(a) Number and Algebra

(iii) Number operations and algebra

Question 1
Complete the statement below to illustrate the meaning of the commutative law for

=

+-×÷

Question 2
Complete the statement below to give a counter example to show that the commutative law is not true for

+-×÷

Question 3
Insert brackets in the statement below to illustrate the associative law for addition.

=

Question 4
Insert brackets in the statement below to give a counter example to show that the associative law is not true for subtraction.

Question 5
Use the distributive law to complete the statement below as an efficient mental method to calculate the answer.

=

×

+

×

=

 
Question 6
Write the number in terms of its prime factors.

=

×

×

×

 
Question 7
What is the highest common factor of the numbers ?

Highest common factor

=

 
Question 8
What is the lowest common multiple of the numbers ?

Lowest common multiple

=

 
Question 9

Cost

=

£

 
Question 10
Divide £ between three brothers, Tim, Chris and Andrew, in the ratio .

Tim gets £

Chris gets £

Andrew gets £

 
Question 11
Simplify, as far as possible:

(a)		=
(b)		=

 
Question 12
Factorise:

(a)		=
(b)		=

 
Question 13
Rearrange the formula:

y =

1

x

-

to give x as a function of y.
You should simplify your answer and multiply out any brackets.

x

=

 
Question 14
The relationship between temperature in ºC (degrees Celsius) and temperature in ºF (degrees Fahrenheit) is given by the formula:

ºF

=

9 5

×

ºC

+

32

What is the temperature in ºF when it is

(a)	ºC	=	ºF
(b)	ºC	=	ºF

 
Question 15
Write down the first five terms of the sequence, u_n, defined by

un

=

Question 16
Write down the next five terms of the sequence

Write down an expression for the nth term of the sequence.
Simplify your answer and multiply out any brackets: