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Algebra Shape Data Number 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.

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Presentation on theme: "Algebra Shape Data Number 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."— Presentation transcript:

1

2 Algebra

3 Shape

4 Data

5 Number

6 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

7 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

8 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

9 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

10 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

11 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

12 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)2 2 x5 b)3 x 2 3 c)3 x 2 4 d)2 x 3 2 x 5 e)3 4 f)2 x 5 2 g)3 x 5 2 h)2 3 x 3 x 5 i)2 3 x 5 2 j)2 3 x 3 2 x 5 2

13 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

14 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

15 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

16 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 toysb.30 toysc.45 toys 6.Tom and Jerry share sweets in the ratio 2:3, how many do they each get if they share: a.20 sweetsb.30 sweetsc.55 sweets 7.Sue and Linda share some money in the ratio 3:7, how many do they each get if they share: a.£30b.£60c.£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 piecesb.72 piecesc.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

17 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 250b. 40% of 500 c. 15% of 220 d. 75% of 84 5)Find: a.35% of 440b. 65% of 450 c. 16% of 220 d. 82% of 96 6)Find: a.94% of 640b. 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

18 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

19 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

20 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 2.Write an equation linking A and B 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 2.Write an equation linking A and B 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 2.Write an equation linking A and B 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

21 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

22 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 10 th 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 its area rounded to the nearest whole number, it becomes 40cm 2. 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= 12000m 2 b)largest= 442m smallest=438m c)largest= 12110.25m 2 smallest=11890.25m 2 5. smallest- 3.95cm largest- 4.05cm 6. largest- 7.9cm smallest- 7.7cm

23 Multiples A. List the first 5 multiples of: 1.5 2.7 3.12 4.14 5.19 B. What is the: 1.9 th multiple of 8 2.7 th multiple of 6 3.12 th multiple of 12 4.11 th multiple of 10 5.13 th multiple of 5 6.5 th multiple of 13 C. List 3 numbers which are in: 1.3 and 4 times tables 2.3 and 5 times tables 3.10 and 4 times tables 4.9 and 2 times tables 5.12 and 10 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

24 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

25 Multiplying and dividing decimals 1a)0.8x7= b)0.5x7= c)0.1x6= d)0.6x4= e)0.3x3= 2a)0.2x0.5= b)0.4x0.7= c)0.8x0.1= d)0.9x = e)0.6x0.1= 3a)1.9x0.3= b)1.6x0.5= c)1.6x0.5= d)1.7x0.2= e)1.3x0.7= 4a)5.4x0.11= b)5.2x0.97= c)8.3x0.73= d)4.6x0.11= e)8.2x0.75= 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

26 Ordering Fractions ANSWERS 1.1/4 3/8½ and 4/83/4 2.2/5½3/5 and 6/102/29 3.1/35/121/14/63/4 4.1/41/22/35/67/8 5.1/42/51/26/103/4 6.1/34/91/22/35/6 7.2/61/45/122/37/9 8.2/72/45/811/143/2

27 Ordering Decimals 1.For each pair of numbers say which is bigger by adding > or <. a)0.20.7 b)0.30.1 c)0.70.9 d)0.30.4 e)0.60.3 f)0.240.2 g)0.30.39 h)0.40.35 i)0.90.85 j)0.220.3 2.Try these: a)0.040.05 b)0.020.09 c)0.120.02 d)0.040.23 e)0.40.04 3. These are trickier: a)2.340.09 b)4.494.0003 c)5.015.1 d)6.326.325 e)7.4367.43 f)8.358.345 4. Put these decimals in ascending order (smallest to biggest): a. 0.20.30.15 b. 0.70.640.072 c. 0.850.90.425 d. 0.734 0.73450.7335 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

28 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

29 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

30 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)14.77 2 Round the following numbers to a) 1 decimal place b) 2 decimals places c) 3 decimal places ANSWERS a)1.51.461.464 b)1.61.571.573 c)3.83.783.783 d)6.46.396.393 e)0.60.640.640 f)0.30.330.326 g)4.24.254.250 h)4.44.454.447 i)1.41.451.448 j)0.10.070.069 a)18.43 b)26.37 c)2.30 d)219.15 e)3.67

31 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

32 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 10 3 2.4.4 x 10 5 3.1.35 x 10 7 4.9.87 x 10 7 5.3.4 x 10 -5 6.9.301 x 10 -5 7.4.3 x 10 -4

