Extra Revision For Block E Assessment
Exercise 1
Multiply the brackets and simplify
1
3a(2b + c) + 3ab + 4ac
2
4x(2y + 3z) + 3xy – 2xz
3
m(3p + q) + mq – mp
4
5a(2x + y) – 3ax – 2ay
5
6st + 3s(u – 2t)
6
5az + 2a(3y – z)
7
2x(3y + 4z) + 3x(y – 2z)
8
5s(2u + 5v) + 2s(u – 10v)
9
7m(2x + y) + 3m(y – 4x)
10
3a(4b + 2c) + a(c – 8b)
11
5x(y + 4z) + 2x(y – 10z)
12
4a(b + 3c) + 3a(b – 4c) – 7ab
13
x(x + 3) + x(x + 4)
14
x(x + 6) + x(x – 2)
15
2x(x + 3) – 3x(x + 1)
16
x(x² + 4x + 2) + x(x² + 5x + 7)
17
x(x² – 5x + 3) + x(x² + 8x – 5)
18
x(x² – 4x – 6) – (x² – 6x – 9)
19
x(x² + 6) – x(x² – 4x + 2)
20
x(x² – 3) + x(x² – 4x + 5)
21
x(x² + x – 4) – x(x² – 2)
22
x(2x² + 3x + 1) + x(3x² – 3x + 2)
23
2x(x² + 3x + 8) + 3x(x² + x – 4)
24
5x(2x² – 6x + 2) – 2x(4x² – 2x + 5)
25
3x(4x² – 2x + 1) + 5(x² + 3x – 2)
26
2x(7x² – 3) + 3(x² + 2x – 1)
27
4x(2x² – 3x + 1) – 2(x3 – 4) + 9x
28
5x(x² + 2x – 3) + x(x – 4) – 6x
29
4(2x² + 7x – 4) – 2x(4x + 3) + 16
30
x²(3x – 2) – 3x(x² – 2x) – 4x²
Exercise 2
If m = 2, t = –2, x = –3 and y = 4 work out the values of
1
2m2
2
(2m)2
3
2t2
4
(2t)2
5
(3y)2
6
m3 + 10
7
2x2 + 1
8
m2 + xt
9
my2
10
(mt)2
11
(xy)2
12
(xt)2
13
yx2
14
m(t + x)
15
y(m + x)
16
t(2m + y)
17
m2(y – x)
18
t2(x2 + m)
19
2𝑦 + 𝑡
3
20
2𝑡 + 𝑚
2
21
𝑥+𝑡
5
22
𝑦− 𝑡
𝑚
23
𝑦− 𝑚
𝑡2
24
𝑥2+ 𝑚
11
Exercise 3
Solve the following equations
1) 3(x + 2) + 2(x + 1) = 23
2) 5(a + 2) – 2(a + 3) = 19
3) 4(x + 3) + 3(x + 2) = 32
4) 8(b + 3) – 4(b + 4) = 12
5) 5(y + 1) + 3(y + 4) = 25
6) 4(c + 2) – 2(c + 5) = 14
7) 3(z + 4) + 2(z – 3) = 26
8) 5(t – 1) – 3(t + 2) = 1
9) 5(t + 2) + 3(t – 1) = 31
10) 6(u – 2) – 2(u + 4) = 8
11) 4(a + 1) + 3(a – 4) = 13
12) 4(x – 2) – 3(x + 4) = 4
13) 2(b + 1) + 4(b – 3) = 20
14) 5(t + 3) – (t – 6) = 29
15) 3x + 2(x + 1) = 3x + 12
16) 3(x – 1) = 2x – 2
17) 4x – 2(x + 4) = x + 1
18) 4(x + 2) = 3x + 10
19) 2x – 3(x + 2) = 2x + 1
20) 2(2x – 1) = x + 4
21) 5x – 2(x – 2) = 6 – 2x
22) 3(x – 1) = 2(x + 1) – 2
23) 3(x + 1) + 2(x + 2) = 10
24) 4(2x – 1) = 3(x + 1) – 2
25) 4(x + 3) + 2(x – 1) = 4
26) 5 + 2(x + 1) = 5(x – 1)
27) 3(x – 2) – 2(x + 1) = 5
28) 6 + 3(x + 2) = 2(x + 5) + 4
29) 5(x – 3) + 3(x + 2) = 7x
30) 5(x + 1) = 2x + 3 + x
31) 3(2x + 1) – 2(2x + 1) = 10
32) 4(2x – 2) = 5x – 17
33) 4(3x – 1) – 3(3x + 2) = 0
34) x + 2(x + 4) = –4
35) 7 – (2 – 3x) = 17
36) 3(t + 4) – 1 = 3 – (4t – 1)
37) 5(6 + y) – 10 = 9 – (2y + 3)
38) 3 – (2d – 5) = – (5d + 1)
39) 4(1 – 3y) = 7 – (4y – 5)
40) 5p – (1 – 2p) = 9 – (p – 8)
41) 7(2x + 1) = 5 – 4(2x – 3)
42) 5(x – 2) = 6 – 3(x + 2)
Exercise 4
Solve these equations:
1)
x
3
2
2)
4)
x
3
8
5) 4 
a
4
6) 7 
x
2
8) 9 
y
4
9)
7) 6 
x
2
5
3)
x
4
6
w
5
2
x4
3
10)
3
w6
4
11)
2d
 8
5
12)
5n
 20
6
13)
3x
 6
5
14)
4c
 4
7
15)
a 3

