Introduction to Algebraic Notation - Worksheets, Questions and Revision

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

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KS3 · Algebra

KS3.M-A4 Introduction to Algebraic Notation

AQA KS3.M-A4 · Calculators not allowed · about 60 minutes
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Write down the algebraic expression for each sentence.
(a)A number x increased by 5.(1)
(b)Three times a number n.(1)
(c)The product of 6 and a number m.(1)
(d)A number p divided by 4.(1)
2
Write each expression in the simplest form by collecting like terms.
(a)2x + 3x(1)
(b)7y - 2y(1)
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
Calculate each value by substituting the given number into the expression.
(a)Find the value of 5x when x = 3.(1)
(b)Find the value of 2a + 4 when a = 5.(1)
7
Simplify each expression by collecting like terms. Show any simple arithmetic used.
(a)Simplify 4x + 2x + 3.(2)
(b)Simplify 8y - 3y - 2.(1)
8
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)
9
Write an algebraic expression for each situation, using standard compact notation where appropriate.
(a)The total cost for n identical pens each costing 7 pounds.(1)
(b)A number x increased by 12 gives the total weight in kilograms.(1)
(c)Twice a number t minus 5.(1)
10
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)
11
Translate each short word problem into an algebraic expression.
(a)Sam saves 5 pounds each week. After w weeks he has saved some money. Write an expression for the amount saved.(1)
(b)A taxi charges a flat fee of 3 pounds plus 2 pounds per mile. For m miles, write an expression for the total fare.(1)
(c)A garden has length l and width 4. Write an expression for its perimeter.(1)
12
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)
Mark scheme · KS3.M-A4 Introduction to Algebraic Notation

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12