Mathsclub.pptx

Adding and Subtracting Decimals
ANSWERS
a) 0.5
b) 1.2
c) 0.8
d) 1.3
e) 1.5
a) 1.47
b) 1.28
c) 1.66
d) 0.97
e) 1.68
•
a) 31.44
b) 70.81
c) 39.46
d) 34.15
e) 50.8
•
a) 0.45
b) 0.54
c) 0.49
d) 0.71
e) 0.7
•
a) 2.94
b) 39.02
c) 67.25
d) 77.03
e) 54.11

Adding and Subtracting Fractions
a) 7/8
b) 8/12
c) 7/9
d) 7/10
e) 2/3
a) 11/12
b) 7/10
c) 8/15
d) 16/12 or 1 ¼
e) 11/24
a) 1 7/12
b) 1 5/56
c) 29/30
d) 29/52
e) 1 1/10
a) 5/8
b) 5/12
c) 1/3
d) 2/5
e) 1/2
a) 7/20
b) 8/21
c) 23/36
d) 9/22
e) 71/126

Adding and Subtracting Decimals
Answers
1.
a)0.5
b)1.2
c)0.8
d)1.3
e) 1.5
2.
a)1.47
b)1.28
c)1.66
d) 0.97
e)1.68
3.
a)31.44
b)70.81
c) 39.46
d)34.15
e)50.8
4.
a)0.45
b)0.54
c) 0.49
d)0.71
e)0.7
5.
a)2.94
b)39.02
c) 67.25
d)77.03
e)54.11

Direct Proportion
1. If A is directly proportional to B, write an equation in the form A=kB linking the two variables
if when A= 8 B= 4.
2. All of the variables below are directly proportional, write an equation linking them:
1. V= 12 when M =4
2. T= 5 when S=1
3. Y= 34 when x=2
4. H=48 when M=4
5. P= 5 when N=10
3. B is directly proportional to C, when B is 18 C is 27.
1. Write an equation linking B and C
2. Find B when C= 66
3. Find C when B = 30
4. Z is directly proportional to Y, when Z =55, Y=5
1. Write an equation linking Z and Y
2. Find Y when Z = 77
3. Find Z when Y=0.1
5. N is directly proportional to L, when N=1.8 L =0.6
1. Write an equation linking N and L
2. Find L when N= 3.2
3. Find N when L=0.5
Answers
1.A=2B
2.
1.V=4M
2.T=5S
3.Y=17X
4.H=12M
5.N=2P
3.
1.C=1.5B
2.B=44
3.C=45
4.
1.z=11y
2.y=7
3.z=1.1
5.
1.N=3L
2.L=1.2
3.N=1.5

Bidmas
A)
1. (3 + 3 ) x 4
2. 4 x 2 – 5
3. (5 + 7) ÷ 6
4. 5 x 3 + 5
5. (9 – 4 ) + 5
6. 1 + 1 – 1
7. 2 x (15 – 2)
8. (5 x 4 ) + 2
9. (8 + 2 ) ÷ 10
10. (21 x 1 ) – 2
B)
1.(1 + 14) – (5 x 3 )
2.(10 + 6 ) ÷ (4 x 2)
3.(1 + 2 ) x (6 – 3)
4.(2 x 6 ) – (14 ÷ 2)
5.(7 x 2) ÷ ( 20 – 6)
6.(3 x 10) – (2 x 2)
7.(9 x 5) – ( 2 x 10)
C)
1. (3 x 3 – 4 ) x (2 + 2)
2. 2 x (13 – 4) – (23 ÷ 23)
3. 3 x (1 + 4) – (5 x 2)
4. 4 x (3 + 2) – ( 24 – 5)
5. 7 x ( 4 ÷ 2 ) ÷ ( 3 x 5 -1 )
6. ((9 + 7 x 3 ) ÷ 10) – 1
A.
1) 24
2) 3
3) 2
4) 20
5) 10
6) 1
7) 26
8) 22
9) 1
10)19
B.
1) 0
2) 2
3) 9
4) 5
5) 1
6) 26
7) 25
C.
1) 20
2) 17
3) 5
4) 1
5) 1
6) 2

Factors and HCF
1) Find all the factors of the following numbers:
1) 20
2) 24
3) 27
4) 32
5) 40
6) 50
7) 56
8) 120
9) 200
2) 2 only has 2 factors (1 and 2), how many numbers can you find between 1 and 30 which have exactly 2
factors? (these are called prime numbers)
3) Find the highest common factors of the following pairs of numbers:
1) 18 and 54
2) 25 and 45
3) 12 and 18
4) 27 and 108
5) 30 and 75
4) Find the HCF of these pairs of numbers:
1) 90 and 450
2) 96 and 480
3) 39 and 195
ANSWERS
1.
1.1,2,4,5,10,20
2.1,2,3,4,6,8,12,24
3.1,3,9,27
4.1,2,4,8,16,32
5.1,2,4,5,8,10,20,40
6.1,2,5,10,25,50
7.1,2,4,6,7,8,14,28,56
8.1,2,3,4,5,6,10,12,20,24,30,40,60,120
9.1,2,4,5,10,20,40,50,100,200
2. 2,3,5,7,11,13,17,19,23,29 (10 of them)
3.
1.18
2.5
3.6
4.27
5.15
4.
1.90
2.96
3.39

Factor Trees
1. Draw factor trees for the following numbers:
a) 20
b) 24
c) 48
d) 90
e) 81
f) 50
g) 75
h) 120
i) 200
j) 1800
2. Using your factor trees from question 1, write the numbers as products of
their prime factors .
Answers
1.
2.
a)22x5
b)3 x 23
c)3 x 24
d)2 x 32 x 5
e)34
f)2 x 52
g)3 x 52
h)23 x 3 x 5
i)23 x 52
j)23 x 32 x 52

Directed Numbers •ANSWERS
1) -13
2) 12
3) -5
4) 10
5) 14
6) -1
7) -11
8) -1
9) 7
10)-7
1) -17
2) -24
3) -23
4) -24
5) -9
6) -8
7) 8
8) -12
9) -14
10)-9
1) 17
2) -5
3) 1
4) 8
5) -10
6) 23
7) 26
8) 36
9) 17
10) 16

Directed Numbers 2
1) I am £250 into my overdraft () but then I get paid £535, how much
will I have in my bank account?
2) The temperature at the North Pole is -17°C; luckily the temperature in
my living room is 40°C warmer than that, what is the temperature in my
living room?
3) I have £32 and each month for 4 months I have to pay £15 to my
mobile phone, if I don’t put any money into my account, how far will I
be into my overdraft?
4) I jump out of a plane 125m above the ocean, I travelled 191m before I
stop, how far am I from the surface of the water?
5) I am playing air hockey with my friend, because I am amazing I agree
start on -9 points, we play first to 14, how many points do I need to
score?
1. 285
2. 23
3. -28
4. 66
5. 23

Equivalent Fractions
2.
a)4
b)15
c)12
d)20
e)60
f)8
g)26
h)32
i)120
j)15
k)64
l)154
m)125
n)400
o)615
p)9720

Ratio
1. There are 10 girls and 15 boys in a class, what is the ratio of girls to boys in its simplest
form?
2. There are 14 cats and 16 dogs in an animal shelter, what is the ratio of cats to dogs in its
simplest form?
3. There 22 caramels and 55 fudges in a bag of sweets, what is the ratio of caramels to fudges
in its simplest form?
4. Simplify these ratio to their simplest forms:
a) 48:60
b) 45:75
c) 63:108
d) 25:40:80
e) 24:56:96
f) 120:180:600
g) 320:400:440
5. Archie and Charlie share their Thomas the tank engine toys in the ratio 1:4, how many do
they each get if they have:
a. 10 toys b.30 toys c.45 toys
6. Tom and Jerry share sweets in the ratio 2:3, how many do they each get if they share:
a. 20 sweets b.30 sweets c.55 sweets
7. Sue and Linda share some money in the ratio 3:7, how many do they each get if they share:
a. £30 b.£60 c.£90
8. Mike, Dave and Henry share some little bits of blue tack in the ratio 1:2:3, how many do
they each get if they share:
a. 60 pieces b.72 pieces c.300 pieces
ANSWERS
1. 2:3
2. 7:8
3. 2:5
4.
a) 4:5
b) 3:5
c) 7:12
d) 5:8:16
e) 3:7:12
5.
a) 2 and 8
b) 6 and 24
c) 9 and 36
6.
a) 8 and 12
b) 12 and 18
c) 22 and 33
7.
a) 9 and 21
b) 18 and 42
c) 27 and 63
8.
a) 10 and 20 and 30
b) 12 and 24 and 36
c) 50 and 100 and
150