8 4
16)
3 m

5 10
17)
4a 3

5 8
18)
3p 4

4 7
19)
2
5
b
3
9
20)
4
2
z
9
3
21)
h 1
3
4
22)
y 5
2
5
23)
a6
3
2
24)
z2
 1
3
25)
2x  1
5
3
26)
3a  4
 1
5
27)
2a  1 3

2
5
28)
7d 5

2
2
29)
2  3h
5

3
6
30)
3  2a
2

4
3
31)
4x  5 3

6
4
32)
5  4y
3

2
5
33)
x  2 3 x

5
4
34)
a 1 a 1

2
3
35)
2x  1 2  x

6
3
36)
2 x  1 5x  1

3
7
Exercise 5
1
The area of each rectangle is given in cm². If the lengths of the sides are in centimetres, find the
value of x in each after setting up an equation rectangle.
b)
a)
5
Area = 35
c)
4
Area = 22
3
x +3
x +2
Area = 18
x -3
e)
d)
4
4x + 2 Area = 12
Area = 24
f)
½
2x - 1
3
Area = 7
3x + 2
Exercise 6
Factorise
1)
x2 + 5x
2)
x2 – 6x
3
7x – x2
4)
y2 + 8y
5)
2y2 + 3y
6
6y2 – 4y
7)
3x2 – 21x
8)
16a – 2a2
9
6c2 – 21c
10)
15x – 9x2
11)
56y – 21y2
3
2
12)
ax + bx + 2cx
2
13)
a b + 2ab
14)
abc – 3b c
15)
2a2e – 5ae2
16)
a3b + ab3
17)
x3y + x2y2
18)
6xy2 – 4x2y
19)
3ab3 + 3a3b
20)
2a3b + 5a2b2
21)
ax2y – 2ax2z
22)
ab – ac – a2
23)
x2 + xy – xz
24)
p3 – p2 + p
25)
xa + ya – za
26)
3a4 + 3a3 – 6a2
27)
2x3 – 4x2 + 6x
Exercise 7
Solve the following inequalities
1) 2x + 1 > 7
2) 2x + 1 ≥ 7
3) 3x – 2 > 10
4) y + 5 ≥ 1
5) 2y + 3 > 3
6) 5y – 1 ≥ –11
7) 4x + 5 > 17
8) 2x – 2 > 18
9) 3x – 1 < 11
10) 5y – 3 ≤ 27
11) 7y + 4 ≤ 4
12) 8y + 3 ≥ 59
13) 3t + 4 > 1
14) 6u + 14 < 2
15) 3v + 2 > –16
16) 5w + 1 ≤ –34
17) 2x + 7 ≥ 3
18) 4y – 1 ≤ –25
19) 2x + 3 > 11
20) 5x – 7 < 13
21) 7x – 8 ≥ 13
22) 6x + 5 ≤ 35
23) 3x + 4 ≥ 16
24) 2x + 1 ≥ 19
25) 5x + 7 < 32
26) 3x – 2 < 10
27) 4x – 3 > 29
28) 8x + 6 ≥ 38
29) 7x – 3 > 39
30) 3x + 12 ≤ 30
31) 2x + 6 < 15
32) 2x – 7 > 8
33) 3p + 1 > p + 7
Exercise 8 (non–calculator)
Work out
1) 3
2
2) 6
5) 23
6) 3
9) 12
10) 10
13) 8
2
2
3) 4 2
4) 7
3
7) 2 4
8) 5
14) 0
2
11) 9
2
2
2
2
12) 2 2
15) 25
16) 0
3
Exercise 9 (calculator)
Work out
1) 7
4
5) 28
5
2) 8
2
6
9) 5
13) 2143
4) 113
7
8) 43
3
7) 6
4
11) 51
6) 34
10) 13
6
3) 3
14) 327
3
4
3
12) 10
2
7
15) 591
16) 205
4
Exercise 10 (non–calculator)
Work out
1)
49
2)
25
3)
64
4)
9
5)
81
6)
4
7)
1
8)
16
27
11)
16
12)
3
1
100
15)
144
16)
3
1000
9)
3
8
10)
13)
4
1
14)
3
4
Exercise 11 (non–calculator)
Work out
1)
0  49
2)
0  81
3)
0  0009
4)
0 16
5)
0  0064
6)
0  0081
7)
1 44
8)
0  000025
9)
81000000 10)
49000000 11)
1 96
12)
160000
16)
13)
3
8000
14)
3
27000000 15)
4
250000
3
125000
Exercise 12
1
There are 10 coloured beads in a box. 1 is red, 2 are green, 3 are blue, and the rest yellow.
a) A bead is taken from the box and then replaced. This is repeated 60 times. How many
times would you expect to get a blue bead?
b) A bead is taken from the box and then replaced. This is repeated 75 times. How many
times would you expect to get a green bead?
