Page 31 - MAT KS3 Y8 Cambridge CheckPoint

2.6 Deriving and using formulae

10 a Shen uses this formula to convert temperatures in degrees Celsius (°C) to degrees Fahrenheit (°F).

C = 0.6F − 17.8 where: C is the temperature in °C
F is the temperature in °F.
Use the formula to work out the temperature in °C when the temperature in °F is:
i 20°F ii 45°F iii 82°F.

b Anders knows this relationship between temperatures in °F and temperatures in °C.

9C = 5F − 160 where: F is the temperature in °F
C is the temperature in °C.

Anders wants to know the temperature in °F when the temperature is 4°C.
This is what he writes.

9C = 5F – 160

Substitute C = 4: 9 × 4 = 5F – 160
Simplify: 36 = 5F – 160

Anders now has to solve the equation 36 = 5F − 160.
Work out the equation that Anders needs to solve when the temperature in °C is:
i 6°C ii 18°C iii 30°C.

Summary

You should now know that: You should be able to:
★ In a linear sequence the terms increase or ★ Generate terms of a linear sequence using
decrease by the same amount each time. term-to-term and position-to-term rules.
★ A sequence can be described using a term-to- ★ Find term-to-term and position-to-term rules of
term rule and a position-to-term rule. sequences, including patterns.
★ The position-to-term rule of a sequence can be ★ Use a linear expression to describe the nth term of
written as an expression called the nth term. a simple sequence.
★ A function can be shown as a function machine, as ★ Express simple functions algebraically and
a mapping diagram or written algebraically as an represent them in mappings.
equation. ★ Know that letters play different roles in equations,
★ When you write a function as an equation, you formulae and functions.
usually use the letter x to represent the input ★ Construct linear expressions.
numbers and the letter y to represent the output ★ Derive and use simple formulae.
numbers.
★ Substitute positive and negative integers into
★ In algebra you use a letter to stand for an unknown
expressions and formulae.
number. The letter is called the variable.
★ Use the order of operations (BIDMAS), including
★ A linear expression is where the variable is
brackets, with more complex calculations.
multiplied by a number only. If the variable is
multiplied by itself, it is not a linear expression. ★ Manipulate numbers and algebraic expressions,
and apply routine algorithms.
★ You can write or derive a formula to help you solve
problems. ★ Use logical argument to establish the truth of a
statement.

2 Sequences, expressions and formulae 29