algebra shape data number adding and subtracting decimals answers a)0.5 b)1.2 c)0.8 d)1.3 e)1.5...
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Algebra Number
Data Shape
Algebra
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Brackets Two BracketsSolving
EquationsCollecting like terms
Simplifying
2 sided equations
Simultaneous equations
Solving simultaneous
equations graphically
FactorisingCurved Graphs
Sequences The Nth termQuadratic Sequences
Substituting Formulae
Quadratic Equation
Factorising Quadratics
Algebraic Fractions
Trial and Improvement
Inequalities
Laws of Indices
Parallel and Perpendicula
r lines
Finding the Gradient
Writing Expressions
y=m x + c
ShapeArea of Circles
Circumference
Area of triangles
Circle theory Double angle
Circle theory
triangles
Construction
Sin and CosSin, cos and
tan Sin, cos and
tan 2
Sine rule Cosine ruleSine and
cosine rules
Trig- missing angles
Pythagoras
Angles on a straight line and around a
point
Angles on parallel
lines
Angles in a triangle
Plans and Elevations
Perimeter
Worded Pythagoras
Reflection 1 Reflection 2 Translation Rotation3D
Pythagoras
Circle theory angles
connected by a chord
Circle theory cyclic quads
Circle theory
tangents
Angles in Polygons
Interior and Exterior angles
Polygons- finding sides
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Data
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MeanMedian and
rangeMean from
tablesMean from
group tables
Tree Diagrams
SamplingMutually Exclusive
Events
Listing Outcomes
Histograms
Cumulative frequency
Reading Pie Charts
Drawing Pie Charts 1
Drawing Pie Charts 2
Drawing Bar Charts
Scatter Graphs
Box and Whisker plots
Sample Space
Diagrams
The Probability
Scale
Probability as Fractions
Stem and Leaf
Diagrams
Relative Frequency
Reading Bar Charts
Reading Pie Charts 2
Mean, Mode, Median and
Range
Number
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Adding, subtracting decimals
BIDMASAdding and subtracting
fractions
Direct Proportion
Factors
Factor Trees
Directed Numbers
Directed Numbers 2
Equivalent Fractions
FDP
Finding % RatioHCF and
LCMIndirect
ProportionLimits
Multiplying and dividing
decimals
Multiplying and Dividing
FractionsMultiples
Ordering Decimals
Ordering Fractions
Percentage Increase
Reverse Percentage
Rounding dp
Rounding sig fig
Standard form
Adding and Subtracting Decimals
Home
ANSWERSa)0.5b)1.2c) 0.8d)1.3e)1.5
f) 1.47g)1.28h)1.66i) 0.97j) 1.68
• a)31.44b)70.81c) 39.46d)34.15e)50.8
• a)0.45b)0.54c) 0.49d)0.71e)0.7
• a)2.94b)39.02c) 67.25d)77.03e)54.11
Adding and Subtracting Fractions
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a) 7/8b) 8/12c) 7/9d) 7/10e) 2/3
f) 11/12g) 7/10h) 8/15i) 16/12 or 1 ¼j) 11/24
k) 1 7/12l) 1 5/56m) 29/30n) 29/52o) 1 1/10
p) 5/8q) 5/12r) 1/3s) 2/5t) 1/2
u) 7/20 v) 8/21w) 23/36x) 9/22y) 71/126
Adding and Subtracting Decimals
Home
Answers1.
a)0.5b)1.2c)0.8d)1.3e)1.5
2. a)1.47b)1.28c)1.66d)0.97e)1.68
3. a)31.44b)70.81c) 39.46d)34.15e)50.8
4. a)0.45b)0.54c) 0.49d)0.71e)0.7
5. a)2.94b)39.02c) 67.25d)77.03e)54.11
Direct Proportion
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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 =42. T= 5 when S=13. Y= 34 when x=24. H=48 when M=45. 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 C2. Find B when C= 663. Find C when B = 30
4. Z is directly proportional to Y, when Z =55, Y=51. Write an equation linking Z and Y2. Find Y when Z = 773. Find Z when Y=0.1
5. N is directly proportional to L, when N=1.8 L =0.61. Write an equation linking N and L2. Find L when N= 3.23. Find N when L=0.5
Answers1.A=2B2.
1.V=4M2.T=5S3.Y=17X4.H=12M5.N=2P
3. 1.C=1.5B2.B=443.C=45
4. 1.z=11y2.y=73.z=1.1
5. 1.N=3L2.L=1.23.N=1.5
Bidmas
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A)1. (3 + 3 ) x 42. 4 x 2 – 53. (5 + 7) ÷ 64. 5 x 3 + 55. (9 – 4 ) + 56. 1 + 1 – 17. 2 x (15 – 2)8. (5 x 4 ) + 29. (8 + 2 ) ÷ 1010. (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) 242) 33) 24) 205) 106) 17) 268) 229) 110)19
B. 1) 02) 23) 94) 55) 16) 267) 25
C. 1) 202) 173) 54) 15) 16) 2
Factors and HCF
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1) Find all the factors of the following numbers:1) 20 2) 24 3) 274) 325) 406) 507) 568) 1209) 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 542) 25 and 453) 12 and 184) 27 and 1085) 30 and 75
4) Find the HCF of these pairs of numbers:1) 90 and 4502) 96 and 4803) 39 and 195
ANSWERS1.
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
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1. Draw factor trees for the following numbers:a) 20b) 24c) 48d) 90e) 81f) 50g) 75h) 120i) 200j) 1800
2. Using your factor trees from question 1, write the numbers as products of their prime factors .
Answers1. 2.
a)22x5b)3 x 23
c)3 x 24
d)2 x 32 x 5e)34
f)2 x 52
g)3 x 52
h)23 x 3 x 5i)23 x 52
j)23 x 32 x 52
Directed Numbers
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•ANSWERS1) -132) 123) -54) 105) 146) -17) -118) -19) 710)-7
11)-1712)-2413)-2314)-2415)-916)-817)818)-1219)-1420)-9
1) 172) -53) 14) 85) -106) 237) 268) 369) 1710) 16
Directed Numbers 2
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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. 233. -284. 665. 23
Equivalent Fractions
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2.a)4b)15c)12d)20e)60f)8g)26h)32i)120j)15k)64l)154m)125n)400o)615p)9720
Ratio
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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) 48:60b) 45:75c) 63:108d) 25:40:80e) 24:56:96f) 120:180:600g) 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 toys6. 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 sweets7. 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.£908. 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. 2:32. 7:83. 2:54.
a) 4:5b) 3:5c) 7:12d) 5:8:16e) 3:7:12
5. a) 2 and 8 b) 6 and 24c) 9 and 36
6. a) 8 and 12b) 12 and 18c) 22 and 33
7. a) 9 and 21b) 18 and 42c) 27 and 63
8. a) 10 and 20 and
30b) 12 and 24 and
36 c) 50 and 100 and
150
Finding Percentages
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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 10b) divide by 2c) divide by 4
2. a) half the answerb) divide by 10c) double d) multiply by 9 or
subtract 10% from original quantity
3. a) divide by 10b) half 50%
4. a) 75b) 200c) 33d) 63
5. a) 154b) 292.5c) 35.2d) 78.72
6. a) 601.6b) 41.6c) 59.4d) 50.88
Equivalent Fractions
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Answers2.
a)4b)15c)12d)20e)60f)8g)26h)32i)120j)15k)64l)154m)125n)400o)615p)9720
HCF and LCM
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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
1.422.123.404.205.806.427.558.14
1.62.53.84.125.106.147.138.19
Indirect Proportion
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1. If A is indirectly proportional to B and when A= 5 B= 6 :1.Find k2.Write an equation linking A and B3.Find A when:
1. B=32.B=15
4.Find B when:1. A=12.A=-3
2. If A is indirectly proportional to B and when A= 7 B= 12 :1.Find k2.Write an equation linking A and B3.Find A when:
1. B=42.B=6
4.Find B when:1. A=102.A=2
3. If A is indirectly proportional to B and when A= -4 B= 10 :1.Find k2.Write an equation linking A and B3.Find A when:
1. B=-82.B=10
4.Find B when:1. A=-12.A=-0.5
4. If A is indirectly proportional to B and when A= 24 B= 0.5 :1.Find k2.Write an equation linking A and B3.Find A when:
a.B=6b.B= -3
4.Find B when:a.A= -2b.A= 100
1. 1.k=302.A x B=303.
1. A=202.A=2
4. 1. B=302.B=-10
2. 1.k=842.A x B=843.
1. A=212.A=14
4. 1. B=8.42.B=42
3. 1.k=-402.A x B=-403.
1. A=52.A=-4
4. 1. B=402.B=80
4. 1.k=122.A x B=123.
1. A=22.A=-4
4. 1. B=-62.B=0.12
Fractions, Decimals and Percentages
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1. a) 75%b) 10%c) 20%d) 35%e) 42%
2. a) 0.7b) 0.25c) 0.3d) 0.15e) 0.05
3. a) 60% b) 70%c) 8%d) 27%e) 80%
4. a) ¼b) 33/100c) 51/100d) 4/5e) 1/5
5. a) 0.4b) 0.9c) 0.74d) 0.03e) 0.05
6. a) 7/10b) 3/5c) 11/50d) 7/20e) 21/50
Limits
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1) These numbers have been rounded to the nearest 10, write down the largest and smallest values they could be:
1) 502) 803) 110
2) These numbers have been rounded to the nearest whole number, write down the upper and lower limits:
1) 32) 173) 234) 1005) -3
3) These lengths have been rounded to the nearest 10th of a cm, write the upper and lower limits:
1) 12.5cm2) 21.7cm3) 35.8cm4) 52.1cm5) 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.
Answers1.
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 12.552.21.65 and 21.753.35.75 and 38.54.52.05 and 52.155.80.35 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
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A. List the first 5 multiples of:1. 52. 73. 124. 145. 19
B. What is the:6. 9th multiple of 87. 7th multiple of 68. 12th multiple of 129. 11th multiple of 1010. 13th multiple of 511. 5th multiple of 13
C. List 3 numbers which are in:1. 3 and 4 times tables2. 3 and 5 times tables3. 10 and 4 times tables4. 9 and 2 times tables5. 12 and 10 times tables
D. What is the lowest common multiple of:1. 5 and 62. 7 and 83. 4 and 84. 9 and 65. 10 and 6
E. What is the lowest common multiple of:6. 13 and 57. 15 and 128. 16 and 109. 14 and 2110. 21 and 70
a) 5,10,15,20,25b) 7.14.21.28.35c) 12,24, 36, 48, 60d) 14,28,42,56,70e) 19,38,57,76,95
f) 72g) 42h) 144i) 110j) 65k) 65
l) 12,24,36m)15,30,45n) 20,40,60o) 18,36,54p) 60,120,180
q) 30r) 56s) 8t) 18u) 30
v) 65w)60x) 80y) 42z) 210
Multiplying and dividing fractions
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Answers1.
a)3/32b)5/48c)1/9d)4/25e)7/16
2. a)65/18 b)11c) 8d)1e)1/2
3. a)4/24 or 1/6b)20/12 or 5/3c)1d)1e)24/42 or 4/7
4. a)39/30 or 13/10b)22/18 or 11/9c) 32/36 or 8/9d)63/28e)50/16 or 25/8
Multiplying and dividing decimals
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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 Dividing1
a)3.2 ÷ 4b)4.8 ÷ 8c) 7.2 ÷ 9d)2.4 ÷ 6e)1.8 ÷ 3
2 f)5.6 ÷ 0.7g)6.3 ÷ 0.7h)2.7 ÷ 0.3i)4.9 ÷ 0.7j)2.8 ÷ 0.7
3 k) 1.65 ÷ 0.15l) 24 ÷ 0.12m) 27.3 ÷ 1.3n) 0.03 ÷ 0.005o) 0.99 ÷ 0.0009
Answers1.
a) 5.6b) 3.5c) 0.6d) 2.4e) 0.9
2. a) 0.1b) 0.28c) 0.08d) 0.81e) 0.06
3. a) 0.57
b)0.8c) 0.75d)0.34e)0.91
4. a)0.594b)5.044c) 6.059d)0.506e)6.15
1. f)0.8g) 0.6h)0.8i)0.4j)0.6
2. k)8l)9m)9n)7o)4
3.p) 11q)200r)21s)6t)1100
Ordering Fractions
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ANSWERS1. 1/4 3/8 ½ and 4/8
3/42. 2/5 ½ 3/5 and 6/10
2/293. 1/3 5/12 1/1 4/6
3/44. 1/4 1/2 2/3 5/6
7/85. 1/4 2/5 1/2 6/10
3/46. 1/3 4/9 1/2 2/3
5/67. 2/6 1/4 5/12 2/3
7/98. 2/7 2/4 5/8 11/14
3/2
Ordering Decimals
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1. For each pair of numbers say which is bigger by adding > or <.
a) 0.2 0.7b)0.3 0.1c)0.7 0.9d)0.3 0.4e)0.6 0.3f)0.24 0.2 g)0.3 0.39h)0.4 0.35i)0.9 0.85j)0.22 0.3
2. Try these:a) 0.04 0.05b)0.02 0.09c)0.12 0.02d)0.04 0.23e)0.4 0.04
3. These are trickier:a) 2.34 0.09
b) 4.49 4.0003c) 5.01 5.1d) 6.32 6.325e) 7.436 7.43f) 8.35 8.345
4. Put these decimals in ascending order (smallest to biggest):a. 0.2 0.3 0.15b. 0.7 0.64 0.072c. 0.85 0.9 0.425d. 0.734 0.7345 0.7335e. 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 0.3b)0.072 0.64 0.7c) 0.425 0.85 0.9d)0.7335 0.734
0.7345e)6.009 6.234 6.4
Percentage Increase/Decrease
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1. Explain how you would use a calculator to increase an amount by a given percent.
2. Increase the following amounts by 42%a)£225b) £306c)£125d)£448e)£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 yearb)2 yearsc)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) £225b) £306c) £125d) £448e) £512
7. A TV costs £120, how much will it cost if its price is decreased by:
f) 19%g) 32%h) 79%i) 73.5%j) 42%
8. A car bought for £6, 500 depreciates in value by 12.5% each year, how much will it be worth after:
k) 1 yearl) 2 yearsm) 5 years?
ANSWERS1. 2.
a) 319.5b)434.52c)177.5d) 636.16e)727.04
3. a)134.40b)157.20c)186d)195e)239.88
4. a)73.50b) 77.91c)91.49
5. 6.
a)162b)220.32c)90d) 322.56e)368.64
7. a)97.20b) 81.60c)25.20d)31.80e)69.60
8. a)5687.50b) 4976.56c)333.91
Rounding to Significant Figures
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Main1. 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 1460ii. 200 160 157iii. 40 37 37.1 iv. 6 6.1 6.09v. 0.006 0.0064 0.00640
3. a) 4.7b) 0.058c) 0.19d) 540
Rounding to Decimal Places
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a) 1.463884266b) 1.572660902c) 3.783345228d) 6.3931313e) 0.640368898f) 0.326119942g) 4.249504359h) 4.44692939i) 1.447852851 j) 0.069143754
Work out the following on a calculator and give the answer to 2 decimal places;
a) 3.104 x 5.938b) 2.99 x 8.82c) 7.1537÷ 3.111d) 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 1.464b)1.6 1.57 1.573c)3.8 3.78 3.783d)6.4 6.39 6.393e)0.6 0.64 0.640f) 0.3 0.33 0.326g)4.2 4.25 4.250h)4.4 4.45 4.447i) 1.4 1.45 1.448j) 0.1 0.07 0.069
• a)18.43b)26.37c)2.30d)219.15e)3.67
Reverse Percentages
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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% increaseb)Cost= £74.75 after 15% increasec)Cost= £61 after 22% increased)Cost= £104 after 30% increasee)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% decreaseb) Cost= £93.5 after 15% decreasec) Cost= £39 after 35% decreased) Cost= £4 9fter 40% decreasee) Cost= £67.50 after 55% decrease6. A Cars value has dropped by 11.5% it is now worth £3053.25, what was it worth when it was new?
Answers1.
a)1.15b)1.25c) 1.04d)1.005e)1.135
2. a)45b)65c) 50d)80e)80
3. 2404.
a)0.85b)0.75c) 0.96d)0.995e)0.865
5. a)80b)110c) 60d)15e)150
6. 3450
Standard Form
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Answers1. a,e,f,g
2. 1. 474000000
2.1903.86200004.640005.350006.663000007.9090000008.60009.8710000000
3. 1.0.0000000001362.0.000000000953.0.000006384.0.00000007965.0.00000566.0.000000005437.0.0000000006328.0.000489.0.000161
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
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Answers1.
1.x2+12x+352.x2+10x + 213.x2 + 5x + 64.x2 + 6x + 85.x2 + 9x + 8
2. 1.x2 – 492.x2 + x – 123.x2 + 8x -204.x2 -17x + 725.x2 -10x + 24
3. 1.6x2+15x – 92.8x2 + 76x -403.9x2-71x – 84.6x2 – 48x + 425.9x2 – 37x + 4
4. 1.6x2 + 12x – 482.28x2 + 21x -493.12x2 -36x – 48
5. 15x2 + 10x – 25
Answers1.