33 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

34 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

35 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

36 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(3x 2 + 5) b)2x(5x 2 + 6) c)5x(3x 3 - 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)X 2 + 3X h)2X 2 + 9X i)4X 2 – 7X j)18X-10X 2 2. a)3X 3 + 5X b)10X 3 + 12X c)15X 4 -35X 3. a)7X - 12 b)17X + 9 c)24X - 15 d)13X + 4 e)28-17X

37 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

38 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

39 Factorising A) Factorise the following completely: 1.10A + 15 2.24A + 36 3.16A - 64 4.15B 2 + 20B 5.14B 2 + 49B 6.9B 2 + 72B 7.33B 2 - 44B 8.2C 3 + 8C 9.5C 4 + 40C 10.10C 3 + 8C B) Factorise the following completely: 1.9AB + 6A 2.16AB – 4B 3.30A 2 B + 24AB 4.10AB 2 – 15B 2 5.12ABC + 20 AB 6.28A 2 BC + 14ABC 7.4AB – 8A + 16B 8.15A – 18B – 21AB 9.9B 3 + 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(C 2 +4) 9.5C(C 3 +8) 10.2C(C 2 +4) B. 1.3A(3B+2) 2.4B(4A-1) 3.6AB(5A+4) 4.5B 2 (2A-3) 5.4AB(3C+5) 6.14ABC(2A+1) 7.4(AB-2A+4B) 8.3(5A-6B-7AB) 9.3B(3B 2 +6C+10 A) 10.AB(C-10+1)

40 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

41 A) Isaac Newtons 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=Z 2 /R 2. a)2 b)27 3. a)4 4. a)10

42 Inequalities ANSWERS 1. 1)x>6 2)x>9 3)x11 4)x2 5)x<12 6)x20 7)x20 8)x<20 2. 1)6 { "@context": "http://schema.org", "@type": "ImageObject", "contentUrl": "http://images.slideplayer.com/7/1651852/slides/slide_42.jpg", "name": "Inequalities ANSWERS 1.1)x>6 2)x>9 3)x11 4)x2 5)x<12 6)x20 7)x20 8)x<20 2.", "description": "1)6

43 Laws of indices 1.Simplify: a)A 2 x A b)A 4 x A 2 c)A 8 x A 2 d)3A 9 x A 3 e)4A 2 x 5A 1 2.Simplify: a)A 10 ÷ A b)A 21 ÷ A 7 c)A 20 ÷ A 4 d)9A 12 ÷ 3A 6 e)12A 6 ÷ 4A 4 3.Simplify: a)(A 2 ) 4 b)(A 3 ) 3 c)(A 2 ) 6 d)(2A 9 ) 2 e)(3A 4 ) 3 4. Simplify : a)A 0 b)B 0 c)99 0 d)52 0 e)0.061 0 5. Simplify: a)A -4 b)A -6 c)A -2 d)2A -4 e)9A -3 6. Simplify fully: a)25A 4 ÷ 5A 7 b)3A 9 x 2A -3 c)(A 2 ) 6 x (2A 2 ) 2 d)(2A 3 ) 8 ÷ (2A 4 ) 6 e)(A 2 ) -6 ANSWERS 1. a)A 3 b)A 6 c)A 10 d)3A 12 e)20A 3 2. a)A 9 b)A 14 c)A1 6 d)3A 6 e)3A 2 3. a)1 b)1 c)1 d)1 e)1 4. a)A 8 b)A 9 c)A 12 d)4A 18 e)27A 12 5. a) 1/A4 b)1/A6 c)1/A2 d)2/A4 e)9/A3 6. a)5/A 3 b)6A 6 c)4A 16 d)4 e)1/A 12

44 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

45 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)3n 2 +2n +1 2)4n 2 +3n -4 3)n 2 + 4n + 2 4)2n 2 +5n + 1 5)4n 2 -2n

46 The quadratic equation 1.For each of these equations, what is a, b and c? (the first one has been done for you) a)2x 2 +4x -3 =0a=2b=4c=-3 b)6x 2 +x - 10=0 c)x 2 -4x -5=0 d)2x 2 -10x + 7=0 e)0.5x 2 +8x + 2=0 2.Use your answers from question one to find the possible values for x. 3.Rearrange these equations to the form ax 2 + bx + c =0, then solve with the quadratic equation: a)2x 2 + 9x -2 =10 b)4x + 5x 2 - 10=2 c)x 2 + 5x -3=x d)2x 2 -10x - 2= x 2 e)3x 2 + 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

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

48 Sequences 1.Copy down the following sequences and add the next three terms: a)3691215 b)27121722 c)410162228 d)1324354657 e)5048464442 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)0.30.71.11.51.9 b)1.41.722.32.6 c)4039.53938.538 d)5.95.34.74.13.5 e)11.412.513.614.715.8 4.Copy the following sequences, write the term to term rule and find the next 3 terms. 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 5.Copy the following sequences, write the term to term rule and find the next 3 terms. a)124816 b)1361015 c)1371321 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...

