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Introduction to Algebraic Notation - Worksheets, Questions and Revision

24 original exam-style questions - 6 pages of questions with a full mark scheme - free printable PDF.

Download PDFJump to mark scheme (page 7)Introduction to Algebraic Notation revision guide

This topic is chapter 1 of KS3 Maths: Algebra Practice Book 1.

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KS3 · Algebra

2.4 Introduction to Algebraic Notation

AQA KS3.M-A4 · Calculators not allowed · about 75 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Identify the coefficient and the constant term in each expression.
(a)In 9x + 6, state the coefficient of x and the constant term.(1)
(b)In -3p - 2, state the coefficient of p and the constant term.(1)
2
Stretch question. Compare two expressions and decide which is larger for given values. Give a reason for your answer.
(a)Which is greater when x = 5: 3x + 2 or 2x + 8? Show your working and give a reason.(4)
3
State the coefficient of the letter in each expression.
(a)Coefficient of x in 4x.(1)
(b)Coefficient of a in 10a + 3.(1)
(c)Coefficient of t in -2t + 7.(1)
4
Use algebraic notation to write each description. Pay attention to multiplication convention.
(a)The product of 4 and the number k.(2)
(b)Two lots of a number n.(2)
5
Identify the term type in each expression. Choose 'term' for each separate part separated by + or -.
(a)In 5x + 2, what are the terms?(2)
(b)In 3a - 4b + 7, list the three terms.(2)
6
Simplify each expression by collecting like terms. Show any simple arithmetic used.
(a)Simplify 4x + 2x + 3.(2)
(b)Simplify 8y - 3y - 2.(1)
7
Work out the value of each expression when the given letter has the value shown. Include negative values where indicated.
(a)If a = -2, find the value of 3a + 5.(1)
(b)If b = 4, find the value of 2b - 3.(1)
(c)If c = 0, find the value of 7c + 2.(1)
8
Write an algebraic expression for each situation, using standard compact notation where appropriate.
(a)The total cost for n identical pens each costing £7.(1)
(b)A number x increased by 12 gives the total weight in kilograms.(1)
(c)Twice a number t minus 5.(1)
9
Write down the expression for: a number y increased by 8.
(1)
10
Write an algebraic expression for: three lots of a number w.
(2)
11
In the expression 6a - 8, identify the two terms.
(2)
12
Work out the value of 3y - 4 when y = -2.
(2)
13
Simplify 5x + 3 + 2x - 7.
(3)
14
A plumber charges a call-out fee of £25 plus £15 for every hour worked. Write an expression for the total charge for h hours, then find the charge for a 3-hour job.
(3)
15
Compare the expressions 4x - 1 and 2x + 5 when x = 4. State which is greater and give a reason.
(3)
16
A number t is trebled, then 4 is added. The result is the same as adding 22 to t. Write an equation using this information, and find the value of t.
(4)
17
Stretch. Two expressions are 2x + 7 and 5x - 8. For what value of x are the two expressions equal? Substitute your answer back in to check, and state the common value.
(4)
18
Write down the expression for: five times a number m.
(1)
19
Write down the expression for: the product of 7 and a number k.
(1)
20
Write down the expression for: a number q divided by 6.
(1)
21
State the coefficient of x in 9x.
(1)
22
State the coefficient of a in -5a + 3.
(1)
23
Simplify 6x + 3x - 2x.
(2)
24
Use algebraic notation to write: the product of 5 and the number p.
(2)
Mark scheme · 2.4 Introduction to Algebraic Notation

Question 1

  • (a) B1 coefficient 9 and constant 6 cao
  • (a) Answer: coefficient 9, constant 6
  • (b) B1 coefficient -3 and constant -2 cao
  • (b) Answer: coefficient -3, constant -2

Question 2

  • (a) M1 substitutes x = 5 into both expressions correctly (3x + 2 = 17 and 2x + 8 = 18 or equivalent working)
  • (a) A1 states 2x + 8 is greater cao
  • (a) A1 gives correct reason: 18 > 17, so 2x + 8 is larger when x = 5
  • (a) A1 arithmetic correct and clear cao
  • (a) Answer: 2x + 8 is greater