Finding Percentages
1) Some percentages I can find easily by doing a single sum, what single sums can I
do to find:
a. 10% b. 50% c.25%
2) If I know 10% how can I find:
a. 5% b. 1% c. 20 % d. 90%
3) If I know 50% how can I find:
a. 5% b. 25%
4) Find:
a. 30% of 250 b. 40% of 500 c. 15% of 220 d. 75% of 84
5) Find:
a. 35% of 440 b. 65% of 450 c. 16% of 220 d. 82% of 96
6) Find:
a. 94% of 640 b. 8% of 520 c. 27% of 220 d. 53% of 96
7) Compare you methods for the questions above with a partner, where they the
same ?
ANSWERS
1.
a) divide by 10
b) divide by 2
c) divide by 4
2.
a) half the answer
b) divide by 10
c) double
d) multiply by 9 or subtract
10% from original
quantity
3.
a) divide by 10
b) half 50%
4.
a) 75
b) 200
c) 33
d) 63
5.
a) 154
b) 292.5
c) 35.2
d) 78.72
6.
a) 601.6
b) 41.6
c) 59.4
d) 50.88

Equivalent Fractions
Answers
2.
a)4
b)15
c)12
d)20
e)60
f)8
g)26
h)32
i)120
j)15
k)64
l)154
m)125
n)400
o)615
p)9720

HCF and LCM
Find the Highest Common Factor
of these numbers:
•18 and 30
•15 and 20
•16 and 24
•12 and 36
•20 and 30
•28 and 70
•39 and 65
•38 and 57
Find the Lowest Common
Multiple of these numbers
•6 and 7
•4 and 6
•5 and 8
•10 and 4
•16 and 5
•14 and 21
•2.2 and 5
•0.4 and 7
1.42
2.12
3.40
4.20
5.80
6.42
7.55
8.14
1.6
2.5
3.8
4.12
5.10
6.14
7.13
8.19

Indirect Proportion
1. If A is indirectly proportional to B and when A= 5 B= 6 :
1.Find k
2.Write an equation linking A and B
3.Find A when:
1. B=3
2.B=15
4.Find B when:
1. A=1
2.A=-3
2. If A is indirectly proportional to B and when A= 7 B= 12 :
1.Find k
3.Find A when:
1. B=4
2.B=6
4.Find B when:
1. A=10
2.A=2
3. If A is indirectly proportional to B and when A= -4 B= 10 :
1.Find k
3.Find A when:
1. B=-8
2.B=10
4.Find B when:
1. A=-1
2.A=-0.5
4. If A is indirectly proportional to B and when A= 24 B= 0.5 :
1.Find k
3.Find A when:
a.B=6
b.B= -3
4.Find B when:
a.A= -2
b.A= 100
1.
1.k=30
2.A x B=30
3.
1. A=20
2.A=2
4.
1. B=30
2.B=-10
2.
1.k=84
2.A x B=84
3.
1. A=21
2.A=14
4.
1. B=8.4
2.B=42
3.
1.k=-40
2.A x B=-40
3.
1. A=5
2.A=-4
4.
1. B=40
2.B=80
4.
1.k=12
2.A x B=12
3.
1. A=2
2.A=-4
4.
1. B=-6
2.B=0.12

Fractions, Decimals and Percentages
1.
a) 75%
b) 10%
c) 20%
d) 35%
e) 42%
2.
a) 0.7
b) 0.25
c) 0.3
d) 0.15
e) 0.05
3.
a) 60%
b) 70%
c) 8%
d) 27%
e) 80%
4.
a) ¼
b) 33/100
c) 51/100
d) 4/5
e) 1/5
5.
a) 0.4
b) 0.9
c) 0.74
d) 0.03
e) 0.05
6.
a) 7/10
b) 3/5
c) 11/50
d) 7/20
e) 21/50

Limits
1) These numbers have been rounded
to the nearest 10, write down the
largest and smallest values they
could be:
1) 50
2) 80
3) 110
2) These numbers have been rounded
to the nearest whole number, write
down the upper and lower limits:
1) 3
2) 17
3) 23
4) 100
5) -3
3) These lengths have been rounded to
the nearest 10th of a cm, write the
upper and lower limits:
1) 12.5cm
2) 21.7cm
3) 35.8cm
4) 52.1cm
5) 80.4cm
4) A field is 100m wide and 120m long, both lengths have been
rounded to the nearest metre.
a) Find the perimeter and area of the field if these
measurements are accurate
b) Find the largest and smallest possible perimeter
c) Find the largest and smallest possible area.
5) A rectangle has it’s area rounded to the nearest whole number,
it becomes 40cm2. One side of the rectangle is exactly 10cm; find
the maximum and minimum lengths the other length could have.
6) Two lengths of wood are stuck together and their combined
length is rounded to the nearest mm and it is 14.9cm, one length
is rounded to the nearest mm and is 7.1cm. Find the minimum
and maximum length of the other length.
Answers
1.
1.45 and 54.9999999..
2.75 and 84.999....
3.105 and 114.9999...
2.
1.2.5 and 3.4999...
2.16.5 and 17.4999...
3.22.5 and 23.49999...
4.99.5 and 100.4999..
5.-3.499999 and -2.5
3.
1. 12.45 and 12.55
2.21.65 and 21.75
3.35.75 and 38.5
4.52.05 and 52.15
5.80.35 and 80.45
4.
a) p=44om and area= 12000m2
b) largest= 442m smallest=438m
c) largest= 12110.25m2
smallest=11890.25m2
5. smallest- 3.95cm largest- 4.05cm
6. largest- 7.9cm smallest- 7.7cm

Multiples
A. List the first 5 multiples of:
1. 5
2. 7
3. 12
4. 14
5. 19
B. What is the:
1. 9th multiple of 8
C. List 3 numbers which are in:
1. 3 and 4 times tables
D. What is the lowest common multiple of:
1. 5 and 6
2. 7 and 8
3. 4 and 8
4. 9 and 6
5. 10 and 6
E. What is the lowest common multiple of:
1. 13 and 5
2. 15 and 12
3. 16 and 10
4. 14 and 21
5. 21 and 70
a) 5,10,15,20,25
b) 7.14.21.28.35
c) 12,24, 36, 48, 60
d) 14,28,42,56,70
e) 19,38,57,76,95
a) 72
b) 42
c) 144
d) 110
e) 65
f) 65
a) 12,24,36
b) 15,30,45
c) 20,40,60
d) 18,36,54
e) 60,120,180
a) 30
b) 56
c) 8
d) 18
e) 30
a) 65
b) 60
c) 80
d) 42
e) 210

Multiplying and dividing fractions
Answers
1.
a)3/32
b) 5/48
c)1/9
d)4/25
e)7/16
2.
a)65/18
b)11
c) 8
d)1
e)1/2
3.
a) 4/24 or 1/6
b)20/12 or 5/3
c)1
d)1
e)24/42 or 4/7
4.
a)39/30 or 13/10
b)22/18 or 11/9
c) 32/36 or 8/9
d)63/28
e)50/16 or 25/8

Multiplying and dividing decimals
1 a) 0.8 x 7 =
b) 0.5 x 7 =
c) 0.1 x 6 =
d) 0.6 x 4 =
e) 0.3 x 3 =
2 a) 0.2 x 0.5 =
b) 0.4 x 0.7 =
c) 0.8 x 0.1 =
d) 0.9 x 0.9 =
e) 0.6 x 0.1 =
3 a) 1.9 x 0.3 =
b) 1.6 x 0.5 =
c) 1.6 x 0.5 =
d) 1.7 x 0.2 =
e) 1.3 x 0.7 =
4 a) 5.4 x 0.11 =
b) 5.2 x 0.97 =
c) 8.3 x 0.73 =
d) 4.6 x 0.11 =
e) 8.2 x 0.75 =
Multiplying
Dividing
1
a) 3.2 ÷ 4
b) 4.8 ÷ 8
c) 7.2 ÷ 9
d) 2.4 ÷ 6
e) 1.8 ÷ 3
2
a)5.6 ÷ 0.7
b)6.3 ÷ 0.7
c)2.7 ÷ 0.3
d)4.9 ÷ 0.7
e)2.8 ÷ 0.7
3
a) 1.65 ÷ 0.15
b) 24 ÷ 0.12
c) 27.3 ÷ 1.3
d) 0.03 ÷ 0.005
e) 0.99 ÷ 0.0009
Answers
1.
a) 5.6
b) 3.5
c) 0.6
d) 2.4
e) 0.9
2.
a) 0.1
b) 0.28
c) 0.08
d) 0.81
e) 0.06
3.
a)0.57
b)0.8
c) 0.75
d)0.34
e)0.91
4.
a)0.594
b)5.044
c) 6.059
d)0.506
e)6.15
1.
a)0.8
b) 0.6
c)0.8
d)0.4
e)0.6
2.
a)8
b)9
c)9
d)7
e)4
3.
a) 11
b)200
c)21
d)6
e)1100

