Unit 12 Section 1 : Substitution into Formulae 1

In this section we practise substituting numbers for the letters in a formula: in other words, we replace the letters in formulae with their numerical values.

In formulae, when we want to add or subtract letters, we use the normal symbols for add (+) and subtract (–).

If we want to multiply, we only write the multiply sign between numbers, not between numbers and letters or between letters and letters. If we want to divide, we write the division as a fraction.
Examples of multiplying and dividing
2 × 5 is written as2 × 5 or 10
2 × ais written as2a
a × bis written asab
2 ÷ 5 is written as
2 or 0.4
5
a ÷ 5 is written as
 a
5
a ÷ bis written as
 a
 b

Example Question

If a = 6. b = 3 and c = 7, calculate the value of:
(a)a + b
(b)ab
(c)3a – c
(d)
a + 2c
b
To answer these questions, we substitute the value of each letter to get an answer:
(a)6 + 3 = 9
(b)6 × 3 = 18
(c)3 × 6 – 7 = 18 – 7 = 11
(d)6 ÷ 3 + 2 × 7 = 2 + 14 = 16
Note that we make sure to do multiplication and division before addition and subtraction.

 

Practice Question
Work out the answers to the question below then click on the button marked Click on this button below to see the correct answer to see whether you are correct.

If p = 6, q = 12, r = 4 and s = 3, calculate the value of:
(a)rs
(b)2r + 3s
(c)p + r – s
(d)
 s
3
(e)
 q
 s
(f)rs – q

 

Exercises

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Question 1
Calculate the values of the following expressions, if x = 2, y = 5 and z = 9:
(a)x + y
(b)x + z
(c)y + z
(d)z – y
(e)y – x
(f)z – x
(g)x + y + z
(h)z + y – x
(i)z – y + x
Question 2
If p = 7, q = 2 and r = 3, evaluate the following expressions:
(a)2p
(b)4r
(c)5q
(d)5p
(e)6r
(f)2q
(g)3p
(h)10p
(i)8r
Question 3
If i = 6, j = 7, k = 3 and l = 4, determine the values of the following expressions:
(a)2i + 3k
(b)2l + 3i
(c)2j + 5l
(d)5j + 6k
(e)4i + 3l
(f)10j + 6l
(g)3i – j
(h)4k – i
(i)6l – 2k
(j)3i – 2j
(k)7k – 2i
(l)8l – 5k
Question 4
If s = 10, t = 12, u = 15 and v = 20, evaluate the following expressions:
(a)
 s
2
(b)
 t
3
(c)
 u
5
(d)
 v
10
(e)
 v
2
(f)
 u
3
(g)
 t
6
(h)
 s
10
(i)
 u
1
Question 5
If e = 10, f = 20, g = 5 and h = 4, determine the values of the following expressions:
(a)eg
(b)gh
(c)ef
(d)eh
(e)
 e
 g
(f)
 f
 h
(g)
 f
 g
(h)
 f
 e
(i)
 e
 g
(j)efg
(k)gfe
(l)feg
(m)heg
(n)
 gh
 f
(o)
 ef
 gh
Question 6
In a sweet shop you can buy packets of mints for 20p each and bars of chocolate for 30p each.
The total cost of m packets of mints and c bars of chocolate is given by the formula

      T = 20m + 30c

Use this formula to calculate the total cost if:
(a)m = 2 and c = 1
(b)m = 8 and c = 0
(c)m = 3 and c = 3
(d)m = 5 and c = 4
(e)m = 1 and c = 10
(f)m = 2 and c = 3

Question 7
The perimeter of the rectangle shown on the right is given by the formula

      p = 2l + 2w

Calculate the perimeter of rectangles for which:
(a)l = 2, w = 1
(b)l = 8, w = 2
(c)l = 10, w = 9
(d)l = 10, w = 3

Question 8
The perimeter of the triangle shown on the right is given by the formula

      p = x + y + z

Determine p if:
(a)x = 4, y = 8 and z = 6
(b)x = 2, y = 3 and z = 4
(c)x = 10, y = 17 and z = 20
(d)x = 9, y = 14 and z = 15

Question 9
The cost of entry to a leisure park for an adult is £5 and for a child is £4.
The total cost in pounds for a adults and c children is given by the formula

      T = 5a + 4c

Calculate the cost if:
(a)a = 2 and c = 4 £
(b)a = 7 and c = 1 £
(c)a = 1 and c = 5 £
(d)a = 2 and c = 3 £
(e)a = 3 and c = 8 £
(f)a = 10 and c = 30 £

Question 10
The time, T hours, taken to drive D kilometres along a motorway at a speed of S kilometres per hour is calculated using the formula

      T =   D
 S

Calculate the time taken if:
(a)D = 200 and S = 100       hours
 (b)D = 160 and S = 80       hours
(c)D = 360 and S = 60       hours
 (d)D = 5 and S = 10       hours

You have now completed Unit 12 Section 1
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Produced by A.J.Reynolds October 2007