Cambridge Essentials Mathematics Extension 9 N2 Further Worksheet

/ N2 Further Worksheet

1 Two numbers have a HCF of 12 and a LCM of 360.

a Find two possible numbers.

b Find other possible numbers.

2 Two lighthouses have flashing beacons. Lighthouse A’s beacon flashes every 18 seconds. Lighthouse B’s beacon flashes every 30 seconds.

The two beacons flash at the same time.

After how many seconds will the beacons next flash at the same time.

3 The number 50 can be written as 5m × n, where m and n are prime numbers.

Find the value of m and the value of n.

4 Xavier was investigating the difference between consecutive cube numbers.

This is what he wrote.

23 – 13 = 8 – 1 = 7 7 is a prime number

33 – 23 = 27 – 8 = 19 19 is a prime number

43 – 33 = 64 – 27 = 37 37 is a prime number

He said, “The difference between consecutive cube numbers is always a prime number.” Do you agree? Explain your answer.

5 a Work these out. Do not use a calculator.

i ii iii 8x0 iv (4xy)0 v

b can be written as or as .

Does it make a difference which way you work out ?

c Work these out. Do not use a calculator.

i ii iii iv v

vi vii viii ix x

6 Write each number in the form 2n

a 8 b 16 c d –8 e

7 Simplify these surds. Leave your answers in surd form.

a b c

d e f

8 Find the area of triangle ABC. Write your answer as simply as possible.

9 Which is the largest? You must show your working out.

One third of 123, half of 76, two fifths of 90 or three quarters of 52.

10 Kevin’s stride is m.

How many strides does he take when he walks 300 m to the bus stop?

11 a is multiplied by a number to give . What is the number?

b The product of two numbers is 24. One number is . What is the other number?

12 x = 0.363636......

a What is 100x? b Work out the value of 99x c What is x as a fraction?

13 is a recurring decimal, = is also a recurring decimal.

Is it true that if you square any fraction that is a recurring decimal, you get a fraction that is also a recurring decimal? Use at least four examples before you decide.

14 is a terminating decimal, is a recurring decimal.

× = which is also a recurring decimal.

Use at least four other examples to see if this always happens.