Week 11 A Substitution into a Formula

Substitution into a Formula

Substituting into a Formula

• Substitute into a formula or expression

• Substitute using negative or fractional values

• Solving problems by substituting into formula

Substitution into an expression

Substitution is when we replace a letter for a number in an expression or formula.

Some points to remember:

*no sign means times

*a fraction means divide

Watch the video on the next page to learn more:

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Multiple Choice

If y = 4, find the value of 3y+5.

• 27
• 12
• 17
• 18

If y = 4, find the value of 3y+5.

• We need to substitute (swap) the y for the 4

• *remember 3y means 3 x y

• 3 x 4 + 5 = 17

Multiple Choice

If a = 4 and b = 6, what is the value of 3a + 5b?

• 40
• 42
• 44
• 46

If a = 4 and b = 6, what is the value of 3a + 5b?

• This time we need to substitute for a and b

• 3 x 4 + 5 x 6

• 12 + 30

• 42

Multiple Choice

If y = 7, find the value of 2(y+4)

• 11

• 22

• 20

• 12

If y = 7, find the value of 2(y+4)

• *remember BIDMAS tells us we need to do the brackets first

• 2(7+4) means 2 x (7+4)

• 2 x 11 = 22

Multiple Choice

Work out the value of the expression when x = 3, y = – 2 and z = – 4.

y + x – z

• -5

• -3

• 3

• 5

Work out the value of the expression when x = 3, y = – 2 and z = – 4.

y + x – z   

• -2 +3 +-4

• *remember +- is the same as -

• -2 +3 -4

• = -3

Multiple Choice

Work out the value of the expression when x = 3, y = – 2 and z = – 4.

2xz

• 1

• 24

• -24

• 9

Work out the value of the expression when x = 3, y = – 2 and z = – 4.

2xz

• When we substitute the numbers in we will get:

• 2 x 3 x -4

• = -24

Multiple Choice

Work out the value of the expression when x = 3, y = – 2 and z = – 4.

• 1
• -1
• 1/5
• -6

Work out the value of the expression  $\frac{3y}{2x}$   when x = 3, y = – 2 and z = – 4.

• *remember a fraction means divide

• 
  

   $\frac{3\times-2}{2\times3}$  

• -6/6

• = -1

Work out the value of the expressions a² + 2b when a = 5 and b = -2

• *remember a² means a x a

• 5 x 5 + 2x-2

• 25 - 4

• = 21

Substitution into a Formula

• In maths a formula is a rule for working something out. 

• What formula would we write to work out the number of table legs in the classroom?

• number of legs = the number of tables x 4

• We can now work out the number of table legs for any given number of tables.

• For example, if there are 16 tables in the classroom:​

• Number of table legs = 16 × 4​

• Number of table legs = 64

Car Hire:

• The cost of hiring a car for a number of days is calculated using the formula

• Hire Cost = 30 x Number of Days + 50

• (a) Calculate the cost of hiring a car for 4 days. 

• Hire Cost = 30 x 4 + 50

• Hire cost = 120 + 50

• Hire Cost = £170

Cooking Chicken

•  The time in minutes, taken to cook a chicken is given by the formula

• Time = 40 minutes per kilogram plus 20 minutes 

•  (a) Work out the time taken to cook a 5kg chicken. 

• Time = 40 x 5 + 20

• Time = 220 mins

• Time = 3 hours and 40 mins

Multiple Choice

The perimeter of a square is given by p =4a

p= perimeter, a = side length

What is the value of p when a = 3m

• 7m

• 8m

• 12m

• 24m

The perimeter of a square is given by p =4a

p= perimeter, a = side length

What is the value of p when a = 3m

• This makes sense because all of the sides of a square are the same.

• We need to not let a = 3m catch us out, the 3m means 3 metres.

• For P = 4a

• P = 4 x 3

• Perimeter = 12m (12 metres)

Multiple Choice

The perimeter of a rectangle is given by

p =2a + 2b

p= perimeter

What is the value of p when a = 3m and b= 2m?

• 12m

• 10m

• 14m

• 20m

The perimeter of a rectangle is given by

p =2a + 2b, where p= perimeter.

What is the value of p when a = 3m and b= 2m?

• just like the last question a = 3m and b = 2m mean 3 metres and 2 metres

• p =2a + 2b

  p = 2 x 3 + 2 x 2

• p =6 + 4

• perimeter = 10m (10 metres)

Multiple Choice

The speed of a falling object is found by the formula:

v = 10t.

If t = 5, find v.

• 15

• 50

• 105

• 2

The velocity (speed) of a falling object is found by the formula: v = 10t.

If t = 5, find v.

• v = 10t

• V = 10 x 5

• Velocity = 50

Multiple Choice

Andy makes dresses, and is paid using the formula: P = 4n + 32,

where P is his pay in pounds, and n is the number of dresses he makes.

Andy makes 5 dresses. What is his pay?

• 52

• 41

• 32

• 20

Andy makes dresses, and is paid using the formula: P = 4n + 32, where P is his pay in pounds, and n is the number of dresses he makes. Andy makes 5 dresses. What is his pay?

• P = 4n + 32

• P = 4 x 5 + 32

• Pay = 52

Exit Ticket

Fantastic work! Be sure to head over to your Microsoft Teams page for Maths and find the Microsoft Forms quiz on the 'assignments' tab. 

If you complete this quiz, that will act as your register for this session. No completed quiz - no mark!