1. x2+12x+352. x2+10x + 213. x2 + 5x + 64. x2 + 6x + 85. x2 + 9x + 8
2. a)x2 – 49b)x2 + x – 12c) x2 + 8x -20d)x2 -17x + 72e)x2 -10x + 24
3. a)6x2+15x – 9b)8x2 + 76x -40c) 9x2-71x – 8d)6x2 – 48x + 42e)9x2 – 37x + 4
4. a)6x2 + 12x – 48b)28x2 + 21x -49c) 12x2 -36x – 48
5. 15x2 + 10x – 25
1. Find xa) 2x + 4 = 3x + 1b) 10x + 8 = 4x + 38c) 7x – 3 = 3x +25d) 11x + 5= 9x + 21e) 4 + 11x = x + 9
2. Solve these equationsa) 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)= 25b) 2(2x + 1) + 6(x + 3)= 70c) 4(3x + 3) – (x + 5)= 92
Answers1. a)x=3b)x=5c)x=7d)x=8e)x=0.52.a)x=5b)x=10c)x=3d)x=2e)x=113.a)x=3b)x=5c)x=9Home
Algebraic Fractions
Home
Answers1. a)x=7b)x=42c)x=2d)x=122.a)x=10b)x=3c)x=28d)x=453.a)x=5b)x=11c)x=4d) x=9
Answers3.a)x=12b)x=5c)x=114.a) x=10b) x=5c) x=2d) x=7e) x=6f) x=4
Brackets
Home
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)
ANSWERS1.
a)2X + 10b)12X + 42c)32X – 16d)15X – 45e)8 – 4Xf) 24 – 32Xg)X2 + 3Xh)2X2 + 9Xi) 4X2 – 7Xj) 18X-10X2
2. a)3X3 + 5Xb)10X3 + 12Xc)15X4-35X
3. a)7X - 12b)17X + 9c)24X - 15d)13X + 4e)28-17X
Collecting like terms
Home
1. Simplifya) 10a + 4ab) 2b + 7bc) 3a + a + 4ad) 11b – 4b e) 14b – 5b + 4bf) 3a – 6a + a
2. Simplifya) 10a + 4b –a +5bb) 8a + 5a +5b – 3bc) 12b – 7a + 3b +ad) 2b – 8b –a + 9ae) -13b + 4a -5b -4af) 11a + 8b + 2c + 6a + 3b -2cg) 6b + 4b –a +6c + 5a – 4ch) 7c + 4b- 3b + a + 10c – 5ai) 10a + 4b + 7a + 10b – 17a – 14bj) 5b + 4c + 18c – 22a + z
Answers1.
a)14ab)9bc)8ad)7be)13bf) -2a
2. a)9a + 9bb)13a + 2bc)15b – 6ad)8a – 6be)-18bf) 17a + 11bg)4a + 10b + 2ch)-4a + b + 17ci) 0j) 5b + 22c -22a + z
Curved Graphs
Home
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
Home
A) Factorise the following completely:
1. 10A + 152. 24A + 363. 16A - 644. 15B2 + 20B5. 14B2 + 49B6. 9B2 + 72B7. 33B2 - 44B8. 2C3 + 8C9. 5C4 + 40C10.10C3 + 8C
B) Factorise the following completely:
1. 9AB + 6A2. 16AB – 4B3. 30A2B + 24AB4. 10AB2 – 15B2
5. 12ABC + 20 AB6. 28A2BC + 14ABC7. 4AB – 8A + 16B8. 15A – 18B – 21AB9. 9B3 + 18BC + 30AB10. ABC-10AB +AB
ANSWERSA.
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+
10A)10.AB(C-10+1)
Finding the gradient
Home
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:f) (2,5) and (3,-3)g) (2,8) and (3,2)h) (4,8) and (8,4)i) (8,15) and (6,33)j) (7,12) and (4,42)k) (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 (4,4.75e) (0,11) and (4,11.4)
Answers1.
a)2b)4c)1
d)5e)3
2. a)-8b)-6c)0d)-1
e)-10f)-6
3. a)0.5
b)-0.5c)0.75d)0.25e)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=5b.M=12 and a=12c.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 mass4.Write a formula for density
a.Find D if i.M=10 and v= 40ii.M=12 and v=72iii.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)5.Write a formula for power6.Find p if:
a.V= 4 and r=8b.V=9 and r=3
7.Find r if:a.P=16 and v=8
8.Find v if:a.P=20 and r=5
Formulae
Home
AnswersA.
1. a)50b) 144c) 6.5
2. a) 5
3. a) 3
B. 1. D=V/M2.
a)4b)6c) 18
3. a) 13
4. a) 88
C. 1. P=Z2/R2.
a)2b) 27
3. a) 4
4. a) 10
Inequalities
Home
ANSWERS1.
1)x>62)x>93)x≥114)x≥25)x<126) x≤207)x≤208)x<20
2. 1)6 <x ≤ 102)9< x <163)11 ≤ x
<154) 2 ≤ x ≤
8
Laws of indices
Home
1. Simplify:a) A2 x Ab) A4 x A2
c) A8 x A2
d) 3A9 x A3
e) 4A2 x 5A1
2. Simplify:a) A10 ÷ Ab) 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:f) A-4
g) A-6
h) A-2
i) 2A-4
j) 9A-3
6. Simplify fully:k) 25A4 ÷ 5A7
l) 3A9 x 2A-3
m)(A2)6 x (2A2)2
n) (2A3)8 ÷ (2A4)6
o) (A2)-6
ANSWERS1.
a)A3
b)A6
c)A10
d) 3A12
e)20A3
2. a)A9
b)A14
c)A16
d) 3A6
e)3A2
3. a) 1b)1c)1d)1e)1
4. a)A8
b) A9
c)A12
d)4A18
e)27A12
5. a) 1/A4b) 1/A6c) 1/A2d) 2/A4e) 9/A3
6. a) 5/A3
b) 6A6
c) 4A16
d) 4e) 1/A12
•
Parallel and Perpendicular lines
Home
ANSWERS1. 2.
a)y=3x-7b)y=5x-10c)y=2x+16d)y=131-9xe)y=-3x-15
ANSWERS1. 2.
a)y=-1/2x+9b)y=-1/4x+17.75c)y=2x-1d)y=(2/3)x-2.67
Find the Nth term of these sequences
1) 6, 17, 34, 57, 862) 3, 18, 41, 72, 1113) 7,14,23, 34, 474) 8, 19, 34, 53, 765) 2, 12, 30, 56, 90
Answers1) 3n2+2n +12) 4n2+3n -43) n2 + 4n + 24) 2n2 +5n + 15) 4n2 -2n
Home
The quadratic equation
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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=-3b) 6x2+x - 10=0c) x2-4x -5=0d) 2x2-10x + 7=0e) 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 =10b) 4x + 5x2 - 10=2c) x2 + 5x -3=xd) 2x2-10x - 2= x2
e) 3x2 + 6 + 2x =8 + 7x
ANSWERS1.
a) b) a=6 b=1 c=-10c) a=1 b=-4 c=-5d) a=2 b=-10 c=7e) a=0.5 b=8 c=2
2. a) x=0.6 and -2.6b) x=1.2 and -1.4c) x=2.8 and -1.8d) x=4.2 and 0.8e) x=-0.3 and -
15.73.
