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Writing an Expression - Worksheets, Questions and Revision

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2.7 Writing an Expression

EDEXCEL 1MA1 · Calculator allowed · about 50 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.

Revision notes: Writing an Expression

Writing an expression means translating a worded description into algebra, using a letter to stand for an unknown number. Key words point to the operation needed: 'sum'/'more than' means add, 'difference'/'less than' means subtract, 'product'/'times' means multiply, and 'quotient'/'shared' means divide.

  1. Choose a letter for the unknown quantity if one is not already given, and write down clearly what it represents.
  2. Translate each part of the sentence into algebra one piece at a time, using the key words to decide the operation.
  3. Be careful with order for subtraction and division: '5 less than x' is x - 5, not 5 - x.
  4. Combine the pieces into a single expression, and simplify by collecting like terms if possible.
Worked example. Sam thinks of a number, n. He doubles it, then adds 7. Write an expression for the result. Then write an expression for 'the cost of 3 adult tickets at a pounds each and 2 child tickets at c pounds each'.
  1. 'Doubles it' means multiply n by 2, giving 2n. 'Then adds 7' means add 7: 2n + 7.
  2. For the tickets: 3 adult tickets at a pounds each cost 3a. 2 child tickets at c pounds each cost 2c.
  3. Total cost = 3a + 2c.
Answer: 2n + 7; total ticket cost = 3a + 2c.
1
Write down an expression for each of the following.
(a)4 more than x(1)
(b)y multiplied by 6(1)
(Total for Question 1 is 2 marks)
2
Write down an expression for 6 less than y.
(Total for Question 2 is 1 mark)
3
There are p pencils in each pack.
(a)Write an expression, in terms of p, for the total number of pencils in 4 packs.(1)
(b)Suri buys 4 packs of pencils and is then given 3 more loose pencils. Write an expression, in terms of p, for the total number of pencils Suri now has.(1)
(Total for Question 3 is 2 marks)
4
A function machine takes a number n. It multiplies n by 3, then adds 2, to give the output.
n × 3 + 2 output
(a)Write an expression, in terms of n, for the output of the function machine.(1)
(b)Work out the output when n = 5.(1)
(Total for Question 4 is 2 marks)
5
A function machine takes a number m. It divides m by 2, then adds 7, to give the output.
m ÷ 2 + 7 output
(a)Write an expression, in terms of m, for the output of the function machine.(1)
(b)Work out the output when m = 10.(1)
(Total for Question 5 is 2 marks)
6
Apples cost 45p each.
(a)Write an expression, in terms of n, for the cost, in pence, of n apples.(1)
(b)Write an expression, in terms of n, for the cost, in pounds, of n apples.(1)
(Total for Question 6 is 2 marks)
7
The diagram shows a rectangle with length x cm and width y cm.
Diagram NOT accurately drawn
x cm x cm y cm y cm
(a)Write an expression, in terms of x and y, for the perimeter of the rectangle.(1)
(b)Simplify your expression.(1)
(Total for Question 7 is 2 marks)
8
Priya is p years old.
(a)Write an expression, in terms of p, for Priya's age in 6 years' time.(1)
(b)Priya's sister is 3 years younger than Priya. Write an expression, in terms of p, for her sister's age now.(1)
(Total for Question 8 is 2 marks)
9
Write down an expression for each of the following.
(a)t is multiplied by 4, then 5 is subtracted from the result.(1)
(b)w is divided by 3, then 2 is added to the result.(1)
(Total for Question 9 is 2 marks)
10
A farm has c chickens and w cows. Each chicken has 2 legs and each cow has 4 legs. Write an expression, in terms of c and w, for the total number of legs on the farm.
(Total for Question 10 is 2 marks)
11
The diagram shows a triangle with sides x cm, (x + 2) cm and 2x cm.
Diagram NOT accurately drawn
2x cm x cm (x + 2) cm Not to scale
(a)Write an expression, in terms of x, for the perimeter of the triangle.(1)
(b)Simplify your expression.(1)
(Total for Question 11 is 2 marks)
12
n sweets are shared equally between 5 friends.
(a)Write an expression, in terms of n, for the number of sweets each friend receives.(1)
(b)Instead, each of 5 friends is given t sweets. Write an expression, in terms of t, for the total number of sweets given out.(1)
(Total for Question 12 is 2 marks)
13
Ben has b marbles. Amy has 4 more marbles than Ben.
(a)Write an expression, in terms of b, for the number of marbles Amy has.(1)
(b)Write an expression, in terms of b, for the total number of marbles Ben and Amy have together. Give your answer in its simplest form.(2)
(Total for Question 13 is 3 marks)
14
At a cinema, an adult ticket costs £6 and a child ticket costs £4. A group buys a adult tickets and c child tickets. Write an expression, in terms of a and c, for the total cost, in pounds, of the tickets.
(Total for Question 14 is 2 marks)
15
A number is x. The sum of x and 5 is multiplied by 3. Write an expression, in terms of x, for the result.
(Total for Question 15 is 2 marks)
16
Kwame makes patterns from matchsticks. Pattern 1 is 1 square made from 4 matchsticks. Pattern 2 is 2 squares in a row made from 7 matchsticks. Pattern 3 is 3 squares in a row made from 10 matchsticks, because each new square after the first only needs 3 extra matchsticks (one matchstick is shared with the square before it).
Pattern 1 4 matchsticks Pattern 2 7 matchsticks Pattern 3 10 matchsticks Diagrams not drawn accurately
(a)Work out the number of matchsticks needed for Pattern 4.(1)
(b)Write an expression, in terms of n, for the number of matchsticks needed for Pattern n.(2)
(Total for Question 16 is 3 marks)
17
A number is x.
(a)Write an expression, in terms of x, for 'x multiplied by 5, then decreased by 3'.(1)
(b)Work out the value of your expression when x = 4.(1)
(Total for Question 17 is 2 marks)
18
Jamal thinks of a number, x. He multiplies it by 3, then adds 6. He then doubles the whole result. Write an expression, in terms of x, for Jamal's final answer. Give your answer in its simplest form.
(Total for Question 18 is 2 marks)
19
Which expression correctly represents '5 subtracted from twice a number, x'?
  • A) 2x - 5
  • B) 5 - 2x
  • C) 2(x - 5)
  • D) x - 10
(Total for Question 19 is 1 mark)
20
A piggy bank contains n 20p coins and m 50p coins. Write an expression, in pence, for the total value of the coins in the piggy bank.
(Total for Question 20 is 2 marks)
21
Write an expression, in terms of w, for the total number of days in w whole weeks and 3 extra days.
(Total for Question 21 is 2 marks)
Mark scheme · 2.7 Writing an Expression

Question 1

Question 2

Question 3

Question 4

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Question 6

Question 7

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Question 11

Question 12

Question 13

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Question 15

Question 16

Question 17

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Question 20

Question 21

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