Ordering Fractions
ANSWERS
1. 1/4 3/8 ½ and 4/8 3/4
2. 2/5 ½ 3/5 and 6/10 2/29
3. 1/3 5/12 1/1 4/6 3/4
4. 1/4 1/2 2/3 5/6 7/8
5. 1/4 2/5 1/2 6/10 3/4
6. 1/3 4/9 1/2 2/3 5/6
7. 2/6 1/4 5/12 2/3 7/9
8. 2/7 2/4 5/8 11/14 3/2

Ordering Decimals
1. For each pair of numbers say
which is bigger by adding > or <.
a) 0.2 0.7
b)0.3 0.1
c)0.7 0.9
d)0.3 0.4
e)0.6 0.3
f)0.24 0.2
g)0.3 0.39
h)0.4 0.35
i)0.9 0.85
j)0.22 0.3
2. Try these:
a) 0.04 0.05
b)0.02 0.09
c)0.12 0.02
d)0.04 0.23
e)0.4 0.04
3. These are trickier:
a) 2.34 0.09
b)4.49 4.0003
c)5.01 5.1
d)6.32 6.325
e)7.436 7.43
f)8.35 8.345
4. Put these decimals in ascending order (smallest to
biggest):
a. 0.2 0.3 0.15
b. 0.7 0.64 0.072
c. 0.85 0.9 0.425
d. 0.734 0.7345 0.7335
e. 6.234 6.009 6.4
a) <
b) >
c) <
d) <
e) >
f) >
g) <
h) >
i) >
j) <
•
a) <
b) <
c) >
d) <
e) >
f) <
•
a) >
b) >
c) <
d) <
e) >
f) >
•
a) 0.15 0.2 0.3
b) 0.072 0.64 0.7
c) 0.425 0.85 0.9
d) 0.7335 0.734
0.7345
e) 6.009 6.234 6.4

Percentage Increase/Decrease
1. Explain how you would use a calculator to increase
an amount by a given percent.
2. Increase the following amounts by 42%
a)£225
b) £306
c)£125
d)£448
e)£512
3. A TV costs £120, how much will it cost if its price is
increased by:
a) 12%
b)31%
c)55%
d)62.5%
e)99.9%
4. Simon puts £70 in a bank, each year the money in
his bank increase by 5.5%, how much does he have
in:
a) 1 year
b)2 years
c)5 years?
5. Explain how you would use a calculator to
decrease an amount by a given percent.
6. Decrease the following amounts by 28%
a) £225
b) £306
c) £125
d) £448
e) £512
7. A TV costs £120, how much will it cost if its
price is decreased by:
a) 19%
b) 32%
c) 79%
d) 73.5%
e) 42%
8. A car bought for £6, 500 depreciates in
value by 12.5% each year, how much will it
be worth after:
a) 1 year
b) 2 years
c) 5 years?
ANSWERS
1.
2.
a) 319.5
b)434.52
c)177.5
d) 636.16
e)727.04
3.
a)134.40
b)157.20
c)186
d)195
e)239.88
4.
a)73.50
b) 77.91
c)91.49
5.
6.
a)162
b)220.32
c)90
d) 322.56
e)368.64
7.
a)97.20
b) 81.60
c)25.20
d)31.80
e)69.60
8.
a)5687.50
b) 4976.56
c)333.91

Rounding to Significant Figures
Main
1. When you are rounding to decimal
places you start counting after the
decimal point, but with significant
figures you start counting at the
first non zero number
2.
i. 1000 1500 1460
ii. 200 160 157
iii. 40 37 37.1
iv. 6 6.1 6.09
v. 0.006 0.0064 0.00640
3.
a) 4.7
b) 0.058
c) 0.19
d) 540

Rounding to Decimal Places
a) 1.463884266
b) 1.572660902
c) 3.783345228
d) 6.3931313
e) 0.640368898
f) 0.326119942
g) 4.249504359
h) 4.44692939
i) 1.447852851
j) 0.069143754
Work out the following on a calculator and give
the answer to 2 decimal places;
a) 3.104 x 5.938
b) 2.99 x 8.82
c) 7.1537÷ 3.111
d) 14.772
•Round the following numbers to a) 1 decimal place b) 2 decimals places c) 3 decimal places
ANSWERS
a) 1.5 1.46 1.464
b) 1.6 1.57 1.573
c) 3.8 3.78 3.783
d) 6.4 6.39 6.393
e) 0.6 0.64 0.640
f) 0.3 0.33 0.326
g) 4.2 4.25 4.250
h) 4.4 4.45 4.447
i) 1.4 1.45 1.448
j) 0.1 0.07 0.069
•
a) 18.43
b) 26.37
c) 2.30
d) 219.15
e) 3.67

Reverse Percentages
1. What would you multiply an amount by to
increase it by:
a) 15%
b)25%
c)4%
d)0.5%
e)13.5%
2. Find the original prices of these prices that
have been increased by the given percentage:
a) Cost= £49.5 after 10% increase
b)Cost= £74.75 after 15% increase
c)Cost= £61 after 22% increase
d)Cost= £104 after 30% increase
e)Cost= £120 after 50% increase
3. I have £252 in my bank account; this is due to
me earning 5% interest on what I originally had
put in. How much money did I have originally
in my bank account?
4. What would you multiply an amount
by to decrease it by:
a) 15%
b)25%
c)4%
d)0.5%
e)13.5%
5. Find the original prices of these items
that have been decreased by the given
percentage:
a) Cost= £72 after 10% decrease
b) Cost= £93.5 after 15% decrease
c) Cost= £39 after 35% decrease
d) Cost= £4 9fter 40% decrease
e) Cost= £67.50 after 55% decrease
6. A Cars value has dropped by 11.5% it
is now worth £3053.25, what was it
worth when it was new?
Answers
1.
a) 1.15
b) 1.25
c) 1.04
d) 1.005
e) 1.135
2.
a) 45
b) 65
c) 50
d) 80
e) 80
3. 240
4.
a) 0.85
b) 0.75
c) 0.96
d) 0.995
e) 0.865
5.
a) 80
b) 110
c) 60
d) 15
e) 150
6. 3450

Standard Form Answers
1. a,e,f,g
2.
1.474000000
2.190
3.8620000
4.64000
5.35000
6.66300000
7.909000000
8.6000
9.8710000000
3.
1.0.000000000136
2.0.00000000095
3.0.00000638
4.0.0000000796
5.0.0000056
6.0.00000000543
7.0.000000000632
8.0.00048
9.0.000161
4.
1.8.3 x 103
2.4.4 x 105
3.1.35 x 107
4.9.87 x 107
5.3.4 x 10-5
6.9.301 x 10-5
7.4.3 x 10-4

Two Brackets
Answers
1.
1.x2+12x+35
2.x2+10x + 21
3.x2 + 5x + 6
4.x2 + 6x + 8
5.x2 + 9x + 8
2.
1.x2 – 49
2.x2 + x – 12
3.x2 + 8x -20
4.x2 -17x + 72
5.x2 -10x + 24
3.
1.6x2+15x – 9
2.8x2 + 76x -40
3.9x2-71x – 8
4.6x2 – 48x + 42
5.9x2 – 37x + 4
4.
1.6x2 + 12x – 48
2.28x2 + 21x -49
3.12x2 -36x – 48
5. 15x2 + 10x – 25
Answers
1.
1. x2+12x+35
2. x2+10x + 21
3. x2 + 5x + 6
4. x2 + 6x + 8
5. x2 + 9x + 8
2.
a) x2 – 49
b) x2 + x – 12
c) x2 + 8x -20
d) x2 -17x + 72
e) x2 -10x + 24
3.
a) 6x2+15x – 9
b) 8x2 + 76x -40
c) 9x2-71x – 8
d) 6x2 – 48x + 42
e) 9x2 – 37x + 4
4.
a) 6x2 + 12x – 48
b) 28x2 + 21x -49
c) 12x2 -36x – 48
5. 15x2 + 10x – 25

1. Find x
a) 2x + 4 = 3x + 1
b) 10x + 8 = 4x + 38
c) 7x – 3 = 3x +25
d) 11x + 5= 9x + 21
e) 4 + 11x = x + 9
2. Solve these equations
a) 2(3x+4)= 2(4x-1)
b) 2(3x-4)= 4(x + 3)
c) 4(3x + 2) = 8(2x -1)
d) 2(4x+2) = 4(3x-1)
e) 4(3x+2)=10(x+4)
3. Solve these equations by multiplying out
brackets and simplifying:
a) 3(x +2) + 5(x-1)= 25
b) 2(2x + 1) + 6(x + 3)= 70
c) 4(3x + 3) – (x + 5)= 92
Answers
1.
a)x=3
b)x=5
c)x=7
d)x=8
e)x=0.5
2.
a)x=5
b)x=10
c)x=3
d)x=2
e)x=11
3.
a)x=3
b)x=5
c)x=9