1. x=1.1 and -5.62. x=1.2 and -23. x=4.6 and -4.64. x=10.2 and -0.25. x=2 and -0.3
Factorising Quadratics
Home
1. Factorise and solve:a) X2 + 8X + 12= 0b) X2 + 7X + 10= 0c) X2 + 13X + 12= 0d) X2 + 17X + 70=0e) X2 + X – 20=0f) X2 - 4X- 12=0g) X2 - 12X + 20=0
2. Rearrange, factorise and solvea) X2 + 21X + 32=12b) X2 + 8X -5 = 15c) X2 + 6X + 23 = 5 – 3X
3. Solvea) 3X2 + 21X + 51=15b) 2X2 +18 + 10=-6c) 4X2 -8X -4= 36 + 4x
ANSWERS1.
a)-6 and -2b)-5 and -2c)-12 and -1d)-7 and -10e)-5 and 4f)6 and -2g)10 and 2
2. a)-20 and -1b)-10 and 2c)-6 and -3
3. a)-4 and -3b)-8 and -1c)5 and -2
Sequences
Home
1. Copy down the following sequences and add the next three terms:a) 3 6 9 12 15b) 2 7 12 17 22c) 4 10 16 22 28d) 13 24 35 46 57e) 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 1.9b) 1.4 1.7 2 2.3 2.6c) 40 39.5 39 38.5 38d) 5.9 5.3 4.7 4.1 3.5e) 11.4 12.5 13.6 14.7 15.8
4. Copy the following sequences, write the term to term rule and find the next 3 terms.a) 5 0 -5 -10 -15b) 3 -1 -5 -9 -13c) -20 -16 -12 -8 -4d) -30 -27.5 -25 -22.5 -20
5. Copy the following sequences, write the term to term rule and find the next 3 terms.a) 1 2 4 8 16b) 1 3 6 10 15c) 1 3 7 13 21
Answers1.
a)18,21,24b)27,32,37c)32,36,40d)68,79,90e)40,38,36
2. a)add 3b)add 5c)add 4d)add 11e)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
Home
•1) Find the nth term of the following sequences:a) 4 7 10 13 16b) 2 7 12 17 22c) 4 10 16 22 28d) 13 24 35 46 57e) 1 9 17 25 33
•2) Take the following nth terms and find the first 5 termsa) 3n + 1b) 4n +2c) 5n + 5d) 4n – 1e) 6n + 3f) 10n -3
•3) If the nth term is 7n + 4 what isa. The 4th term b. The 12th term c. The 100th term
•4) If the nth term is 8n - 2 what isa. The 4th term b. The 12th term c. The 100th term
•5) If the nth term is 11n + 3 what isa. The 4th term b. The 12th term c. The 100th term
•6) If the nth term is n + 9 what isa. The 4th term b. The 12th term c. The 100th term
Answers1.
a)3n+1b)5n-3c) 6n-2d)11n+2e)8n-7
2. a)4,7,10,13,16b) 6,10,14,18,2
2c)10,15,20,25,30d)9,15,21,27,33e)7,17,27,37,47
3. a)32b) 88c)704
4. a)30b) 94c)798
5. a)47b)135c) 1103
6. a)13b) 21c)109
Simplifying Expressions
Home
Answers1.
a)20a4
b)18a7
c)63a8
d)20a2b4
e)18a2b7
f)63a2b8
g)8a2b2c5
h)60a2b2c14
i) 36a8b8cj) 12a5b4c4
2. a)4ab)3a4
c)7a2
d)6a3b3
e)9a4/b5
3. a)10a2
b)10ab2
c)ab6/10d)ab2
e)119a3b8
Simultaneous Equations
Home
1. Find a and b for each pair of simultaneous equations:a) 5a + 2b= 14 6a + 2b= 16b) 7a + 3b= 27 6a + 3b= 24c) 10a - 2b= 30 3a - 2b= 2d) 9a - 6b= 42 6a - 6b= 18
2. Find a and b for each pair of simultaneous equations:a) 4a + 7b= 27 4a - 7b= 13b) 3a + 2b= 35 2a - 2b= 10c) 11a - 8b= 4 a + 8b= 44d) 5a + 3b= 69 7a - 3b= 75
3. Find a and b for each pair of simultaneous equations:a) 5a + 6b= 28 6a + 2b= 18b) 4a + 4b= 36 6a - 2b= 22c) 2a - 8b= 16 3a + 2b= 29d) 9a + 6b= 84 3a - 3b= 25.5
Answers1.
a)a=2 b=2b)a=3 b=2c)a=4 b=5d)a=8 b=5
2. a)a=5 b=1b)a=9 b=4c)a=4 b=5d)a=12 b=3
3. a)a=2 b=3b)a=5 b=4c)a=10
b=0.5d)a=9
b=0.5
Solving Equations
Home
1. Find x if:a) 7x= 42b) 12x=36c) 5x = 40d) 10x = 110e) How did you answer these questions?
2. Find x if:a) X + 10 = 17b) X + 15 = 27c) X + 25 = 30d) X- 9 = 15e) X – 13 = 40f) How did you answer these questions?
3. Find x ifa) 3x + 6 =21b) 7x + 11 = 67c) 5x + 4 = 24d) 9x – 2 =25e) 11x – 14= 30f) 10x - 7= 53g) 12x + 11= 155h) 15x - 14= 61i) 13x + 25 = 90j) How did you answer these questions?
