CSSE Essex Style Problem Solving Paper 2 - Worksheets, Questions and Revision

8 original exam-style questions - 5 pages of questions with a full mark scheme - free printable PDF.

Download PDFJump to mark scheme (page 6)
« Previous: CSSE Essex Style Problem Solving Paper 1Next: Kent Test Style Maths Paper 1 »
Revision Library
revisionlibrary.co.uk
11+ · Mixed Problem Solving

EP.M153 CSSE Essex Style Problem Solving Paper 2

CSSE CSSE-MOCK-2 · Calculators not allowed · about 70 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
A gardener is planting a rectangular flower bed that is 4.8 metres long and 2.1 metres wide. She lays turf over the whole bed.
(a)Work out the area of the flower bed in square metres. Give your answer to 2 decimal places.(2)
(b)If turf is sold in rolls that each cover 0.75 m2, how many whole rolls must she buy?(1)
(Total for Question 1 is 3 marks)
2
A school choir sells tickets to a concert. Adult tickets cost £6.50 and child tickets cost £3.80. They sold 72 tickets in total and collected £357.30.
(a)Let A be the number of adult tickets and C the number of child tickets. Write two equations linking A and C.(1)
(b)Solve the equations to find how many adult tickets were sold.(3)
(Total for Question 2 is 4 marks)
3
A recipe for a fruit punch serves 8 people and uses 180 ml of orange juice, 120 ml of apple juice and 200 ml of water.
(a)Calculate the total volume of punch the recipe makes.(1)
(b)A party needs 1.8 litres of punch. How many times bigger than the recipe must the quantities be? Give your answer as a decimal to 1 decimal place.(2)
(c)Using the factor from part (b), calculate how much orange juice in litres is needed for the party. Give your answer to 2 decimal places.(1)
(Total for Question 3 is 4 marks)
4
The numbers 1, 2, 3, 5, 7 are written on five cards. Daniel shuffles the cards, then takes the first two cards to form a two-digit number where the first card is the tens digit and the second is the units digit.
(a)How many different two-digit numbers can he make?(1)
(b)What is the probability that the two-digit number Daniel makes is a prime number? Give your answer as a fraction in simplest form.(2)
(Total for Question 4 is 3 marks)
5
A local charity runs a cake stall. They sell cupcakes at £0.90 each and slices of cake at £1.50 each. On one day they sold a total of 134 items and raised £148.80.
(a)Let C be the number of cupcakes and S the number of cake slices. Write two equations linking C and S.(1)
(b)Solve the equations to find how many cupcakes and how many cake slices were sold.(7)
(Total for Question 5 is 8 marks)
6
A triangular field has sides of lengths 15 m, 20 m and 25 m.
(a)Show that the triangle is a right-angled triangle. State which angle is the right angle.(3)
(b)Calculate the area of the triangular field in square metres.(3)
(c)A second field is mathematically similar to this one, but larger, with an area of 242 m2. Calculate the scale factor of the enlargement, then use it to find the length of the longest side of the larger field. Give both answers to 2 decimal places.(4)
(Total for Question 6 is 10 marks)
7
A class of 25 pupils takes a test. The teacher records the following: 40% of the pupils scored at least 70 marks. Of those who scored at least 70, 60% scored at least 85 marks. The rest of the class scored below 70.
(a)How many pupils scored at least 70 marks?(2)
(b)How many pupils scored at least 85 marks?(3)
(c)The teacher wants to award a prize to one pupil chosen at random from those who scored at least 70. What is the probability that the prize goes to a pupil who scored at least 85? Give your answer as a fraction in simplest form.(3)
(d)One of the pupils who scored below 70 is picked at random to receive help. How many pupils are eligible for this help and what is the probability that a particular pupil chosen at random from the whole class is one of those eligible? Give the probability as a decimal to 3 decimal places.(4)
(Total for Question 7 is 12 marks)
8
Four friends share a taxi fare. The taxi driver charges a fixed booking fee of £2.40 plus 85 pence per mile. They travel together for 18 miles. They decide to split the fare in the ratio 2:1:1:? where the fourth friend pays the remainder so that the shares are whole numbers of pence. Work through the steps below.
(a)Calculate the total taxi fare in pounds and pence.(3)
(b)Express the total fare in pence and show how to divide it into parts following ratio 2:1:1:x where x is chosen so that all shares are whole pence. Find a suitable integer x and explain your choice.(6)
(c)Using x = 2, calculate how many pence and how many pounds and pence each friend pays. Give answers for all four friends.(7)
(Total for Question 8 is 16 marks)
Mark scheme · EP.M153 CSSE Essex Style Problem Solving Paper 2

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8