Algebraic Fractions
Answers
1.
a)x=7
b)x=42
c)x=2
d)x=12
2.
a)x=10
b)x=3
c)x=28
d)x=45
3.
a)x=5
b)x=11
c)x=4
d) x=9
Answers
3.
a)x=12
b)x=5
c)x=11
4.
a) x=10
b) x=5
c) x=2
d) x=7
e) x=6
f) x=4

Brackets
1. Remove the brackets from these expression by multiplying them out:
a) 2(x +5)
b) 6(2x +7)
c) 8(4x -2)
d) 5(3x -9)
e) 2(4 -2x)
f) 8(3 – 4x)
g) x(x + 3)
h) x(2x +9)
i) x(4x -7)
j) 2x(9 -5x)
2. Multiply out the brackets:
a) x(3x2 + 5)
b) 2x(5x2 + 6)
c) 5x(3x3 - 7)
3. Multiply out the brackets and simplify:
a) 3(x + 4) + 4(x-6)
b) 7(x + 7) + 5(2x-8)
c) 3(4x + 1) + 2(6x-9)
d) 5(5x - 4) - 4(3x-6)
e) 2(13 -4x) - 9(x+ 6)
ANSWERS
1.
a) 2X + 10
b) 12X + 42
c) 32X – 16
d) 15X – 45
e) 8 – 4X
f) 24 – 32X
g) X2 + 3X
h) 2X2 + 9X
i) 4X2 – 7X
j) 18X-10X2
2.
a) 3X3 + 5X
b) 10X3 + 12X
c) 15X4-35X
3.
a) 7X - 12
b) 17X + 9
c) 24X - 15
d) 13X + 4
e) 28-17X

Collecting like terms
1. Simplify
a) 10a + 4a
b)2b + 7b
c) 3a + a + 4a
d)11b – 4b
e) 14b – 5b + 4b
f) 3a – 6a + a
2. Simplify
a) 10a + 4b –a +5b
b)8a + 5a +5b – 3b
c) 12b – 7a + 3b +a
d)2b – 8b –a + 9a
e) -13b + 4a -5b -4a
f) 11a + 8b + 2c + 6a + 3b -2c
g) 6b + 4b –a +6c + 5a – 4c
h)7c + 4b- 3b + a + 10c – 5a
i) 10a + 4b + 7a + 10b – 17a – 14b
j) 5b + 4c + 18c – 22a + z
Answers
1.
a) 14a
b) 9b
c) 8a
d) 7b
e) 13b
f) -2a
2.
a) 9a + 9b
b) 13a + 2b
c) 15b – 6a
d) 8a – 6b
e) -18b
f) 17a + 11b
g) 4a + 10b + 2c
h) -4a + b + 17c
i) 0
j) 5b + 22c -22a + z

Curved Graphs
9 5 5 9 17
13 6 1 -2 -3
-4 -8 -6 2 16
-2,9 -1,5 0,5 1,9 2,17
-2,13 -1,6 0,1 1,-2 2,-3
-2,-4 -1,-8 0,-6 1,2 2,16

Factorising
A) Factorise the following
completely:
1. 10A + 15
2. 24A + 36
3. 16A - 64
4. 15B2 + 20B
5. 14B2 + 49B
6. 9B2 + 72B
7. 33B2 - 44B
8. 2C3 + 8C
9. 5C4 + 40C
10.10C3 + 8C
B) Factorise the
following
completely:
1. 9AB + 6A
2. 16AB – 4B
3. 30A2B + 24AB
4. 10AB2 – 15B2
5. 12ABC + 20 AB
6. 28A2BC + 14ABC
7. 4AB – 8A + 16B
8. 15A – 18B – 21AB
9. 9B3 + 18BC + 30AB
10. ABC-10AB +AB
ANSWERS
A.
1. 5(2A + 3)
2. 12 (2A + 3)
3. 16(A-4)
4. 5B(3B+4)
5. 7B(2B+7)
6. 9B(B+8)
7. 11B(3B-4)
8. 2C(C2+4)
9. 5C(C3+8)
10.2C(C2+4)
B.
1. 3A(3B+2)
2. 4B(4A-1)
3. 6AB(5A+4)
4. 5B2(2A-3)
5. 4AB(3C+5)
6. 14ABC(2A+1)
7. 4(AB-2A+4B)
8. 3(5A-6B-7AB)
9. 3B(3B2+6C+10
A)
10.AB(C-10+1)

Finding the gradient
1) Find the gradient between the points:
a) (3,5) and (4,7)
b) (5,9) and (7,17)
c) (4,6) and (5,7)
d) (1,4) and (4,19)
e) (0,11) and (4,23)
2) Find the gradient between these points:
a) (2,5) and (3,-3)
b) (2,8) and (3,2)
c) (4,8) and (8,4)
d) (8,15) and (6,33)
e) (7,12) and (4,42)
f) (4,8) and (3,14)
a) Find the gradient between these points:
a) (3,5) and (4,5.5)
b) (5,9) and (7,8)
c) (4,6) and (5,6.75)
d) (1,4) and (4,4.75
e) (0,11) and (4,11.4)
Answers
1.
a)2
b)4
c)1
d)5
e)3
2.
a)-8
b)-6
c)0
d)-1
e)-10
f)-6
3.
a)0.5
b)-0.5
c)0.75
d)0.25
e)0.1

A) Isaac Newton’s second law of motion states F=ma (force= mass x acceleration)
1.Find F if:
a.M=10 and a=5
b.M=12 and a=12
c.M=0.5 and a=11
2.Find a if:
a.F=100 and M=20
3.Find m if:
a.F=36 and a=12
B) Density equal volume divided by mass
1.Write a formula for density
a.Find D if
i.M=10 and v= 40
ii.M=12 and v=72
iii.M=5 and v=90
b.Find M if:
i.D=4 and v=52
c.Find v if:
i.D=8 and m=11
C) Electrical power (p) is equal to voltage (V) squared divided by resistance (r)
1.Write a formula for power
2.Find p if:
a.V= 4 and r=8
b.V=9 and r=3
3.Find r if:
a.P=16 and v=8
4.Find v if:
a.P=20 and r=5
Formulae Answers
A.
1.
a) 50
b) 144
c) 6.5
2.
a) 5
3.
a) 3
B.
1. D=V/M
2.
a) 4
b) 6
c) 18
3.
a) 13
4.
a) 88
C.
1. P=Z2/R
2.
a) 2
b) 27
3.
a) 4
4.
a) 10

Inequalities
ANSWERS
1.
1)x>6
2)x>9
3)x≥11
4)x≥2
5)x<12
6) x≤20
7)x≤20
8)x<20
2.
1)6 <x ≤ 10
2)9< x <16
3)11 ≤ x <15
4) 2 ≤ x ≤ 8

Laws of indices
1. Simplify:
a) A2 x A
b) A4 x A2
c) A8 x A2
d) 3A9 x A3
e) 4A2 x 5A1
2. Simplify:
a) A10 ÷ A
b) A21 ÷ A7
c) A20 ÷ A4
d) 9A12÷ 3A6
e) 12A6 ÷ 4A4
3. Simplify:
a) (A2)4
b) (A3)3
c) (A2)6
d) (2A9)2
e) (3A4)3
4. Simplify:
a) A0
b) B0
c) 990
d) 520
e) 0.0610
5. Simplify:
a) A-4
b) A-6
c) A-2
d) 2A-4
e) 9A-3
6. Simplify fully:
a) 25A4 ÷ 5A7
b) 3A9 x 2A-3
c) (A2)6 x (2A2)2
d) (2A3)8 ÷ (2A4)6
e) (A2)-6
ANSWERS
1.
a)A3
b)A6
c)A10
d) 3A12
e)20A3
2.
a)A9
b)A14
c)A16
d) 3A6
e)3A2
3.
a) 1
b)1
c)1
d)1
e)1
4.
a)A8
b) A9
c)A12
d)4A18
e)27A12
5.
a) 1/A4
b) 1/A6
c) 1/A2
d) 2/A4
e) 9/A3
6.
a) 5/A3
b) 6A6
c) 4A16
d) 4
e) 1/A12
•

Parallel and Perpendicular lines
ANSWERS
1.
2.
a)y=3x-7
b)y=5x-10
c)y=2x+16
d)y=131-9x
e)y=-3x-15
ANSWERS
1.
2.
a)y=-1/2x+9
b)y=-1/4x+17.75
c)y=2x-1
d)y=(2/3)x-2.67

