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11+ · CSSE

EP.T57 CSSE-Style Maths Mock 6 (Essex)

CSSE EP.T57 · Calculators not allowed · about 60 minutes

Total Marks

Name: _______________________________ Date: ____ / ____ / ______

CSSE-style Mathematics Mock 6 - 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 89 marks in total. This is a different set of questions from Mock 1 (EP.T4), Mock 2 (EP.T15), Mock 3 (EP.T19), Mock 4 (EP.T29) and Mock 5 (EP.T43). The questions get harder as the paper goes on - the final five are genuine problem-solving puzzles designed to stretch even strong candidates, so keep an eye on the clock and do not spend too long on any one question.

SECTION A: MATHEMATICS (60 minutes - this paper has one section). This is a different set of questions from Mock 1 (EP.T4), Mock 2 (EP.T15), Mock 3 (EP.T19), Mock 4 (EP.T29) and Mock 5 (EP.T43). Work out (8 + 5) x 4 - 9, using the correct order of operations.

(Total for Question 1 is 1 mark)

Write the number six thousand two hundred and four in figures.

(Total for Question 2 is 1 mark)

Round 8456 to the nearest hundred.

(Total for Question 3 is 1 mark)

Work out 6000 - 3748.

(Total for Question 4 is 2 marks)

Work out 74 x 6.

(Total for Question 5 is 2 marks)

Work out 312 / 8.

(Total for Question 6 is 2 marks)

Find 5/9 of 108.

(Total for Question 7 is 2 marks)

Work out 7.4 x 5.

(Total for Question 8 is 2 marks)

The temperature in Maldon at 6 a.m. one winter morning was -6 degrees C. By 1 p.m. it had risen by 14 degrees C. Work out the temperature at 1 p.m.

(Total for Question 9 is 2 marks)

A bicycle in a Chelmsford shop costs £240 before a price increase of 12%.

(a)Work out 12% of £240.(2)

(b)Work out the new price of the bicycle after the increase.(1)

(Total for Question 10 is 3 marks)

Daniel has 96 marbles and 72 balloons. He wants to put them into identical bags so that each bag has the same number of marbles and the same number of balloons, with none left over. Work out the greatest number of bags he can make.

(Total for Question 11 is 3 marks)

Leah and Kwame share 96 stickers in the ratio 5 : 3. After sharing, Kwame gives 6 of his stickers to Leah. How many stickers does Leah have now?

(Total for Question 12 is 3 marks)

Work out √196 + 3^3.

(Total for Question 13 is 2 marks)

Solve the equation 7x - 9 = 40 to find the value of x.

(Total for Question 14 is 3 marks)

In a quadrilateral, three of the angles are 96 degrees, 77 degrees and 84 degrees.

(a)Work out the size of the fourth angle.(2)

(b)Could this quadrilateral be a square? Give a reason for your answer.(1)

(Total for Question 15 is 3 marks)

A patio can be thought of as a rectangle measuring 12 m by 8 m with a rectangular section measuring 5 m by 3 m removed.

(a)Work out the area of the patio.(3)

(b)Paving slabs cost £4.50 per square metre. Work out the total cost of paving the patio.(1)

(Total for Question 16 is 4 marks)

A toy chest is a cuboid measuring 90 cm by 40 cm by 50 cm. Work out the volume of the toy chest.

(Total for Question 17 is 3 marks)

A train timetable at Wivenhoe shows a service departs at 10:37 and the journey takes 1 hour 36 minutes.

(a)At what time does the train arrive?(1)

(b)The return service departs 38 minutes after the train arrives, and takes the same journey time. At what time does the return service arrive back?(2)

(Total for Question 18 is 3 marks)

Amara buys 3 notebooks at 65p each and a pencil case for £2.15 from a shop in Billericay. She pays with a £5 note. How much change does she get?

(Total for Question 19 is 2 marks)

A pattern is made from matchsticks arranged in a row of joined triangles. Pattern 1 uses 3 matchsticks (1 triangle), Pattern 2 uses 5 matchsticks (2 triangles), and Pattern 3 uses 7 matchsticks (3 triangles).

(a)How many matchsticks are needed for Pattern 8?(1)

(b)Find an expression, in terms of n, for the number of matchsticks in Pattern n.(2)

(Total for Question 20 is 3 marks)

The number of runs scored by a cricket team's top batter in 9 innings were: 12, 45, 12, 30, 8, 12, 51, 19, 25.

(a)Find the mode of the number of runs scored.(1)

(b)Find the median of the number of runs scored.(1)

(c)Find the range of the number of runs scored.(1)

(Total for Question 21 is 3 marks)

A bag contains 6 yellow counters, 4 white counters and 10 purple counters. A counter is picked at random from the bag.

(a)Work out the probability that the counter is white. Give your answer as a fraction in its simplest form.(2)

(b)Work out the probability that the counter is NOT purple.(1)

(Total for Question 22 is 3 marks)

A cyclist travels from Witham to Hatfield Peverel, a distance of 10 km, at an average speed of 15 km/h.

