UNIT 2 HIGHER EDEXCEL GCSE Milestone (2) Content Fractions Decimals Estimation Lesson

UNIT 2 HIGHER EDEXCEL GCSEMilestone (2)

ContentFractionsDecimalsEstimation

Lesson

Grade DMilestone (2)



Grade CMilestone (2)









Grade BMilestone (2)

ANSWERSMilestone (2)

Practice question

1.

Milestone (2)

2.

Practice questionMilestone (2)

3.


4.


5.

6.

7.

8.

Practice questionsMilestone (2)

Grade D

9.

Milestone (2)

2

2

2

2

18.0

9963

18

9903.6

18

9.93.6

4

77

18

9963

Write down the value, as fractions or integers, of

Use the information that

a)

b)

c)

Grade D

10.

Milestone (2)

Jim and Jenni are collecting money for charity. Jim collects a kilometre of 2p pieces. Jenni wants to collect 1p pieces. How many 1p pieces does she need to collect to get the same amount of money as Jim? (Diameter of 2p piece = 2.6cm, diameter of 1p piece = 2cm)

Grade D

*11.

Milestone (2)

Grade D

12.

13.

Milestone (2)

Grade D

14.

15.

Milestone (2)

Grade C

16.

Milestone (2)

Grade C

17.

Milestone (2)

GRADE C

18.

Milestone (2)

The height of a room is 285 cm. The width of the room is 790 cm and the length is 880 cm. A number of people are to work in the room. Building regulations state that for every person working in the room there must be 4.25 m3.

Calculate an estimate for the number of people who could work in the room.

GRADE C

19.

Milestone (2)

ANSWERSMilestone (2)


1. Find the missing numbers in each case

a) 2 x ? + (-3) = (-7)

b) (-4) x ? + 5 = (-3)

c) ? ÷ 2 + 4 = (-4)


2. Neal works part time in a local supermarket, stacking shelves. He has been asked to usethis pattern to advertise a new brand of beans.

This stack is 3 cans high.

a) How many cans will be need to build a stack 10 cans high?

b) If he has been given 200 cans, how many cans high would his stack be?

Next he is asked to stack cans of tomato soup in a similar shape, but this time it is two cans deep

c) How many cans will he need to build a stack 10 cans high?

d) If he has been given 400 cans, how many cans high would his stack be?


3. A chocolate company wishes to produce a presentation box of 36 chocolates for Valentine’s Day. The company decides that a rectangular shaped box is the most efficient shape, but can’t decide how to arrange the chocolates.

How many different possible arrangements are there:

a) Using one layer

b) Using two layers

c) Using three layers


4. One is a square number and a cube number. Find another number which is both a square and a cube number.


5. Use the calculation 42 x 62 = 576

To work out:

402 x 602

4002 x 62

5760 ÷ 62

42 x 602

43 x 62


6. Work out

2 + 4 ÷ 4

53 ÷ 5 + 5

(22)3 – (23)2

Grade C/BMilestone (1)

7. Simplify

a)

b)

c)

d)37

12

55

5

6

35

3

33

10

74

4

44

34 )2(


8. Express 252 as a product of its prime factors

Express 6 x 252 as a product of prime factors


9. James thinks of two numbers. He says:

‘The highest common factor (HCF) of my two numbers is 3.

The lowest common multiple (LCM) of my two numbers is 45’.

Write down the two numbers James could be thinking of


10. Write 84 as a product of its prime factors. Hence or otherwise write 1682 as a product of its prime factors.

11. A car’s service book states that the air filter must be replaced every 10 000 miles and the diesel fuel filter every 24 000 miles.

After how many miles will both need replacing at the same time?

Grade B/AMilestone (1)

12. Work out

a)

b)

c)

d)

22

43

81

23 )216(

3)49(

3

32

8

17

Grade A/A*Milestone (1)

13. Work out the value of x

x28 2 930

Grade A*Milestone (1)

14. Take a piece of A4 paper. If you fold it in half you create two equal pieces. Fold it in half again; you now have four equal pieces. It is said that no matter how large and how thin you make the paper, it cannot be folded more than seven times. Try it.

If you fold it seven times, how many equal pieces does the paper now have?

15. In 2001, there were two rabbits left on an island. A simple growth model predicts that in 2002 there will be four rabbits and in 2003, eight rabbits.

The population of rabbits continues to double every year. Assuming no rabbits die, how long is it before there are over one million rabbits on the island?

Grade A*Milestone (1)

16. Is each statement true or false? If the statement is false, give an example to show it.

a) The sum of two prime numbers is always a prime number.

b) The sum of two square numbers is never a prime number.

c) The difference between consecutive prime numbers is never 2

d) The product of two prime numbers is always a prime number.

e) No prime number is a square number.

ANSWERSMilestone

GRADE D

1) a)-2 b)2 c)-4

2) a)100 b) 14 (with 4 spare) c) 200 d)14 (with 8 spare)

3) a) 5 (1x36,2x18,3x12,4x9,6x6)

b) 3 (1x18,2x9,3x6)

c) 3 (1x12,2x6,3x4)

GRADE C

4) 64

5) a) 5 760 000 b) 5 760 000 c) 160 d) 57 000 e) 2304

6) a) 3 b) 30 c) 0

7) a) 32 b)4 c) 212 d) 52

8) a) 22x32x7 b) 23x33x7

9) 9,15

10) a) 22x3x7 b) 26x32x72

11) 120 000 miles

GRADE B

12) a)48 b)36 c)343 d)25

13) 3

GRADE A*

14)a) 27 = 128 15)2020

16) a)F eg 3+5=8 b)F eg 4+9=13

c)F eg 5-3=2 d)F eg 2x3=6 e) true

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UNIT 2 HIGHER EDEXCEL GCSE Milestone (2) Content Fractions Decimals Estimation Lesson