Find the Nth term of these sequences
1) 6, 17, 34, 57, 86
2) 3, 18, 41, 72, 111
3) 7,14,23, 34, 47
4) 8, 19, 34, 53, 76
5) 2, 12, 30, 56, 90
Answers
1) 3n2+2n +1
2) 4n2+3n -4
3) n2 + 4n + 2
4) 2n2 +5n + 1
5) 4n2 -2n

The quadratic equation
1. For each of these equations, what is a, b and c? (the first one has been
done for you)
a) 2x2+4x -3 =0 a=2 b=4 c=-3
b) 6x2+x - 10=0
c) x2-4x -5=0
d) 2x2-10x + 7=0
e) 0.5x2+8x + 2=0
2. Use your answers from question one to find the possible values for x.
3. Rearrange these equations to the form ax2 + bx + c =0, then solve with
the quadratic equation:
a) 2x2+ 9x -2 =10
b) 4x + 5x2 - 10=2
c) x2 + 5x -3=x
d) 2x2-10x - 2= x2
e) 3x2 + 6 + 2x =8 + 7x
ANSWERS
1.
a)
b) a=6 b=1 c=-10
c) a=1 b=-4 c=-5
d) a=2 b=-10 c=7
e) a=0.5 b=8 c=2
2.
a) x=0.6 and -2.6
b) x=1.2 and -1.4
c) x=2.8 and -1.8
d) x=4.2 and 0.8
e) x=-0.3 and -15.7
3.
1. x=1.1 and -5.6
2. x=1.2 and -2
3. x=4.6 and -4.6
4. x=10.2 and -0.2
5. x=2 and -0.3

Factorising Quadratics
1. Factorise and solve:
a) X2 + 8X + 12= 0
b) X2 + 7X + 10= 0
c) X2 + 13X + 12= 0
d) X2 + 17X + 70=0
e) X2 + X – 20=0
f) X2 - 4X- 12=0
g) X2 - 12X + 20=0
2. Rearrange, factorise and solve
a) X2 + 21X + 32=12
b) X2 + 8X -5 = 15
c) X2 + 6X + 23 = 5 – 3X
3. Solve
a) 3X2 + 21X + 51=15
b) 2X2 +18 + 10=-6
c) 4X2 -8X -4= 36 + 4x
ANSWERS
1.
a)-6 and -2
b)-5 and -2
c)-12 and -1
d)-7 and -10
e) -5 and 4
f)6 and -2
g)10 and 2
2.
a)-20 and -1
b) -10 and 2
c)-6 and -3
3.
a) -4 and -3
b)-8 and -1
c)5 and -2

Sequences
1. Copy down the following sequences and add the next three terms:
a) 36 9 12 15
b) 27 12 17 22
c) 410 16 22 28
d) 13 24 35 46 57
e) 50 48 46 44 42
2. For each of the questions in question what is rule to find the next term in the
sequence. (This is called the term to term rule)
3. Copy the following sequences, write the term to term rule and find the next 3 terms.
a) 0.3 0.7 1.1 1.5 1.9
b) 1.4 1.7 2 2.3 2.6
c) 40 39.5 39 38.5 38
d) 5.9 5.3 4.7 4.1 3.5
e) 11.4 12.5 13.6 14.7 15.8
a) 50 -5 -10 -15
b) 3 -1 -5 -9 -13
c) -20 -16 -12 -8 -4
d) -30 -27.5 -25 -22.5 -20
a) 1 2 4 8 16
b) 1 3 6 10 15
c) 1 3 7 13 21
Answers
1.
a) 18,21,24
b)27,32,37
c)32,36,40
d)68,79,90
e)40,38,36
2.
a)add 3
b)add 5
c)add 4
d) add 11
e)take away 2
3.
a)2.3,2.7,3.1 (add 0.4)
b) 12.9,3.2,3.5 (add 0.3)
c)37.5,37,36.5 (take away 0.5)
d)2.9,2.3,1.7 (take away 0.6)
e)16.9,18,19.1 (add 1.1)
4.
a)-20,-25,-30 (take away 5)
b) -17,-21,-24 (take away 4 )
c)0,4,8 (add 4)
d)-17.5,-15,-12.5 (add 2.5)
5.
a)32,64,128 (double the last number)
b) 21,28,36 (add on the next number
1 then 2 then 3 ....)
c)31,43,57 (add on the next even
number 2,4,8...

The Nth term
•1) Find the nth term of the following sequences:
a) 4 7 10 13 16
b) 2 7 12 17 22
c) 4 10 16 22 28
d) 13 24 35 46 57
e) 1 9 17 25 33
•2) Take the following nth terms and find the first 5 terms
a) 3n + 1
b) 4n +2
c) 5n + 5
d) 4n – 1
e) 6n + 3
f) 10n -3
•3) If the nth term is 7n + 4 what is
a. The 4th term b. The 12th term c. The 100th term
•4) If the nth term is 8n - 2 what is
•5) If the nth term is 11n + 3 what is
•6) If the nth term is n + 9 what is
Answers
1.
a)3n+1
b)5n-3
c) 6n-2
d)11n+2
e)8n-7
2.
a)4,7,10,13,16
b) 6,10,14,18,22
c)10,15,20,25,30
d)9,15,21,27,33
e)7,17,27,37,47
3.
a)32
b) 88
c)704
4.
a)30
b) 94
c)798
5.
a)47
b)135
c) 1103
6.
a)13
b) 21
c)109

Simplifying ExpressionsAnswers
1.
a)20a4
b)18a7
c)63a8
d)20a2b4
e)18a2b7
f)63a2b8
g)8a2b2c5
h)60a2b2c14
i)36a8b8c
j)12a5b4c4
2.
a)4a
b)3a4
c)7a2
d)6a3b3
e)9a4/b5
3.
a)10a2
b)10ab2
c)ab6/10
d)ab2
e)119a3b8

Simultaneous Equations
1. Find a and b for each pair of simultaneous equations:
a) 5a + 2b= 14 6a + 2b= 16
b) 7a + 3b= 27 6a + 3b= 24
c) 10a - 2b= 30 3a - 2b= 2
d) 9a - 6b= 42 6a - 6b= 18
a) 4a + 7b= 27 4a - 7b= 13
b) 3a + 2b= 35 2a - 2b= 10
c) 11a - 8b= 4 a + 8b= 44
d) 5a + 3b= 69 7a - 3b= 75
a) 5a + 6b= 28 6a + 2b= 18
b) 4a + 4b= 36 6a - 2b= 22
c) 2a - 8b= 16 3a + 2b= 29
d) 9a + 6b= 84 3a - 3b= 25.5
Answers
1.
a) a=2 b=2
b) a=3 b=2
c) a=4 b=5
d) a=8 b=5
2.
a) a=5 b=1
b) a=9 b=4
c) a=4 b=5
d) a=12 b=3
3.
a) a=2 b=3
b) a=5 b=4
c) a=10 b=0.5
d) a=9 b=0.5

Solving Equations
1. Find x if:
a) 7x= 42
b) 12x=36
c) 5x = 40
d) 10x = 110
e) How did you answer these questions?
2. Find x if:
a) X + 10 = 17
b) X + 15 = 27
c) X + 25 = 30
d) X- 9 = 15
e) X – 13 = 40
f) How did you answer these questions?
3. Find x if
a) 3x + 6 =21
b) 7x + 11 = 67
c) 5x + 4 = 24
d) 9x – 2 =25
e) 11x – 14= 30
f) 10x - 7= 53
g) 12x + 11= 155
h) 15x - 14= 61
i) 13x + 25 = 90
j) How did you answer these questions?
Answers
1.
a) 8
b) 6
c) 3
d) 10
2.
a) 7
b) 12
c) 5
d) 16
e) 27
3.
a) 5
b) 8
c) 4
d) 3
e) 4
f) 6
g) 12
h) 5
i) 5

Graphical Simultaneous
Equations
Solve these simultaneous equations graphically
(draw x axis to 10 and y axis to 15):
1. y=2x + 4 and y=3x -1
2. y=5x - 3 and y=4x + 1
3. y=x + 7 and y=2x + 4
4. y=2x + 2 and y=6-3x
5. y=10 – 2x and y=12-3x
1. (5,14)
2. (2,7)
3. (3,10)
4. (1,3)
5. (2,6)

Substituting
1. If A is 5 what is:
a) 5A
b)11A
c) 6A – 10
d)9A + 15
e) 100-5A
2. If B is 7 what is
a) 2(B+8)
b)3(B-5)
c) B(B+5)
d)9(10-B)
e) (3+B)X(B-5)
3. If A= 6 and B=7 what is:
a) A+B
b)B-A
c) 6A+2B
d)AB
e) A(B+1)
f) A2B
ANSWERS
1.
a) 2
b) 55
c)20
d)60
e)75
2.
a)30
b) 15
c)84
d)27
e)20
3.
a)13
b)1
c) 50
d)42
e)48
f)252
4.
a)8
b)-2
c) 30
d)12
e)8
5.
a)-33
b)0
c)9
d) -16
e)-18
f)-50
g)31