(a)Work out how long the journey takes. Give your answer in hours and minutes.(2)

(b)He sets off at 08:47. At what time does he arrive in Hatfield Peverel?(2)

(Total for Question 23 is 4 marks)

Buses to Basildon leave a station every 18 minutes, and buses to Southend leave the same station every 30 minutes. Both a Basildon bus and a Southend bus leave together at 07:20.

(a)Work out how many minutes later the two buses next leave together again.(3)

(b)At what clock time do the two buses next leave together?(1)

(Total for Question 24 is 4 marks)

A television in a Colchester electronics store was priced at £650. In March the price was reduced by 20%. In April the new price was reduced by a further 15%.

(a)Work out the price after the March reduction.(2)

(b)Work out the price after the April reduction.(2)

(Total for Question 25 is 4 marks)

A three-digit number has a digit sum of 16. Its hundreds digit and its units digit are equal. Its tens digit is 4 more than its units digit. Find the three-digit number, showing your reasoning clearly.

(Total for Question 26 is 4 marks)

At a school fete near Rochford, 4 packets of biscuits and 3 boxes of muffins cost £12.00 in total. 2 packets of biscuits and 5 boxes of muffins cost £13.00 in total. All packets of biscuits cost the same as each other, and all boxes of muffins cost the same as each other. Find the cost of one packet of biscuits and the cost of one box of muffins.

(Total for Question 27 is 5 marks)

Two walkers, one from Great Dunmow and one from Takeley, start at the same time and walk towards each other along the same 40 km route. The Great Dunmow walker walks at a constant 8 km/h and the Takeley walker walks at a constant 12 km/h.

(a)Work out how long it takes for the two walkers to meet. Give your answer in minutes.(3)

(b)Work out the distance from Great Dunmow at which the two walkers meet.(2)

(Total for Question 28 is 5 marks)

A delivery van travels from a depot in Epping to a warehouse in Harlow, a distance of 15 km, at an average speed of 20 km/h. It then returns from Harlow to Epping along the same road at an average speed of 12 km/h.

(a)Work out the total time taken for the whole journey. Give your answer in hours.(3)

(b)Work out the average speed for the whole journey (there and back), in km/h.(2)

(Total for Question 29 is 5 marks)

Six friends - Aisha, Nathan, Freya, Oliwia, Ellis and Reuben - each collected a different number of conkers: 4, 8, 12, 16, 20 and 24, in some order. Freya collected exactly four times as many conkers as Nathan. Oliwia collected 8 more conkers than Ellis. Reuben collected fewer conkers than Aisha. Work out how many conkers each friend collected, showing your reasoning clearly.

(Total for Question 30 is 5 marks)

Mark scheme · EP.T57 CSSE-Style Maths Mock 6 (Essex)

Question 1

B1 43 cao
Answer: 43

Question 2

B1 6204 cao
Answer: 6204

Question 3

B1 8500 cao
Answer: 8500

Question 4

M1 Correct method shown, e.g. borrowing across the columns
A1 2252 cao
Answer: 2252

Question 5

M1 70 x 6 = 420 and 4 x 6 = 24 (or an equivalent method)
A1 444 cao
Answer: 444

Question 6

M1 Correct division method shown, e.g. 8 x 30 = 240, then 312 - 240 = 72
A1 39 cao
Answer: 39

Question 7

M1 108 / 9 = 12
A1 60 cao
Answer: 60

Question 8

M1 7 x 5 = 35 and 0.4 x 5 = 2 (or an equivalent method)
A1 37 cao
Answer: 37

Question 9

M1 Correct method shown, e.g. -6 + 14
A1 8 degrees C cao
Answer: 8 degrees C

Question 10

(a) M1 Finds 10% of £240 = £24 and 2% of £240 = £4.80 (or another valid method)
(a) A1 £28.80 cao
(a) Answer: £28.80
(b) B1 £268.80 ft (£240 plus the candidate's answer to part a)
(b) Answer: £268.80

Question 11

M1 Prime factorises 96, e.g. 96 = 2⁵ x 3
M1 Prime factorises 72, e.g. 72 = 2³ x 3²
A1 24 cao
Answer: 24 bags

Question 12

M1 5 + 3 = 8 parts, 96 / 8 = 12 per part
M1 Leah = 5 x 12 = 60, Kwame = 3 x 12 = 36
A1 66 cao
Answer: 66 stickers

Question 13

M1 √196 = 14 and 3³ = 27
A1 41 cao
Answer: 41

Question 14

M1 Adds 9 to both sides: 7x = 49
M1 Divides both sides by 7
A1 x = 7 cao
Answer: x = 7

