Week 23A-Substituting into and rearranging formulae

Week 23A-Substituting into and rearranging formulae

Watch the video on the following slide

Substituting into an expression

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Multiple Choice

Taxi fare = £2.50 + 20p per mile

Fred travels 8 miles. What is his taxi fare?

• £18.50

• £162.50

• £3.50

• £4.10

Multiple Choice

Cost of Virgin Media = £35 installation + £20 per month

How much does it cost to have Virgin Media for 6 months?

• £135

• £155

• £160

• £165

An algebraic expression is a mathematical relationship with at least one variable

A variable is an algebraic term like x or y that could have any value..

Substituting Into & Evaluating Algebraic Expressions

In order to solve an algebraic formula, you need to replace the variables with their numeric values

Substituting is when you replace a variable with its numeric value

After you replace all the variables in a formula with their numeric values you can calculate the value for that formula

When substituting values in, we need to be careful to include any hidden multiplication signs ....

Example

Substitute x = 3 into this expression

2x - 1

Multiple Choice

Pressure = Force ÷ Area

find the pressure when the force is 36N and the area is 9cm²

• 4 N/m²

• 12 N/cm²

• 3 N/cm²

• 4 N/cm²

Multiple Choice

Circumference = πd

Find the circumference of a circle with a radius of 15m (in terms of π)

• 30π

• 15π

• 60π

• 225π

Open Ended

The height of a growing tree is given by the formula h = 2t + 15. Find the value of h when t = 7

Example

Substitute x = -2 and y = 5 into this expression:
 $x^3\ +\ y\$  

Multiple Choice

t = u + av

Find t when v = 3, u = 4 and a = 5

• 15

• 19

• 17

• 34

Open Ended

y = 3a + 5b

Find y when a = 4 and b = 6

Watch the video on the following slide

Rearranging a formula

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Multiple Choice

Make a the subject of

a + b = c

• a = c - b

• a = b - c

• a = b + c

• a = bc

Open Ended

Make w the subject of

A = lw

Multiple Choice

Make r the subject:
A = πr²

• r = √(A/π)
• r = √Aπ
• r = Aπ²
• r = (Aπ)²

Multiple Choice

Make x the subject of y = mx + c

• x = (y - c)/m
• x = y - c/m
• x = y/m - c
• x = my + c

Open Ended

Make x the subject of y = mx + 1