Question 3

  • (a) B1 4 cao
  • (a) Answer: 4
  • (b) B1 10 cao
  • (b) Answer: 10
  • (c) B1 -2 cao
  • (c) Answer: -2

Question 4

  • (a) M1 uses multiplication notation such as 4k or 4 x k
  • (a) A1 4k cao
  • (a) Answer: 4k
  • (b) M1 recognises 'two lots of' means 2 times n
  • (b) A1 2n cao
  • (b) Answer: 2n

Question 5

  • (a) M1 identifies both parts as separate terms
  • (a) A1 5x and 2 cao
  • (a) Answer: 5x and 2
  • (b) M1 identifies three separate terms
  • (b) A1 3a, -4b and 7 cao
  • (b) Answer: 3a, -4b and 7

Question 6

  • (a) M1 adds like terms 4x and 2x to get 6x
  • (a) A1 6x + 3 cao
  • (a) Answer: 6x + 3
  • (b) B1 5y - 2 cao
  • (b) Answer: 5y - 2

Question 7

  • (a) B1 -1 cao
  • (a) Answer: -1
  • (b) B1 5 cao
  • (b) Answer: 5
  • (c) B1 2 cao
  • (c) Answer: 2

Question 8

  • (a) B1 7n cao
  • (a) Answer: 7n
  • (b) B1 x + 12 cao
  • (b) Answer: x + 12
  • (c) B1 2t - 5 cao
  • (c) Answer: 2t - 5

Question 9

  • B1 y + 8 cao
  • Answer: y + 8

Question 10

  • M1 recognises 'three lots of' means 3 times w
  • A1 3w cao
  • Answer: 3w

Question 11

  • M1 identifies both parts as separate terms
  • A1 6a and -8 cao
  • Answer: 6a and -8

Question 12

  • M1 substitutes y = -2 correctly, e.g. 3(-2) - 4
  • A1 -10 cao
  • Answer: -10

Question 13

  • M1 collects the x terms correctly, e.g. 5x + 2x = 7x
  • M1 collects the constants correctly, e.g. 3 - 7 = -4
  • A1 7x - 4 cao
  • Answer: 7x - 4

Question 14

  • B1 25 + 15h or 15h + 25 cao
  • M1 substitutes h = 3 correctly
  • A1 £70 cao
  • Answer: 25 + 15h; the charge for 3 hours is £70

Question 15

  • M1 substitutes x = 4 into both expressions correctly (4x - 1 = 15 and 2x + 5 = 13 or equivalent working)
  • A1 states 4x - 1 is greater cao
  • A1 gives correct reason: 15 > 13
  • Answer: 4x - 1 is greater

Question 16

  • M1 writes 'trebled then 4 added' as 3t + 4
  • M1 forms the full equation 3t + 4 = t + 22
  • M1 correct rearrangement, e.g. 2t = 18
  • A1 t = 9 cao
  • Answer: 3t + 4 = t + 22; t = 9

Question 17

  • M1 sets the two expressions equal, e.g. 2x + 7 = 5x - 8
  • M1 correct rearrangement, e.g. 15 = 3x
  • A1 x = 5 cao
  • A1 checks both expressions give 17 when x = 5
  • Answer: x = 5; the common value is 17

Question 18

  • B1 5m cao
  • Answer: 5m

Question 19

  • B1 7k cao
  • Answer: 7k

Question 20

  • B1 q/6 cao
  • Answer: q/6

Question 21

  • B1 9 cao
  • Answer: 9

Question 22

  • B1 -5 cao
  • Answer: -5

Question 23

  • M1 collects the like terms correctly
  • A1 7x cao
  • Answer: 7x

Question 24

  • M1 uses multiplication notation such as 5p or 5 x p
  • A1 5p cao
  • Answer: 5p

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