# Use Simple Formulae

In this worksheet, students will be asked to use simple algebraic formula to solve different mathematical problems.

Key stage:  KS 2

Curriculum topic:   Algebra

Curriculum subtopic:   Use Algebra Formulae

Difficulty level:

### QUESTION 1 of 10

Sometimes in Maths numbers can be replaced by letters...do not be put off by letters!

Letters are used for a special type of Maths, called algebra.

When we use algebra, we use 'formula'; formula is a concise, simple way of showing information with symbols.

There are lots of formulas in Maths to find, for example: area, perimeter and circumference.

Example 1:

If a = 6, b = 3 and c = 7, calculate the value of:

1. a + b =             2. a - b =            3. c + b - a =

Solution:

1. a + b

= 6 + 3 = 9

2. a - b

= 6 - 3 = 3

3. c + b - a

= 7 + 3 - 6 = 4

Reminders:

There are some rules to remember when using formula:

We write:

2 x a as 2a

a x b = ab

a ÷ b as a/b

Example 2:

If p = 6, q = 12, r = 4 and s = 3 calculate the value of:

1. rs           2. 2r + 3s            3. s/3

Solution:

1. rs = r x s

= 4 x 3 = 12

2. 2r + 3s  = 2 x r + 3 x s

= 2 x 4 + 3 x 3

=8 + 9 = 17

3. s/3 = 3 / 3

= 1

Can you find the correct answer for the following expressions if

x = 2, y = 5 and z = 9?

## Column B

x + y =
16
x + y + z =
3
y - x =
6
z - y + x =
7

If p = 7, q = 2 and r = 3, find the value of the following expressions.

## Column B

2q
84
12p
28
13r
4
14q
39

If s = 10, t = 12 and v = 20, find the value of the following expressions.

## Column B

s/2
10
v/10
2
t/3
4
v/2
5

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 packet of mints and c bars of chocolate is given by the formula below.

= 20m + 30 c

Use this formula to calculate the total cost if

m = 3 and c = 3

In a sweet shop, you can buy packets of mints for 20 p each and bars of chocolate for 30 p each.

The total cost of m packet of mints and c bars of chocolate is given by the formula.

= 20m + 30 c

Use this formula to calculate the total cost if

m = 8 and c = 0

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

T = D/S

Calculate the time taken if

D = 360 and S = 60

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 below.

T = D/S

Calculate the time taken if

D = 5 and S = 10

So, as a formula, we can say: C = 4L +10.

£68

£52

£58

£46

So, as a formula, we can say C = 4L + 10.

£114

£112

£134

£104

Are the following algebraic equations correct or incorrect?

1. a - 6 = 4 therefore a = 10

2. d/6 = 3 therefore d = 18

3. 13 - z = 8 therefore z = 4

 Correct Incorrect 1 2 3
• Question 1

Can you find the correct answer for the following expressions if

x = 2, y = 5 and z = 9?

## Column B

x + y =
7
x + y + z =
16
y - x =
3
z - y + x =
6
EDDIE SAYS
Work through carefully and double check what each letter is worth. 1. x + y = 2 + 5 = 7 2. x + y + z = 2 + 5 + 9 = 16 3. y - x = 5 - 2 = 3 4. z - y + x = 9 - 5 = 4+ 2 = 6 Is this starting to make sense?
• Question 2

If p = 7, q = 2 and r = 3, find the value of the following expressions.

## Column B

2q
4
12p
84
13r
39
14q
28
EDDIE SAYS
Just like the last question, we need to double check the value of each letter. 1. 2q = 2 x 2 = 4 2. 12p = 12 x 7 = 84 3. 13r =13 x 3 = 39 4. 14q = 14 x 2 = 28
• Question 3

If s = 10, t = 12 and v = 20, find the value of the following expressions.

## Column B

s/2
5
v/10
2
t/3
4
v/2
10
EDDIE SAYS
With practise, it starts to get easier to remember to check the value of each letter. 1. s/2 = 10/2 = 5 2. v/10 = 20/10 = 2 3. t/3 = 12/3 = 4 4. v/2 = 20/ 2 = 10
• Question 4

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 packet of mints and c bars of chocolate is given by the formula below.

= 20m + 30 c

Use this formula to calculate the total cost if

m = 3 and c = 3

£1.50
150p
EDDIE SAYS
This should be solved with the following steps: 20m + 30c = 20 x 3 + 30 x 3 = 60 + 90 = 150 = £1.50 You're getting better with each activity you attempt! Great focus.
• Question 5

In a sweet shop, you can buy packets of mints for 20 p each and bars of chocolate for 30 p each.

The total cost of m packet of mints and c bars of chocolate is given by the formula.

= 20m + 30 c

Use this formula to calculate the total cost if

m = 8 and c = 0

£1.60
160p
EDDIE SAYS
Another sweetie challenge that involves using ordered steps. 20m + 30c = 20 x 8 + 30 x 0 = 160 + 30 = 160 = £1.60 If you approach each question calmly it's really not that difficult! You're halfway through the activity.
• Question 6

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

T = D/S

Calculate the time taken if

D = 360 and S = 60

6 hours
6
EDDIE SAYS
Be careful with this division question. You would work out like this: T = D/S T = 360/60 = 6 Which is then written as 6 hours, don't forget your units in the exam!
• Question 7

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 below.

T = D/S

Calculate the time taken if

D = 5 and S = 10

Half an hour
30 minutes
30 mins
1/2 hour
EDDIE SAYS
A tricky division question as the answer is a decimal number that we then have to correctly convert to units of time. T = D/S T = 5/ 10 = 0.5 = 0.5 hours = 30 minutes or 1/2 hour
• Question 8

So, as a formula, we can say: C = 4L +10.

£58
EDDIE SAYS
Our knowledge of the 12x table will help you solve this one. C = 4L + 10. C = 4 x 12 + 10n= C = 48 + 10 = 58 = £58
• Question 9

So, as a formula, we can say C = 4L + 10.

£114
EDDIE SAYS
A bit of a harder multiplication this time, it is OK to use a written method of multiplication for 4 x 26 if it helps you. C = 4L + 10. C = 4 x 26 + 10 = C = 104 + 10= 114 = £114
• Question 10

Are the following algebraic equations correct or incorrect?

1. a - 6 = 4 therefore a = 10

2. d/6 = 3 therefore d = 18

3. 13 - z = 8 therefore z = 4

 Correct Incorrect 1 2 3
EDDIE SAYS
1. Correct. 10 - 6 = 4 therefore a = 10 2. Correct. 18 / 6 = 3 therefore d = 18 3. Incorrect. 13 - 4 = 9 not 8 therefore z = 5 Great work! That's another activity completed. Why not attempt another one?
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