1. Use trial and improvement to find the positive solution to these
quadratic equations to 1 dp, you may like to use a table, the
table for the first question has been drawn for you (all answers
are between 1 and 5).
a) X2 + 3x -30=0
b) X2 + 2x -20=0
c) X2 + 4x -10=0
d) X2 -2x -5=0
2. Use trial and improvement to find the positive solution to these
quadratic equations to 2dp (all answers are between 1 and 5)
a) 3X2 - 5x -10=0
b) 2X2 + 2x -25=0
Trial and Improvement
x X2 +3x -30 Big or small?
ANSWERS
1.
a) x=4.2
b)x=3.6
c)x=1.7
d)x=3.4
2.
a) x=2.84
b) x=3.07

Writing Expressions
1. My age is C, write expressions for the ages of the members of my family if:
a) My brother is 3 years older than me
b) My sister is 2 years younger than me
c) My mum is double my age
d) My dad is 5 years older than my mum
e) My Gran is 4 times my age
f) My Grand Dad is twice my Dads age
2. If I have S sweets, write an expression for the number of sweets my friends have if I:
a) I give Tom all my sweets and he has 5 of his own
b) I give Alan half of my sweets
c) I eat four sweets then give Simon the rest
d) I give Lucy a quarter of my sweets, then an extra 1
3. My favourite song last M minutes, how long do I spend listening to music if:
a) I listen to the song once and hour all day (and including when I’m asleep)
b) I listen to half the song 8 times
c) I listen to the intro (a quarter of the song) 5 times
d) I listen to my song, then the next one which is exactly twice as long
e) I listen to my song, then the next one which is exactly twice as long, and do this 5
times throughout the day
4. If a rectangle has lengths x and y, write an expression for:
a) The area of the rectangle
b) The area covered by 6 rectangles
c) The perimeter of the rectangle
Answers
1.
a)C + 3
b)C – 2
c)2C
d) 2C+5
e)4C
f)2(2C+5) OR 4C +
10
2.
a)S+5
b) S/2
c)S-4
d)S/4 + 1
3.
a)24M
b)M/2 X 8 OR 4M
c)5M/4
d) 3M
e)15M
4.
a) xy
b)6xy
c)2x + 2y or 2(x +
y)

y=mx +c
1. Copy and complete:
a) A line with a positive gradient will go from ________ left to ________right
b) A line with a negative gradient will go from ________ left to ________right
2. Look at the equations below, write down the gradient and the coordinates of the intercept of the line they represent.
a) Y=3x+4
b) Y= 2x-5
c) Y=6x+9
d) Y=x- 7
e) Y=10x
f) Y=5+8x
g) Y=7-11x
3. Draw an axis from -10 to 10, plot the following lines
a) Y = 2x + 3
b) Y = 3x – 2
c) Y = -2x + 5
d) Y = -3x + 9
4. Find the gradient of the line between these pairs of coordinates by dividing the change in y by the change in x.
a) (3,3) (5,5)
b) (5,5) (6,7)
c) (1,2) (3,8)
d) (10,9) (6,1)
e) (15,20) (10,5)
5. Using the gradient worked out in the last question and one of the coordinates, find the value of c for the line between
the pairs of points in question 4.
6. Write out the equation of the line between the pairs of points in question 4 in the form y=mx+c
Answers
1.
a) bottom / top
b) top / bottom
2.
a) gradient- 3 intersection- (0,4)
b) gradient- 2 intersection- (0,-5)
c) gradient- 6 intersection- (0,9)
d) gradient- 1 intersection- (0,-7)
e) gradient- 10 intersection- (0,0)
f) gradient- 8 intersection- (0,5)
g) gradient- -11 intersection- (0,7)
3.
4.
a) 1
b) 2
c) 3
d) 2
e) 3
5.
a) 0
b) -5
c) -1
d) -11
e) -25

Finding the Area of Circles
You can find the area of a circle by using the formula-
Area= π x Radius2
For Example-
Area= π x 72
= π x 49
= 153.93804
= 153.9 (to 1dp) cm2
7cm
2a 12.6
b 78.5
c 15.2
d 380.1
e 314.2
f 153.9
g 100.5
h 28.3
ANSWERS

Area of Triangles
1. Find the area of the
triangles on the left
2. Find the missing
lengths of the triangles
on the right
Answers:
1. 6m2
2. 24m2
3. 3m2
4. 20m2
5. 12m2
6. 35m2
7. 44m2
8. 15m2
9. 31.5m2
10.72m2
Answers:
1. 10m
2. 14m
3. 6m
4. 10m
5. 10m
6. 3m
7. 20m

Circumference
11cm 23cm 4cm 7cm
5cm
3cm
20cm
30cm
30cm
9cm 4cm
6cm 12cm
8cm
5cm
14cm
18cm
6cm
Answers:
1. 34.6cm
2. 72.3
3. 25.1cm
4. 44.0cm
5. 77.1cm
6. 51.4cm
7. 10.7cm
8. 17.9cm
9. 95.1cm
10.23.4cm
11.51.0cm
12.81.4cm
1 2 3 4
5 6 7 8
9 10 11 12

25°
x
160°
100°
60°
135°
90°
x
x
x
x
x
1
2 3
6
4 5
Answers
1) 50
2)120
3)180
4)50
5)67.5
6)80
Double angle theorem

60°
x
1 2 3
3
1 2
72°
x
x x
x y
y
x
100°
x
30°
22°
y
Answers
1) X=30
2)x=18
3)x=45
4)X=40 y=40
5)x=30 y= 120
6)x=22 y=136
x
Triangles inside circles

25°
x
1
2
3
6
4
5
y
15°
y
z
z
x
y
x
z
x
y
y
z
x
25° 53°
30°
z
y
x
80°
17°
95°
35°
40°
125°
15°
40°
10°
100°
Answers
1) x=25 y=15
2)x=125 y= 40 z=15
3)x=10 y=70 z=100
4)X=105 y=40 z=35
5)x=53 y= 30 z=72
6)x=85 y=80 z=17
Angles connected by a chord

40°
x
y
z
3
120°
x
4
140°
x
2
x
35 °
1
y
z
Tangents to a circle
Answers:
1. x=55
2. x=40
3. x=50 y=50
z=40
4. x=60 y=60
z=30

x
y
x
y
x
y
95° 110° 54°
75°
20°
80°
x 2a
4b
15° 70° a
b
1
25°
y
z
w
2 3
4 5
Answers
1) x=70 y=85
2)x=126 y=105
3)x=100 y=160
4)w=15 x=70
y=65 z= 25
5)a=60 b=36
Cyclic Quadrilaterals

Trigonometry- Sin and Cos
Answers:
1.
1. d=hypotenuse
2. e=adjacent
3. f= opposite
4. h=hypotenuse
5. g=adjacent
6. i=opposite
7. j=hypotenuse
8. k=adjacent
9. l=opposite
10. m=hypotenuse
11. o=adjacent
12. n=opposite
13. p=hypotenuse
14. q=adjacent
15. r=opposite
Answers:
2.
a) 6.1
b) 3.5
e)7.1
f) 7.1
g)2.6
i)3.1
k) 2.1
l) 14.9
n) 11.3
o)3.8
p)12.6
r)18

Trigonometry- finding angles
24cm
32cm
Answers:
1) 41.4
2) 76.2
3) 49.3
4) 51.4
5) 70.6
6) 53.1
29cm

Cosine rule
Answers:
1. 32cm
2. 3.5cm
3. 45.4c˚
4. 139.5 ˚
5. 25.2 or
11.1cm
6. 16.7cm
22cm
5cm

Answers:
1) 10cm
2) 3.0cm
3) 3.4 cm
4) 25.7cm
5) 50.2cm
6) 26.7cm
The Sine rule

Trigonometry- Sin,
Cos and Tan
Answers:
1.
a)15.7
b)46.7
c)32.2
d)30.6
e)21.9
f)63.5
2.
a)6.1
b) 11.9
c) 69.3
d) 15.6
e) 2.1
f)7.7
15.7cm

Sine and Cosine Rule
Answers:
1)25.6˚
2)6.5cm
3)20.4cm
4)21.6 or
15.6 cm
5)9.73cm
6)40 ˚
7)34 ˚
8)5.3cm
9)14.3˚
10)42cm
11) 24.46cm
12)27.6 or
3.6 cm
8cm
10cm
14cm
15cm
22cm
19cm

Sin, cos and tan 2
Answers:
1) 3.1cm
2) 6.1cm
3) 5.1cm
4) 17.1cm
5) 4.5cm
6) 8.6cm
7) 20.5cm
8) 31.1cm
9) 117.6cm
10)1.5cm
11)4.1cm
12)108.9cm