Answers
1. a)8b)6c)3d)10
2. a)7b)12c)5d)16e)27
3. a)5b)8c)4d)3e)4f) 6g)12h)5i) 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 -12. y=5x - 3 and y=4x + 13. y=x + 7 and y=2x + 44. y=2x + 2 and y=6-3x5. y=10 – 2x and y=12-3x
1. (5,14)2. (2,7)3. (3,10)4. (1,3)5. (2,6)
Home
Substituting
Home
1. If A is 5 what is:a) 5Ab) 11Ac) 6A – 10d) 9A + 15e) 100-5A
2. If B is 7 what isa) 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+Bb) B-Ac) 6A+2Bd) ABe) A(B+1)f) A2B
ANSWERS1.
a) 2 b) 55c)20d)60e)75
2. a)30b) 15c)84d)27e)20
3. a)13b)1c) 50d)42e)48f)252
4. a)8b)-2c) 30d)12e)8
5. a)-33b)0c)9d) -16e)-18f)-50g)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=0b) X2 + 2x -20=0c) X2 + 4x -10=0d) 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=0b) 2X2 + 2x -25=0
Trial and Improvement
Home
x X2 +3x -30 Big or small?
ANSWERS1.
a) x=4.2b)x=3.6c)x=1.7d)x=3.4
2. a) x=2.8
4b) x=3.0
7
Writing Expressions
Home
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 meb) My sister is 2 years younger than mec) My mum is double my aged) My dad is 5 years older than my mume) My Gran is 4 times my agef) 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 ownb) I give Alan half of my sweetsc) I eat four sweets then give Simon the restd) 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 timesc) I listen to the intro (a quarter of the song) 5 timesd) I listen to my song, then the next one which is exactly twice as longe) I listen to my song, then the next one which is exactly twice as long, and do this 5
times throughout the day4. If a rectangle has lengths x and y, write an expression for:
a) The area of the rectangleb) The area covered by 6 rectanglesc) The perimeter of the rectangle
Answers1.
a)C + 3b)C – 2c)2Cd) 2C+5e)4Cf)2(2C+5) OR 4C + 10
2. a)S+5b) S/2c)S-4d)S/4 + 1
3. a)24Mb)M/2 X 8 OR 4Mc)5M/4d) 3Me)15M
4. a) xyb)6xyc)2x + 2y or 2(x + y)
y=mx +c
Home
1. Copy and complete:a) A line with a positive gradient will go from ________ left to ________rightb) 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+4b) Y= 2x-5c) Y=6x+9d) Y=x- 7e) Y=10xf) Y=5+8xg) Y=7-11x
3. Draw an axis from -10 to 10, plot the following linesa) Y = 2x + 3b) Y = 3x – 2c) Y = -2x + 5d) 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
Answers1.
a)bottom / topb)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)1b)2c)3d)2e)3
5. a)0b)-5c)-1d)-11e)-25
Finding the Area of CirclesYou 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 12.6b 78.5c 15.2d 380.1e 314.2f 153.9g 100.5h 28.3
ANSWERS
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Area of Triangles
Home
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. 10m2. 14m3. 6m4. 10m5. 10m6. 3m7. 20m
Circumference11cm 23cm 4cm 7cm
5cm
3cm20cm30cm
30cm
9cm 4cm
6cm 12cm8cm
5cm14cm
18cm
6cm
Answers:1. 34.6cm2. 72.33. 25.1cm4. 44.0cm5. 77.1cm6. 51.4cm7. 10.7cm8. 17.9cm9. 95.1cm10.23.4cm11.51.0cm12.81.4cm
1 2 3 4
5 6 7 8
9 10 11 12
Home
25°
x
160°100°
60°
135°
90°
xx
xxx
12 3
64 5
Answers1) 502)1203)1804)505)67.56)80
Home
Double angle theorem
60°
x
1 2 3
31 2
72°
x
x x
x y
y
x
100°
x30°
22°
y
Answers1) X=302)x=183)x=45
4)X=40 y=405)x=30 y= 1206)x=22 y=136
x
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Triangles inside circles
25°x
12
3
645
y15°
yz
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°
Answers1) x=25 y=152)x=125 y= 40 z=153)x=10 y=70 z=1004)X=105 y=40 z=355)x=53 y= 30 z=726)x=85 y=80 z=17
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Angles connected by a chord
40°xy
z
3
120°
x
4
140°
x
2
x35 °
1
y
z
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Tangents to a circleAnswers:
1. x=552. x=403. x=50 y=50
z=404. x=60 y=60
z=30
x
yx
y
x
y
95° 110° 54°
75°
20°
80°
x 2a
4b
15° 70° a
b
1
25°
yz
w
2 3
4 5Answers1) x=70 y=852)x=126 y=1053)x=100 y=1604)w=15 x=70 y=65 z= 255)a=60 b=36
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Cyclic Quadrilaterals
Construction
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Trigonometry- Sin and Cos
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Answers:
1. 1. d=hypotenuse2. e=adjacent3. f= opposite4. h=hypotenuse5. g=adjacent6. i=opposite7. j=hypotenuse8. k=adjacent9. l=opposite10. m=hypotenuse11. o=adjacent12. n=opposite13. p=hypotenuse14. q=adjacent15. r=opposite
Answers:
2. a) 6.1b) 3.5e)7.1f) 7.1g)2.6i)3.1k) 2.1l) 14.9n) 11.3o)3.8p)12.6r)18
Trigonometry- finding angles
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24cm
32cm
Answers:1) 41.42) 76.23) 49.34) 51.45) 70.66) 53.1
29cm
Cosine rule
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Answers:1. 32cm2. 3.5cm3. 45.4c˚4. 139.5 ˚5. 25.2 or
11.1cm6. 16.7cm
22cm
5cm
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Answers:1) 10cm2) 3.0cm3) 3.4 cm4) 25.7cm5) 50.2cm6) 26.7cm
The Sine rule
Trigonometry- Sin, Cos and Tan
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Answers:1.
