1 Write an expression for the output of each function machine.
a x
+2
b x
÷3
c w
×5
d p
−9
2 Write an expression for the output of each function machine.
a x
×6
+5
b x
×4
−3
c x
÷3
−7
d x
÷8
+1
e x
+4
×5
f x
−5
÷ 10
g x
×7
−3
h x
÷2
+1
i x
−1
×6
j x
+5
÷2
3 Draw a function machine to represent each expression.
a 2g + 7
b 3(h − 9)
x
e __
​ ​ −
5
4
m
f ​ __ ​ +
6
9
w
j ​ __ ​ +
12
2
i 4a + 3
c 4(t + 3)
f+4
g ​ _____
​ 2
d 5r − 10
k 8(b − 1)
k − 12
h ​ ______
7 ​ s+1
l ​ _____
​ 10
4 Here are two reverse function machines. Write the value of x for each. a x
+4
×5
7
b x
÷9
+7
11
103
Algebra A2.2 Functions and equations
5 Write the inverse of each operation.
a Add 6
b Multiply by 5
c Subtract 1
d Divide by 2
e + 5
f × 6
g ÷ 3
h − 9
i × 10
j + 3.4
k − 9.8
l ÷ 7.2
x
6 This function machine represents the equation ​ __
5 = 6.
​ −
4
x
÷4
−5
6
a Copy and complete the reverse function machine. Use inverse operations.
x
?
?
6
x
b Use the reverse function machine to solve the equation ​ __ ​ −
5 = 6.
4
7 i Draw a function machine for each of the following equations.
ii Draw the reverse function machine for each.
iii Use the reverse function machine to solve the equation.
a 4x + 12 = 20
b 3n − 14 = 22
c 5y − 7 = 43
d 4p + 1 = 25
e 2t + 9 = 20
r
h ___
​ ​ + 1 = 16
10
f 2(m − 8) = 3
a
i ​ __ ​ − 9 = 5
3
g 5(y − 7) = 45
8 Sam is solving the equation 2(m − 3) = 9.
He divides both sides by 2. This removes the 2 that is multiplying the bracket. He is not sure what to do next.
a Sarah suggests adding 3 to both sides to
remove the subtract 3. Is she right?
b What is the answer?
c Solve 5(p + 12) = 100. Explain each step.
104
Algebra A2.2 Functions and equations
9 A teacher explains how to solve 2m + 4 = 17.
Solve the following equations. Show your method.
a 6t + 9 = 51
b 2n − 15 = 25
c 9m + 3 = 48
d 6y − 8 = 4
e 2(p + 3) = 11 f 4x − 16 = 24
g 2w + 2 = 7
h 7m − 3 = 4
i 3(x + 8) = 21
10 Rashid is solving the equation 6y − 7 = 11. Look at his working out. The teacher has marked some of his first line wrong.
a Explain what Rashid has done wrong.
b Show Rashid how to solve the equation correctly.
11 Katherine is solving the equation 2x + 7 = 16. Look at Katherine’s attempt.
a Explain what Katherine has done wrong.
b Show Katherine how to solve the equation correctly.
105