Reflection 1
Reflect these shapes in the mirror lines

3D Pythagoras
Find the length of the longest diagonal of these cuboids
1) Answers
2) 11.2cm
3) 12.0cm
4) 12.2cm
5) 9.4cm
6) 13.4cm
7) 15.2cm

5cm
8cm
8cm
5cm
4cm
9cm 9cm
4cm
12cm
10cm
3cm
15cm
7cm
11cm
Find the Perimeter of
these shapes
8cm
8cm
5cm
4cm
9cm
4cm
8cm
3cm
5cm
4cm 12cm
11cm
13cm
All of these shapes are regular
Answers
1. 26cm
2. 26cm
3. 30cm
4. 25cm
5. 36cm
Answers
1. 21cm
2. 17cm
Answers
1. 16cm
2. 25cm
3. 72cm
4. 39cm
5. 96cm
6. 110cm
7. 42cm

Worded Pythagoras
1. A hunter fires an arrow to kill a bird, the bird falls 20m and the hunter has to walk 40m to pick it up,
how far did the arrow travel to the bird?
2. A boat travels 45 miles east then 60 miles north, how far is it from where it started?
3. A swimming pool is 25m by 12m, if someone swam from one corner to the other, how far would they
have swum?
4. A kite is flying on a string which is 10m, the kite is flying 6m of the ground, if the kite plummets
straight down how far will the kite flyer have to walk to pick it up?
5. A totem pole is tied to the ground with ropes stuck in the ground with pegs, if the rope is 14m long
and the pole is 9m long, how far will the pegs be from the base of the totem pole?
6. A lighthouse shines a light on a ship, the light beam is 80m long, the ship is 60m away from the base
of the lighthouse, how tall is the lighthouse?
Answers
1. 44.7m
2. 74miles
3. 27.7m
4. 8m
5. 10.7m
6. 52.9m

a
b
110 °
Find a, b and c giving reasons for each answer.
c
a
b
c
120 °
a
b
c
55 °
a
115 °
b
c
a b
c
25 °
a
b
c
10°
a
27°
Find a, b and c giving reasons for each answer.
120°
b
a
75°
45°
b
110 °
c
95 °
c
Answers
1. a=27 (corresponding)
2. b= 120 (alternate)
3. c = 85 (interior)
4. a= 105 (interior)
5. b=45 (alternate)
6. c= 110 (alternate)
Answers
1. 70,70,110
2. 60,60,60
3. 55,125,55
4. 115,65,65
5. 155,25,25
6. 170,170,10

45 °
130 °
30 °
Find the values of x
x
x
x
x
45 °
55°
25°
x
x
x
x
95°
15°
60°
35°
30°
120°
x
95°
35 °
x
110°
70 ° 120°
25 °
2x
x
2x
3x°
80 °
4x
2x
x
x x
5x
Answers
1. 135
2. 150
3. 90
4. 50
Answers
1. 105
2. 120
3. 105
4. 30
Answers
1. 145
2. 145
Answers
1. 45
2. 36
3. 80
4. 31

Angles in a triangle
ANSWERS
1.100
2.80
3.90
4.100
5.60
6.72
7.71
8.93
9.85
ANSWERS
1.50
2.65
3.60
ANSWERS
1.80
2.130
3.40
4.75

Plans and Elevations
Draw the plan and the
front and side elevations
for these shapes

1. What is the sum of the angles in a:
a) 3 sided shape
b) 5 sided shape
c) 8 sided shape
d) 10 sided shape
e) 20 sided shape
f) 30 sided shape
2. Find the missing angles
30° 150° 88°
75°
84° 72°
x
110°
100°
x
40°
113°
90°
x
53°
330°
15°
92°
162°
157°
41°
x
83°
99° x
327°
95°
285°
45°
100°
95°
x
x
106°
154°
125°
90°
88°
3x
290°
x
96°
153°
153°
172°
93°
32°
11°
x 265°
342°
100°
ANSWERS
1.
1. 180
2. 540
3. 1080
4. 1440
5. 3240
6. 5040
2.
1. 260
2. 149
3. 260
4. 151
5. 219
6. x= 45
7. 140

Find the exterior and
interior angles of a
regular shape which
has:
a) 9 sides
b)10 sides
c) 12 sides
d)15 sides
e) 25 sides
ANSWERS
1.
a) I=140, E=40
b) I=144, E=36
c) I=150, E=30
d) I=156,E=24
e) I=165.6, E=14.4

1. How many sides does a regular polygon
have if it’s exterior angles are:
a) 45
b) 40
c) 30
d) 22.5
e) 20
f) 3
ANSWERS
1.
a) 8
b) 9
c) 12
d) 16
e) 18
f) 120
2. How many sides does a regular polygon
have if it’s interior angles are:
a) 150
b) 156
c) 157.5
d) 162
e) 165
f) 168.75
ANSWERS
2.
a) 8
b) 9
c) 12
d) 16
e) 18
f) 120

Pythagoras
ANSWERS
1.
a)5m
b)10m
c)13m
d)10.8m
e)6.3m
f)3.3m
g)6.9m
h)8.7m
2. 5.8
3. 1.9m

Mean
1. Find the mean from these numbers:
a) 5,3,4
b) 10, 11, 1, 7
c) 15, 8, 7, 10
d) 14, 2, 4, 1, 4
e) 7, 8, 5, 10, 4, 2
f) 24, 26, 32, 17, 1
g) 0.2, 0.1, 0. 5, 0.2
h) 20, 9, 3, 8, 8, 7,1
i) 17, 18, 15, 10, 8, 2, 9,1
j) 0,0,0,0,0,18
2. How would you find the:
a) Mean age of players in a football team
b) Mean height of a family
c) Mean number of sweets eaten by boys in a day
d) Mean number of hours spent watching TV for a pupil each night
e) Mean number of times someone says “LOL” a day
3. Write down 3 possible lists of numbers if there are:
a) 4 numbers with a mean of 6
b) 5 numbers with a mean of 8
c) 7 numbers with a mean of 9
ANSWERS
1.
a) 4
b) 7
c) 10
d) 5
e) 6
f) 20
g) 0.25
h) 8
i) 10
j) 3
2.
a) Add all players ages,
divide by the number
of players
b) Add all the heights
together divide by
number of people
c) Add up number of
sweets eaten by boys,
divide by number of
boys
d) Add all the hours
together divide by the
number of pupils
e) Add together how
many someone says lol
each day for lots of
days, divide by the
number of days

Mean, Mode, Median and Range
1. Which of these could you not find a median for?
a) Height
b) Favourite colour
c) Score in a test
d) Favourite football team
2. Find the mean, mode, median and range for these sets of numbers:
a) 5,7,2,8,8
b) 2,12,6,3,2
c) 15,4,11,6,4
d) 20,30,35,15,15
e) 4,7,0,14,0,19,5
f) 2,9,18,12,7,2,6
g) 21,13,15,2,15,3,1
3. Write 3 different lists of 5 numbers which have a mean of 7.
4. Write 3 lists of numbers which have a median of 11
5. Would mode be a good thing to find if we were looking at pupils exact journey time to school? Explain
your answer.
6. Can any of mean, median, mode and range be negative? Explain your answer
ANSWERS
1. favourite colour
and favourite
football team
2.
a)6,8,7,6
b)5,2,3,10
c)8,4,6,11
d)23,15,20,20
e)7,0,5,19
f)8,2,7,16
g)10,15,13,20
3.
4.Either the mean or
the median
5.All can be negative
except the range.