a)15.7b)46.7c)32.2d)30.6e)21.9f)63.5
2. a)6.1b) 11.9c) 69.3d) 15.6e) 2.1f) 7.7
15.7cm
Sine and Cosine Rule
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Answers:1)25.6˚2)6.5cm3)20.4cm4)21.6 or 15.6
cm5)9.73cm6)40 ˚7)34 ˚8)5.3cm9)14.3˚10)42cm11) 24.46cm12)27.6 or 3.6
cm
8cm
10cm
14cm
15cm
22cm
19cm
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Sin, cos and tan 2
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Answers:1) 3.1cm2) 6.1cm3) 5.1cm4) 17.1cm5) 4.5cm6) 8.6cm7) 20.5cm8) 31.1cm9) 117.6cm10)1.5cm11)4.1cm12)108.9cm
Translation
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Reflection 2
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Reflection 1
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Reflect these shapes in the mirror lines
3D Pythagoras
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Find the length of the longest diagonal of these cuboids
1) Answers2) 11.2cm3) 12.0cm4) 12.2cm5) 9.4cm6) 13.4cm7) 15.2cm
Rotation
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5cm
8cm
8cm
5cm
4cm
9cm 9cm
4cm
12cm
10cm3cm
15cm7cm
11cm
Find the Perimeter of these shapes
8cm8cm
5cm
4cm
9cm
4cm
8cm
3cm
5cm4cm 12cm
11cm
13cm
All of these shapes are regular
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Answers1. 26cm2. 26cm3. 30cm4. 25cm5. 36cm
Answers1. 21cm2. 17cm
Answers1. 16cm2. 25cm3. 72cm4. 39cm5. 96cm6. 110cm7. 42cm
Worded Pythagoras
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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?
Answers1. 44.7m2. 74miles3. 27.7m4. 8m5. 10.7m6. 52.9m
a
b110 °
Find a, b and c giving reasons for each answer.
c a
bc
120 °a
bc
55 °
a
115 °
b
ca b
c25 °
a
b
c
10°
a
27°
Find a, b and c giving reasons for each answer.
120°
b
a75°
45°b
110 °c
95 °c
Answers1. a=27 (corresponding)2. b= 120 (alternate)3. c = 85 (interior)4. a= 105 (interior)5. b=45 (alternate)6. c= 110 (alternate)
Answers1. 70,70,1102. 60,60,603. 55,125,554. 115,65,655. 155,25,256. 170,170,10
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45 °
130 °
30 °
Find the values of x
xx
xx
45 °
55°
25°
Find the values of x
xx
xx
95°15°
60°
35°
30°
120°
Find the values of x
x95°
35 °x
110°70 ° 120°25 °2x
x2x
3x°80 °
4x2x
x
x x5x
Answers1. 1352. 1503. 904. 50
Answers1. 1052. 1203. 1054. 30
Answers1. 1452. 145
Answers1. 452. 363. 804. 31
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Angles in a triangle
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ANSWERS
1.1002.803.904.1005.606.727.718.939.85
ANSWERS
1.502.653.60
ANSWERS
1.802.1303.404.75
Plans and Elevations
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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 shapeb) 5 sided shapec) 8 sided shaped) 10 sided shapee) 20 sided shapef) 30 sided shape
2. Find the missing angles
30° 150° 88° 75°
84° 72°
x
110°
100°x
40°
113°
90°
x53°
330°15°
92°
162°
157°
41°
x
83°
99° x
327°
95°
285°45°
100°
95°
x
x
106°154°
125°
90°88°
3x290°
x
96°
153°153°
172°
93°
32°11°
x 265°
342°
100°
Angles in
Polygons 1
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ANSWERS1.
1. 1802. 5403. 10804. 14405. 32406. 5040
2. 1. 2602. 1493. 2604. 1515. 2196. x= 457. 140
Find the exterior and interior angles of a regular shape which has:a) 9 sidesb) 10 sidesc) 12 sides d) 15 sidese) 25 sides
ANSWERS1.
a) I=140, E=40b) I=144, E=36c) I=150, E=30d) I=156,E=24e) I=165.6, E=14.4
Interior and
exterior angles
1. How many sides does a regular polygon have if it’s exterior angles are:
a) 45b) 40c) 30d) 22.5e) 20f) 3
ANSWERS1.
a) 8b) 9c) 12d) 16e) 18f) 120
Regular polygons –
finding number of sides
2. How many sides does a regular polygon have if it’s interior angles are:
a) 150b) 156c) 157.5d) 162e) 165f) 168.75
ANSWERS2.
a) 8b) 9c) 12d) 16e) 18f) 120
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Pythagoras
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ANSWERS
1. a)5mb)10mc)13md)10.8me)6.3mf)3.3mg)6.9m h)8.7m
2. 5.83. 1.9m
Mean
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1. Find the mean from these numbers:a) 5,3,4b) 10, 11, 1, 7c) 15, 8, 7, 10d) 14, 2, 4, 1, 4e) 7, 8, 5, 10, 4, 2f) 24, 26, 32, 17, 1g) 0.2, 0.1, 0. 5, 0.2h) 20, 9, 3, 8, 8, 7,1i) 17, 18, 15, 10, 8, 2, 9,1j) 0,0,0,0,0,18
2. How would you find the:a) Mean age of players in a football teamb) Mean height of a familyc) Mean number of sweets eaten by boys in a dayd) Mean number of hours spent watching TV for a pupil each nighte) 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 6b) 5 numbers with a mean of 8c) 7 numbers with a mean of 9
ANSWERS
1. a)4b)7c) 10d)5e)6f) 20g)0.25h)8i) 10j) 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
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1. Which of these could you not find a median for?a) Heightb) Favourite colourc) Score in a test d) Favourite football team
2. Find the mean, mode, median and range for these sets of numbers:a) 5,7,2,8,8b) 2,12,6,3,2c) 15,4,11,6,4d) 20,30,35,15,15e) 4,7,0,14,0,19,5f) 2,9,18,12,7,2,6g) 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 115. 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)6,8,7,6b)5,2,3,10c)8,4,6,11d)23,15,20,20e)7,0,5,19f)8,2,7,16g)10,15,13,20
3. 4.Either the mean
or the median5.All can be
negative except the range.
