Introduction to Algebra - Worksheets, Questions and Revision

20 original exam-style questions - 7 pages of questions with a full mark scheme - free printable PDF.

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KS2 · Algebra

KS2.M-ALG Introduction to Algebra

NCETM National Curriculum (2014) Mathematics - KS2 Algebra · Calculators not allowed · about 60 minutes
Total Marks
Name: _______________________________    Date: ____ / ____ / ______
Answer ALL questions. Show all your working.
1
Look at the function machines below. Each one shows an input, an operation and an output.
(a)Input: 8 -> add 5 -> Output: ?(1)
(b)Input: ? -> add 5 -> Output: 20(1)
2
Find the missing number in each equation.
(a)9 + ___ = 14(1)
(b)___ - 7 = 8(1)
(c)3 x ___ = 18(1)
3
Write an expression for each of the following. Use the letter given.
(a)A number, n, add 6(1)
(b)5 less than a number, y(1)
(c)Double a number, m, then add 3(1)
4
a = 4. Work out the value of each expression.
(a)a + 9(1)
(b)3a(1)
(c)2a - 5(2)
5
A function machine multiplies the input by 2, then adds 3.
Figure (to be drawn): input -> x2 -> +3 -> output
(a)Find the output when the input is 6.(1)
(b)Find the output when the input is 10.(1)
(c)The output is 25. Find the input.(2)
6
A sequence starts at 5 and increases by 4 each time.
(a)Write the first four terms of the sequence.(1)
(b)The nth term rule for this sequence is 4n + 1. Use the rule to find the 10th term.(2)
7
A square has side length s cm.
(a)Write a formula for the perimeter, P, of the square in terms of s.(1)
(b)Use your formula to find P when s = 7 cm.(1)
8
Solve each equation to find the value of the letter.
(a)n + 8 = 15(1)
(b)m - 6 = 9(1)
(c)5p = 35(1)
9
Solve each two-step equation to find the value of the letter. Show your working.
(a)3n + 2 = 17(2)
(b)2m - 5 = 11(2)
10
Priya has p pounds. Tom has 3 pounds more than Priya.
(a)Write an expression for the amount of money Tom has, in terms of p.(1)
(b)Priya has 12 pounds. Work out how much money Tom has.(1)
(c)The total amount of money they have together can be written as 2p + 3. Work out the value of 2p + 3 when p = 12, and use it to check your answer to part (b).(2)
11
The table shows the position and term of a number pattern.
Position: 1, 2, 3, 4
Term: 4, 7, 10, 13
(a)Describe the term-to-term rule for this pattern.(1)
(b)Find the rule connecting the position number and the term. Write your rule using algebra, letting the position number be p.(2)
(c)Use your rule to find the 20th term.(1)
12
Solve the equation to find the value of n. Show your working.
2n + 3 = n + 9
(2)
13
The area of a rectangle can be found using the formula A = l x w, where l is the length and w is the width.
(a)A rectangle has length 9 cm and width 4 cm. Work out its area.(1)
(b)A different rectangle has an area of 48 cm2 and a width of 6 cm. Work out its length.(2)
14
a and b are two whole numbers. a + b = 20 and a is 6 more than b. Find the value of a and the value of b. Show your working.
(3)
15
Sam says: 'If you double a number and then add 3, the answer is always odd.' Is Sam correct? Explain your answer using at least one example.
(2)
16
A function machine subtracts 4, then multiplies by 3.
Figure (to be drawn): input -> subtract 4 -> x3 -> output
(a)Find the output when the input is 10.(1)
(b)Find the output when the input is 6.(1)
(c)The output is 30. Find the input.(2)
17
Simplify each expression by collecting like terms.
(a)3n + 2n(1)
(b)5m + 2 - 2m(2)
18
A rectangle has length (x + 3) cm and width 5 cm. The perimeter of the rectangle is 36 cm. Work out the value of x. Show your working.
(3)
19
A matchstick pattern is made so that position n uses 3n + 1 matchsticks.
(a)How many matchsticks are used in position 5?(1)
(b)A pattern in this sequence uses 40 matchsticks. Which position is it?(2)
20
Prove that the sum of any two consecutive whole numbers is always odd. Let the first whole number be n, so the next consecutive whole number is n + 1.
(3)
Mark scheme · KS2.M-ALG Introduction to Algebra

Question 1

Question 2

Question 3

Question 4

Question 5

Question 6

Question 7

Question 8

Question 9

Question 10

Question 11

Question 12

Question 13

Question 14

Question 15

Question 16

Question 17

Question 18

Question 19

Question 20