Question 15

(a) M1 360 - 96 - 77 - 84
(a) A1 103 degrees cao
(a) Answer: 103 degrees
(b) B1 No, because a square has four angles of 90 degrees each, and none of 96, 77, 84 or 103 is 90 degrees
(b) Answer: No; a square needs four 90 degree angles, but none of these four angles is 90 degrees

Question 16

(a) M1 Area of full rectangle = 12 x 8 = 96 m²
(a) M1 Area removed = 5 x 3 = 15 m²
(a) A1 81 m² cao
(a) Answer: 81 m²
(b) B1 £364.50 ft (the candidate's part a area multiplied by £4.50)
(b) Answer: £364.50

Question 17

M1 90 x 40 = 3600
M1 Multiplies by the third dimension: 3600 x 50
A1 180000 cm³ cao
Answer: 180000 cm³

Question 18

(a) B1 12:13 cao
(a) Answer: 12:13
(b) M1 Return departure = 12:13 + 38 minutes = 12:51
(b) A1 14:27 cao
(b) Answer: 14:27

Question 19

M1 Total cost = (3 x 65p) + £2.15 = £1.95 + £2.15 = £4.10
A1 £0.90 cao
Answer: £0.90

Question 20

(a) B1 17 cao
(a) Answer: 17
(b) M1 Uses the common difference of 2 to start the expression 2n
(b) A1 2n + 1 oe
(b) Answer: 2n + 1

Question 21

(a) B1 12 cao
(a) Answer: 12
(b) B1 19 cao
(b) Answer: 19
(c) B1 43 cao
(c) Answer: 43

Question 22

(a) M1 Total number of counters = 6 + 4 + 10 = 20
(a) A1 1/5 oe
(a) Answer: 1/5
(b) B1 1/2 ft oe
(b) Answer: 1/2

Question 23

(a) M1 Time = 10 / 15 = 2/3 hours
(a) A1 40 minutes cao
(a) Answer: 40 minutes
(b) M1 Adds 40 minutes to 08:47
(b) A1 09:27 ft cao
(b) Answer: 09:27

Question 24

(a) M1 Prime factorises 18, e.g. 18 = 2 x 3²
(a) M1 Prime factorises 30, e.g. 30 = 2 x 3 x 5
(a) A1 90 minutes cao
(a) Answer: 90 minutes
(b) B1 08:50 ft (07:20 plus the candidate's part a answer)
(b) Answer: 08:50

Question 25

(a) M1 20% of £650 = £130
(a) A1 £520 cao
(a) Answer: £520
(b) M1 10% of the candidate's part a price = £52 and 5% = £26 (or an equivalent method)
(b) A1 £442 ft cao
(b) Answer: £442

Question 26

M1 Lets the units digit be u, so the hundreds digit is also u and the tens digit is u + 4
M1 Forms the equation u + (u + 4) + u = 16
dM1 Solves to give 3u + 4 = 16 and u = 4; dependent on the previous method mark
A1 484 cao
Answer: 484

Question 27

M1 Forms two equations in pence, e.g. 4b + 3m = 1200 and 2b + 5m = 1300, where b is the cost of a packet of biscuits and m is the cost of a box of muffins
M1 Scales one equation so a variable can be eliminated, e.g. doubles the second equation to give 4b + 10m = 2600
dM1 Subtracts to eliminate b: (4b + 10m) - (4b + 3m) = 2600 - 1200, giving m = 200; dependent on the previous method mark
A1 Muffins = £2.00 cao
A1 Biscuits = £1.50 ft (substituted back into either original equation)
Answer: Biscuits = £1.50, muffins = £2.00

Question 28

(a) M1 Combined speed = 8 + 12 = 20 km/h
(a) M1 Time = 40 / 20 hours
(a) A1 120 minutes cao
(a) Answer: 120 minutes
(b) M1 Distance = candidate's time (in hours) x 8, e.g. 2 x 8
(b) A1 16 km ft cao
(b) Answer: 16 km

Question 29

(a) M1 Outward time = 15 / 20 = 0.75 hours
(a) M1 Return time = 15 / 12 = 1.25 hours
(a) A1 2 hours cao
(a) Answer: 2 hours
(b) M1 Total distance = 15 + 15 = 30 km, then uses total distance / total time
(b) A1 15 km/h ft cao
(b) Answer: 15 km/h

Question 30

M1 Tests pairs of values in the list for the quadruple relationship, finding that only 4 and 16 satisfy Freya = 4 x Nathan
M1 Assigns Nathan = 4 and Freya = 16
M1 Tests the remaining values 8, 12, 20, 24 for a difference of 8, finding that only 12 and 20 work
A1 Ellis = 12 and Oliwia = 20 cao
B1 Reuben = 8 and Aisha = 24 (the two values left, with Reuben smaller than Aisha)
Answer: Nathan = 4, Freya = 16, Ellis = 12, Oliwia = 20, Reuben = 8, Aisha = 24

CSSE-Style Maths Mock 6 (Essex) - Worksheets, Questions and Revision