Median and Range
ANSWERS
1.
a) Median-6, range-10
b) Median-17, range-8
c) Median-11, range-4
d) Median-2, range-5
e) Median--6, range-9
2.
a) Median=21, range=34
b) Median=35, range=55
c) Median=574, range=669
d) Median=-50, range=97
e) Median=-18, range=83
3.
a) Median=22, range-36
b) Median=18.5, range=80
c) Median=223.5,
range=336
d) Median=7.5, range=17
e) Median=-32, range=96

Mean from grouped tables
ANSWERS
1.
1.40
2.18.25
3.Midpoints are
an
approximation
of the scores
2. 9.05

Mean from tables
ANSWERS
1.
a)18
b)24
c)1.3
2.
a)30
b) 44
c)1.5
3.
a)47
b) 107
c)2.3

Drawing Pie charts 1
1.
a) 8
b) dog=1/8,
cat=1/4,
fish=5/8
2.
a) green=1/10
Pink=1/4
Blue=3/10
Red 2/5
b) green=2/20
Pink=4/20
Blue=6/20
Red= 8/20

1a. 36
ii)10°
b)40,70,100,
150
2a. 72
ii)5°
b)30,45,60,45
,180
3a. 180
ii)2°
b)50,144,64,20,
81
4a. 720
ii)0.5°
b)100,60,50,45,50,
65

Probability as Fractions
1. I have some counters in a bag. There are 3 blue,
5 red and 2 green. What is the probability I pick
out:
a) A blue
b) A red
c) A green
d) A purple
e) A blue or red
f) A red or green
2. I am picking my socks at random today, I have 4
pairs with stripes on, 10 with spots, 5 with
clowns and 1 with maths pictures. What is the
probability I will pick out:
a) Spotty socks
b) Clown socks
c) Maths Socks
d) Clown or spotty socks
e) Maths or stripe socks
3. I have a pack of card (without jokers)
what is the probability I pick:
a) A Red card
b) A heart
c) A Club
d) A heart or a club
e) A 2
f) A King
g) A picture card
h) A number card smaller than 6
i) A number card greater than 6
j) An even number
k) An odd number
l) A red number 3
m) A black Queen or red Jack
n) A King of Hearts or a 5
ANSWERS
1.
a) 3/10
b) ½
c) 1/5
d) 0
e) 4/5
f) 7/10
2.
a) ½
b) ¼
c) 1/20
d) ¾
3.
a) ½
b) ¼
c) ¼
d) ½
e) 1/13
f) 1/13
g) 4/13
h) 4/13
i) 4/13
j) 5/13
k) 4/13
l) 1/26
m) 1/13
n) 5/52

Relative Frequency
ANSWERS
1.
a) 75
b) 37.5
c) 125
2.
a) Blue-0.25, red -0.5,
yellow – 0.1, black
0.15
b) Blue-20,red-
40,yellow-8, black-12
3.
a) 0.1,0.25,0.15,0.05,
0.45
b) 50,125, 75,25, 225

1. If I flip a coin and roll a dice, list all the possible outcomes I could get.
2. I spin two fair spinners number 1 to 3.
a) Copy and complete the table to show all the possible outcomes.
3. When I have breakfast I have a drink and something to eat. The drinks I choose from
are tea, coffee and juice and I eat a bagel, toast or cereal. Write down all the different
combinations I could have for breakfast.
4. If I toss 1 coin there are 2 possible outcomes, find the number of outcomes for:
a. 2 coins b. 3 coins c. 4 coins d. X coins
5. Lucy, Amy and George are going to have their photo taken so they sit in a line:
a) How many different ways could they order themselves?
b) Andy joins them, how many different ways could they order themselves now?
Listing Outcomes
Spinner 1 Spinner 2 Total
ANSWERS
1.H1,H2,H3,H4,H5,H6,T1,T
2,T3,T4,T5,T6
2.
1.1+1=2
2.1+2=3
3.1+3=4
4.2+1=3
5.2+2=4
6.2+3=5
7.3+1=4
8.3+2=5
9.3+3=6
3.
Tb,Tt,Tc,Cb,Ct,Cc,Jb,Jt,
Jc
4.
a) 4
b) 8
c) 64
d) 2x
5.
a) 6
b) 24

Tree Diagrams
A) I have a bag with 20 balls in, there are 13 pink, 7 orange pull a ball out, put it back then pull another.
1.Draw a tree diagram showing all possible outcomes
2.Use your tree diagram to find the probability of getting:
a.2 pink
b.2 orange,
c.A pink and an orange.
B) The probability I have toast for breakfast is 0.6, the probability I will miss my bus is completely unrelated to my breakfast choice and is 0.2
1.What is the probability I will NOT:
a.Have toast for breakfast
b.Miss my bus
2.Draw a tree diagram showing all possible outcomes
3.Use your tree diagram to find the probability of:
a.Having toast and missing my bus
b.Not having toast and missing my bus
c.Not having toast and not missing my bus
C) I am tossing a coin and rolling a dice:
1.Draw a tree diagram to show all possible outcomes.
2.Use your tree diagram to find the probability of:
a.A head a 3
b.A tails and a number bigger than 4
c.A tails with a 3 or a heads with a 1
D) I have some songs on my mp3 player, 4 are rock, 7 are Pop and 11 are Hip Hop. I put my mp3 player on shuffle and listen to 2 songs (it is
possible to listen to the same song twice in a row)
1.Draw a tree diagram to show all the possible outcomes,
a.Find the probability that I will listen to:
i.Hip Hop then Pop
ii.Rock twice
iii.A Rock song and a pop song in any order
iv.2 songs which are the same style (rock and rock or pop and pop ect.)
ANSWERS
A.
2.
a) 169/400
b) 49/400
c) 91/400
B.
1.
a) 0.4
b) 0.8
3.
a)0.12
b)0.08
c)0.32
C.
2.
a) 1/12
b) 1/6
c) 1/6
D.
a)
i. 7/44
ii. 4/121
iii. 14/121
iv. 93/242

Stem and Leaf Diagrams
ANSWERS
2.
a) Range-42 ,
median-34,
mode-22
b) range- 4.8,
median-22.2
,mode-22.4

Questions
Plot a scatter graph for each table.
Say if there is a positive, negative or
no correlation and try to give a
reason why
Temperature Ice Creams sold
17 63
31 53
12 77
35 31
39 28
34 43
34 46
22 64
37 28
31 35
Time taken to
walk to school
Score in
spelling test
27 2
10 40
14 5
27 1
40 6
14 42
15 47
17 22
35 4
38 31
17 13
18 2
27 13
Hours
spent on
internet
Score on ICT
test
13 14
33 39
27 37
38 45
13 18
39 62
10 19
30 54
19 36
29 34
16 22
25 42
28 33

The Probability Line
ANSWERS
2.
i. 0.1
ii. 0.5
iii. 0.2
iv. 0.2
v. 0
vi. 1
vii. 0.4
viii.0.6

Mutually Exclusive Events
ANSWERS
1.
a) 0.7
b) 0.6
c) 0.48
d) 0.79
e) 75%
f) 2%
g) 3/5
h) 4/10
i) 3/15
2.
a) Mutually
exclusive
b) Not mutually
exclusive
c) Not mutually
exclusive
d) Mutually
exclusive
3.
a) 0.1
b) 0.2
c) 0.23
4. 0.24

Sample Space Diagrams
ANSWERS
1.
a)
i. 1/36
ii.1/12
iii.1/9
b) 7, it appears the
most
2.
a)0
3.
4.
1.
2.
a)6/25
b)19/25
c) 9/25
d)8/25

Sampling
ANSWERS
1.
• Year 7- 20
• Year 8-18
• Year9 -24
• Year 10- 15
• Year 11-23
2.
• Football-16
• Hockey-5
• Basketball-11
• Swimming-13
• Badminton-1
• Tennis-4
3.
Male and maths- 5
Male and english-6
Female and maths-10
Female and english-4

Histograms
ANSWERS
1.
i. Histograms have uneven
class intervals,
ii. the frequency is
represented by the
area of the bar not the
height,
iii.frequency density is
displayed on the y axis
10 0.5
5 1
15 5
30 2.5
60 4
15

Drawing Cumulative Frequency Graphs

Pie Charts
40 people
100 people 40 people 36 people
48 people
320 people 640 people 720 people
Answers:
1. 20 and 20
2. All are 25
3. All are 5
4. Yellow and blue
are 9 red is 18
5. Yellow and red are
12 others are 6
6. Red is 120 yellow
is 80 others are
40
7. Red and blue are
80 others are 160
8. Green and yellow
are both 90
others are 270

Find the number of people represented by these slices of pie charts
Pie Charts 2
Favourite Colour Angle
Blue 60
Green 30
Turqoise 120
Purple 120
Black 30
Favourite Country Angle
USA 20
Mexico 20
Turkey 40
France 100
Spain 180
How do you get to school Angle
Bus 10
Train 80
Walk 140
Car 90
Metro 40
Favourite Sport Angle
Football 36
Hockey 108
Swimming 36
Water polo 108
Basket Ball 72
Favourite food Angle
Pizza 6
Chinese 54
Roast Dinner 96
Curry 186
Mexican 18
Favourite Maths Topic Angle
Fractions 18
Area 90
Algebra 54
Percentages 72
Pie Charts 126
156 people were asked
people
26
13
52
52
13
people
5
40
70
45
20
people
4
36
64
124
12
people
8
40
24
32
56
people
40
120
40
120
80
people
4
4
8
20
36

Reading Bar
Charts
ANSWERS
1.
a) 5
b) 3
c) 5
d) 39
2.
a) Punk
b) RnB
c) 51
d) Punk, RnB,
Metal/Rap,
Pop/Reggae
Bart Homer Marge Lisa Maggie
Heavy
Metal
Punk RnB Rap Pop Reggae
Favourite Music Style
0
14
12
10
8
6
2
4
0
14
12
10
8
6
2
4
1
16
13
11
9
7
3
5
15

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