c) A bead is selected from the box. It is blue. The bead is not put back. What is the probability
that the next bead selected is also blue?
2
There are only 3 possible outcomes to an experiment, namely A, B and C.
If Pr(A) = 0∙1 and Pr(B) = 0∙2, what is Pr(C)?
3
A card is selected at random from a normal pack of playing cards.
What is the probability of obtaining a face card?
4
There are 18 coloured beads in a box. 2 are pink, 3 are black, 4 are cream and the rest purple.
a) What is the probability of obtaining a purple bead when one is selected
at random?
b) A bead is selected at random and replaced 45 times.
How many times would you expect to get a pink bead?
c) A bead is selected at random and replaced 42 times.
How many times would you expect to get a black bead?
d) A bead is selected at random and replaced 54 times.
How many times would you expect to get a cream bead?
e) One bead of each colour is taken out.
What is the probability now of selecting at random a black bead?
f) Two beads of each colour are taken out.
What is the probability now of selecting at random a pink bead?
5
An ordinary die is thrown 60 times.
a) How many times would you expect to obtain a multiple of 3?
b) How many times would you expect to obtain a prime number?
6
There are only 3 possible outcomes to an experiment, namely A, B and C.
a) If Pr(A) =
1
1
and Pr(B) = , what is Pr(C)?
2
3
b) If all 3 outcomes are equally likely, what is Pr(C)?
c) If Pr(A) =
7
1
and B and C are equally likely, what is Pr(C)?
2
A letter is selected at random from the word PARALLELOGRAM.
What is the probability of selecting a letter which has a vowel next to it on both sides?
8 An experiment has probability 0∙3 of success. If the experiment is repeated 40 times, how
many times would you expect it to fail?
Exercise 13
In each question find the mean, median, mode and range:1) a) 2, 3, 5, 5
c) 3, 4, 5, 8, 12, 12, 14, 16
3) a) 6, 5, 3, 2, 6
b) 4, 4, 6, 10, 11, 15
d) 0, 0, 1, 1, 5, 9, 10, 10, 10, 16
b) 6, 3, 4, 6, 11
c) 9, 8, 9, 12, 7
d) 14, 15, 13, 11, 11, 19, 15
e) 22, 29, 27, 41, 32, 23, 22
f) 14, 15, 14, 15, 14, 12, 13, 16
4) a) 5, 4, 2, 5
b) 6, 3, 6, 9
c) 23, 18, 11, 11, 16, 17
d) 26, 28, 31, 23, 23, 37
e) 50, 45, 44, 45
f) 48, 56, 62, 68, 56, 52
g) 70, 73, 74, 76, 73, 72
Exercise 14
1
20 pupils were asked how many children were in their family.
Add a c x f column and find the mean and modal number of children.
No. of Children Frequency
1
2
2
4
3
5
4
7
5
2
In the same way add a c x f column and find the mean and mode for each of these
tables:2 No. Frequency
1
10
2
4
3
2
4
3
5
1
3 No. Frequency
1
3
2
1
3
3
4
5
5
8
4 No. Frequency
1
6
2
2
3
9
4
2
5
1
Exercise 15
1
A selection of schools was asked how many fifth year sections they had.
