# (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.
 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, un, 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.