Download Revision-Chapter 1,2 and 3 Grade 8

Revision-Chapter 1,2 and 3
Grade 8
1. Work out the following.
(a)
–5 + –3 – –1
(d)
3
√27
(b) –3 × –6  2
(h)
(c) (15 – –6)  –3
3
√1000
2. Write down the factors, LCM and HCF of 12 and 21.
3. for each sequence below:
(i)
describe the term-to-term rule
(ii)
write down the next three terms in the sequence.
(a)
21, 19, 17, 15, ......................
(b)
10, 5, 0, –5, ......................
4. Write down the first five terms of the sequence whose nth term is:
(a)
5n + 1
(b)
3n – 3
5. Write down two positive numbers with an HCF of 2 and an LCM of 30.
6.The diagram shows the prime factors of 66.
(a)
Complete the diagram
(b)
Use your completed diagram to find:
(i)
the highest common factor of 66 and 72
(ii)
the lowest common multiple of 66 and 72.
7. Ian only uses his mobile phone in the evening, when it is cheaper. The costs of some calls he
makes to his friend Martin’s mobile are shown in the table below.
Length of call
Cost on Ian’s bill
1 minute
7p
2 minutes
9p
3 minutes
11p
4 minutes
13p
The cost in pence is calculated as 2n + 5, where n is length of the call in minutes.
Write down the cost of:
(b)
(i)
a 5-minute call
(ii)
a 15-minute call.
The costs of some of Martin’s calls to Ian are shown in the table below.
Length of call
Cost on Martin’s bill
1 minute
4p
2 minutes
7p
3 minutes
10p
4 minutes
13p
Write down an expression for the cost in pence of an n-minute call from Martin to Ian.
6
8. Use alternate and corresponding angles to work out the size of each lettered angle in the
diagrams below. (The diagrams are not drawn accurately.)
9. Work out the size of each lettered angle in the diagrams below.
(a)
(c)
(b)
(d)
(e)
10. Use a ruler and protractor to draw an angle of 70º. Now use ruler and compasses to
construct the bisector of the angle. Leave all construction lines on your diagram.
Check with your protractor that the two angles formed are both 35º.
11. Using ruler and compasses, construct the right-angled triangle shown below.
12. Four types of quadrilateral are described on the left below. The quadrilaterals are drawn on
the right in a different order.
Match each description to the correct drawing.
(a)
Four right angles and four lines of symmetry.
1
2
(b)
Opposite sides parallel, opposite sides equal and no
symmetry.
lines of
3
>
(c)
(d)
Four equal sides, opposite angles equal and two lines
symmetry.
One pair of parallel sides.
4
of
>
13. A Bag contains a large number of green balls and one red ball. There are no other balls in
1
the bag. The probability of picking a red ball from the bag is
.
30
(a)
What is the probability of picking a green ball from the bag?
(b)
How many green balls are there in the bag?
14. Jason eats a packet of chocolate spangles every day. He keeps a record of the number of
chocolates in the packet every day for two months. His results are shown in the table below.
(a)
Estimate the probability that the next packet of spangles that Jason opens will have 10
or more chocolates in it.
(b)
How could Jason improve this estimate?
Number of chocolates
in packet
Number of
packets
Fewer than 10
22
10 or more
38
15. The table below shows the possible outcomes of rolling two dice.
First dice
Second
dice
1
2
3
1
1, 1
1, 2
1, 3
2
2, 1
2, 2
3
4
5
6
(a) Complete the table.
4
5
6
(b)
Calculate the probability of rolling:
(i)
two sixes
(ii)
a one and a six
(iii)
two even numbers
(iv)
one even number and one odd number
(v)
two numbers that are both greater than three
16. rolls a dice 300 times and records the score. The table shows his results.
Number on dice
Frequency
1
49
2
64
3
48
4
52
5
36
6
51
(a)
What is the theoretical probability of rolling a 5?
(b)
How many 5s would you expect Alex to get in 300 rolls of the dice?
(c)
Do you think his dice is biased? Give a reason for your answer.