The table summarises their replies.
Number of
Number of schools
Cumulative
sections
frequency
(frequency)
a)
b)
c)
d)
4
3
5
5
6
8
7
10
8
7
Construct a cumulative frequency column.
How many schools were considered?
What is the modal number of fifth year sections?
What is the median number of sections?
2
A survey on house size was conducted in the village of Newton.
Residents were asked how many rooms their house had.
The results are shown in the table.
Number of
Number of houses
Cumulative
rooms
frequency
(frequency)
5
6
6
8
7
10
8
12
9
6
a) Construct a cumulative frequency column.
b) How many houses were examined?
c) What is the median number of rooms?
3
In a survey on the overuse of the car in the urban environment, a study
was made of the number of passengers in buses. Working to the nearest
10 passengers, a random sample of 70 buses produced the following table.
Number of
passengers
0
10
20
30
40
50
60
Number of buses
(frequency)
2
5
13
15
19
12
4
Cumulative
frequency
What is the median number of passengers.
4 In the fishing season a register is kept of the number of salmon caught by
each licensed angler. The results are shown in the table.
Number of
Number of anglers
Cumulative
salmon
frequency
(frequency)
1
5
2
6
3
12
4
8
5
4
a) Construct a cumulative frequency column.
b) How many anglers were questioned?
c) What is the median number of salmon caught.
Exercise 16
1) 1  1
1
2
2
3
2) 1  1
1
3
3
4
6) 3  2
5
1
1
6
4
10) 3 
1
5
4
15
14) 2  1
2
5
3
10
18)
5) 2  1
9) 2
13) 1  2
17) 1  2
1
3
1
4
1
3
3
8
1
2
4) 2  1
1
3
1
4
8) 1  1
3) 2  1
1
4
7) 1  1
1
4
1
4
1
6
3
4
3 7
4 16
11) 1  2
3
5
15) 3
4
8
1
5 15
16) 2  1
19) 2
2
1
2
9
3
20) 1  1
7
15
4
7
2
5
10
5
16
2
3
12) 2
1
9
1
4 16
1
5
1
10
2
3
3
4
Exercise 17
2
1
1
3
2
3
1
7)  3
5
3
1
1
13) 1  1
2
3
1
3
19) 1  3
5
4
3 2
25) 3 
4 5
1)
3
1
1
4
3
1
8) 1  3
2
2
1
14) 1  1
3
5
5
1
20) 1  3
7
2
1
2
26) 2  1
10
3
2)
2
1
3
2
2
4) 1  2
5) 2  3
5
2
4
3
4
3
5
1
1 4
9)
1
10)  3
11) 1 
7
4
8
5
4 5
3
1
3
1
1
1
15) 1  1
16) 1  1
17) 3  1
4
7
5
4
5
4
1
2
1 2
7 3
21) 2  2
22) 1 
23) 1 
4
3
8 3
9 8
2
1
1
7
1 3
27) 2  1
28) 1  1
29) 1 
5
9
5
8
9 5
3)
5
6
2 5
12) 1 
5 7
3
3
18) 3  1
4
5
1 4
24) 2 
12 5
2 6
30) 2 
9 25
6) 3  1
Exercise 18
7
4
1) 1  5
2) 2  7
8
5
2 4
1
1
6) 2 
7) 3  4
3 5
2
5
2
2
2
2
11) 1  2
12) 2  1
3
9
9
3
1
5
1
7
16) 3  2
17) 3  1
7
14
5 25
1
3
7
1
21) 1  1
22) 1  2
15 5
8
2
4
2
1
4
26)
2
27) 2  2
9
3
10
5
3 2
3) 1 
5 3
2 1
8) 1 3
3 3
1
2
13) 3  1
3
3
4
5
18) 2  1
7
7
1 3
23) 1 
8 4
2 8
28) 2 
5 15
4
1
3
5
5
1
1
9) 1  2
2
4
2
1
14) 4  1
5 10
19
2
19) 1  1
26 13
1 3
24) 1 
20 5
1 3
29) 2 
4 10
4)
5) 6  1
3
5
1
1
10) 2  1
4
2
1
3
15) 4  3
6
4
2
25
20) 1  1
17
51
3 9
25) 3 
5 10
7
1
30) 1  4
8
6