Median and Range
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ANSWERS
1. a)Median-6, range-
10b)Median-17, range-
8 c)Median-11, range-
4 d)Median-2, range-5 e)Median--6, range-
9
2. a)Median=21,
range=34b)Median=35,
range=55 c) Median=574,
range=669 d)Median=-50,
range=97 e)Median=-18,
range=83
3.a)Median=22, range-
36b)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
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ANSWERS
1. 1.402.18.253.Midpoints
are an approximation of the scores
2. 9.05
Mean from tables
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ANSWERS
1. a)18b)24c)1.3
2. a)30b) 44c)1.5
3. a)47b) 107c)2.3
Drawing Pie charts 1
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1. a) 8b) dog=1/8,
cat=1/4, fish=5/8
2.c) green=1/10
Pink=1/4Blue=3/10Red 2/5
b) green=2/20Pink=4/20Blue=6/20Red= 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
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Probability as Fractions
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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 blueb) A red c) A greend) A purplee) A blue or redf) 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 socksb) Clown socksc) Maths Socksd) Clown or spotty sockse) Maths or stripe socks
3. I have a pack of card (without jokers) what is the probability I pick:
a) A Red cardb) A heartc) A Clubd) A heart or a clube) A 2f) A Kingg) A picture cardh) A number card smaller than 6i) A number card greater than 6j) An even numberk) An odd numberl) A red number 3m) A black Queen or red Jackn) A King of Hearts or a 5
ANSWERS
1. a)3/10b)½c) 1/5d)0e)4/5f) 7/10
2. a)½b)¼c) 1/20d)¾
3. a) ½b) ¼c) ¼d) ½e) 1/13f) 1/13g) 4/13h) 4/13i) 4/13j) 5/13k) 4/13l) 1/26m) 1/13n) 5/52
Relative Frequency
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ANSWERS
1. a)75b)37.5c)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,
0.45b) 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
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Spinner 1 Spinner 2 Total
ANSWERS
1.H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6
2. 1.1+1=22.1+2=33.1+3=44.2+1=35.2+2=46.2+3=57.3+1=48.3+2=59.3+3=6
3. Tb,Tt,Tc,Cb,Ct,Cc,Jb,Jt,Jc
4. a)4b)8c)64d)2x
5. a) 6b) 24
Drawing Bar Charts
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Tree Diagrams
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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 outcomes2.Use your tree diagram to find the probability of getting:
a.2 pinkb.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 0.23.What is the probability I will NOT:
a.Have toast for breakfastb.Miss my bus
4.Draw a tree diagram showing all possible outcomes5.Use your tree diagram to find the probability of:
a.Having toast and missing my busb.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:6.Draw a tree diagram to show all possible outcomes.7.Use your tree diagram to find the probability of:
a.A head a 3b.A tails and a number bigger than 4c.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)
8.Draw a tree diagram to show all the possible outcomes,a.Find the probability that I will listen to:
i.Hip Hop then Popii.Rock twiceiii.A Rock song and a pop song in any orderiv.2 songs which are the same style (rock and rock or pop and pop ect.)
ANSWERS A.
2. a) 169/400b) 49/400c) 91/400
B. 1.
a) 0.4b) 0.8
3.
a)0.12
b)0.08
c)0.32C.
2. a) 1/12b) 1/6c) 1/6
D. a)
i. 7/44ii. 4/121iii. 14/121iv. 93/242
Stem and Leaf Diagrams
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ANSWERS
2. a)Range-42 ,
median-34, mode-22
b) range- 4.8, median-22.2 ,mode-22.4
QuestionsPlot 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 sold17 6331 5312 7735 3139 2834 4334 4622 6437 2831 35
Time taken to walk to school
Score in spelling test
27 210 4014 527 140 614 4215 4717 2235 438 3117 1318 227 13
Hours spent on internet
Score on ICT test
13 1433 3927 3738 4513 1839 6210 1930 5419 3629 3416 2225 4228 33
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The Probability Line
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ANSWERS
2. i. 0.1ii. 0.5iii. 0.2iv. 0.2v. 0vi. 1vii.0.4viii.0.6
Box and Whisker plots
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Mutually Exclusive Events
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ANSWERS
1. a)0.7b)0.6c) 0.48d)0.79e)75%f) 2%g)3/5h)4/10i) 3/15
2. a)Mutually
exclusiveb)Not mutually
exclusivec) Not mutually
exclusived)Mutually
exclusive3.
a) 0.1b)0.2c) 0.23
4. 0.24
Sample Space Diagrams
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ANSWERS
1. a)
i. 1/36ii.1/12iii.1/9
b) 7, it appears the most
2. a)0
3. 4.
1. 2.
a)6/25b)19/25c) 9/25d)8/25
Sampling
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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- 5Male and english-6Female and maths-10Female and english-4
Histograms
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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 0.55 1
15 530 2.560 415
Drawing Cumulative Frequency Graphs
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Pie Charts
40 people100 people 40 people 36 people
48 people320 people 640 people 720 people
Answers:1. 20 and 202. All are 253. All are 54. Yellow and blue
are 9 red is 185. 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 270Home
Find the number of people represented by these slices of pie chartsPie Charts 2Favourite Colour Angle
Blue 60Green 30
Turqoise 120Purple 120Black 30
Favourite Country AngleUSA 20
Mexico 20Turkey 40France 100Spain 180
How do you get to school AngleBus 10
Train 80
Walk 140
Car 90
Metro 40
Favourite Sport AngleFootball 36
Hockey 108
Swimming 36
Water polo 108
Basket Ball 72
Favourite food AnglePizza 6
Chinese 54
Roast Dinner 96
Curry 186
Mexican 18
Favourite Maths Topic AngleFractions 18
Area 90
Algebra 54
Percentages 72
Pie Charts 126
156 people were asked
180 people were asked
240 people were asked
72 people were asked
400 people were asked
160 people were asked
people26
13
52
52
13
people5
40
70
45
20
people4
3664
12412
people8
40243256
people40
12040
12080
people448
2036
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Reading Bar Charts
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ANSWERS
1. a)5b)3c)5d)39
2. a)Punkb)RnBc)51d)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
Presentation Courtesy- TES