 90, using x for the smaller angle and 2x for the larger
A1 30 degrees and 60 degrees cso
Answer: 30 degrees and 60 degrees
Question 24
M1 One year's interest = 4% of £450 = £18
M1 Interest for 3 years = 3 x £18 = £54
M1 Adds the interest to the original £450
A1 £504 cao
Answer: £504
Question 25
M1 2 + 0 + 3 + 1 + 4 = 10
M1 Divides the total by the number of matches (5)
A1 2 goals cao
Answer: 2 goals
Question 26
M1 Lets Freya = x, so Oliver = 2x and Zara = 2x + 5
M1 Forms and solves x + 2x + (2x + 5) = 45 to give 5x = 40, x = 8
A1 Freya = 8 and Oliver = 16 cao
A1 Zara = 21 ft (5 more than the candidate's value for Oliver)
Answer: Freya = 8, Oliver = 16, Zara = 21
Question 27
M1 Lets the tens digit be t and the units digit be u, and forms t + u = 11
M1 Forms the reversal equation (10u + t) - (10t + u) = 45, which simplifies to u - t = 5 oe
M1 Solves the two equations simultaneously to find the digits, e.g. adding the equations to get 2u = 16
A1 38 cso
Answer: 38
Question 28
M1 Forms an equation linking the coins to the total, e.g. 20a + 50b = 340 (or 2a + 5b = 34), where a is the number of 20p coins and b is the number of 50p coins
M1 Finds at least two valid whole-number combinations satisfying the total and a > b, e.g. (a,b) = (17,0), (12,2) and (7,4)
dM1 Compares the total number of coins (a+b) for each valid combination found; dependent on the previous method mark
A1 7 twenty pence coins and 4 fifty pence coins cao
B1 States the total number of coins used is 11
Answer: 7 twenty pence coins and 4 fifty pence coins (11 coins in total)
Question 29
(a) M1 Hour hand is at 4 x 30 = 120 degrees from the 12, while the minute hand is at 0 degrees
(a) A1 120 degrees cao
(a) Answer: 120 degrees
(b) M1 Minute hand position = 20 x 6 = 120 degrees from the 12
(b) M1 Hour hand position = 120 + (20 x 0.5) = 130 degrees from the 12, since the hour hand moves 0.5 degrees per minute
(b) A1 10 degrees cao
(b) Answer: 10 degrees
Question 30
(a) M1 Forms the equation 2x + 9 = 3x - 60
(a) M1 Correctly rearranges to collect x terms and number terms, e.g. 9 + 60 = 3x - 2x
(a) A1 x = 69 cao
(a) Answer: x = 69
(b) M1 Uses a valid test of divisibility, e.g. the digit sum 6 + 9 = 15 is divisible by 3, or trial division 69 / 3 = 23
(b) A1 Correct conclusion: 69 is not prime, since 69 = 3 x 23 cao