49 The Nth term 1) Find the nth term of the following sequences: a)47101316 b)27121722 c)410162228 d)1324354657 e)19172533 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 4 th termb. The 12 th termc. The 100 th term 4) If the nth term is 8n - 2 what is a.The 4 th termb. The 12 th termc. The 100 th term 5) If the nth term is 11n + 3 what is a.The 4 th termb. The 12 th termc. The 100 th term 6) If the nth term is n + 9 what is a.The 4 th termb. The 12 th termc. The 100 th term 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

50 Simplifying Expressions Answers 1. a)20a 4 b)18a 7 c)63a 8 d)20a 2 b 4 e)18a 2 b 7 f)63a 2 b 8 g)8a 2 b 2 c 5 h)60a 2 b 2 c 14 i)36a 8 b 8 c j)12a 5 b 4 c 4 2. a)4a b)3a 4 c)7a 2 d)6a 3 b 3 e)9a 4 /b 5 3. a)10a 2 b)10ab 2 c)ab 6 /10 d)ab 2 e)119a 3 b 8

51 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 2.Find a and b for each pair of simultaneous equations: 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 3.Find a and b for each pair of simultaneous equations: a)5a + 6b= 28 6a + 2b= 18 b)4a + 4b= 36 6a - 2b= 22 c)2a - 8b= 163a + 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

52 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

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

54 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)A 2 B 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

55 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)X 2 + 3x -30=0 b)X 2 + 2x -20=0 c)X 2 + 4x -10=0 d)X 2 -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)3X 2 - 5x -10=0 b)2X 2 + 2x -25=0 Trial and Improvement xX2X2 +3x-30Big 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

56 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 Im 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)

57 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

58 Finding the Area of Circles You can find the area of a circle by using the formula- Area= π x Radius 2 For Example- Area= π x 7 2 = π x 49 = 153.93804 = 153.9 (to 1dp) cm 2 7cm 2a12.6 b78.5 c15.2 d380.1 e314.2 f153.9 g100.5 h28.3 ANSWERS

59 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: 1.6m 2 2.24m 2 3.3m 2 4.20m 2 5.12m 2 6.35m 2 7.44m 2 8.15m 2 9.31.5m 2 10.72m 2 Answers: 1.10m 2.14m 3.6m 4.10m 5.10m 6.3m 7.20m

60 Circumference 11cm 23cm 4cm 7cm 5cm 3cm20cm 30cm 9cm4cm 6cm12cm 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

61 25° x 160° 100° 60° 135° 90° xx xxx 1 2 3 6 4 5 Answers 1) 50 2)120 3)180 4)50 5)67.5 6)80 Double angle theorem

62 60° x 1 23 3 12 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

63 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

64 40° x y z 3 120° x 4 1 140° 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

65 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 45 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

66 Construction

67 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

68 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

69 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

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

71 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

72 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

73 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

74 Translation

75 Reflection 2

76 Reflection 1 Reflect these shapes in the mirror lines

77 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

78 Rotation

79 5cm 8cm 5cm 4cm 9cm 4cm 12cm 10cm3cm 15cm 7cm 11cm Find the Perimeter of these shapes 8cm 5cm 4cm 9cm 4cm 8cm 3cm 5cm4cm12cm 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

80 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

81 a b 110 ° Find a, b and c giving reasons for each answer. c a b c 120 ° a bc 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

82 45 ° 130 ° 30 ° Find the values of x x x x x 45 ° 55° 25° Find the values of x x x x x 95° 15° 60° 35° 30° 120° Find the values of x x 95° 35 °x 110° 70 ° 120° 25 °2x x 3x° 80 ° 4x 2x x xx 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

83 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

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

85 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° 172° 93° 32° 11° x265° 342° 100° Angles in Polygons 1 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

86 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 Interior and exterior angles

87 1. How many sides does a regular polygon have if its 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 Regular polygons – finding number of sides 2. How many sides does a regular polygon have if its 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

88 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

89 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

90 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.

91 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

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

93 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

94 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

95 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

96 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

97 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

98 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 coinsb. 3 coinsc. 4 coinsd. 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 1Spinner 2Total 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)2 x 5. a)6 b)24

99 Drawing Bar Charts

100 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

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

102 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 TemperatureIce Creams sold 1763 3153 1277 3531 3928 3443 3446 2264 3728 3135 Time taken to walk to school Score in spelling test 272 1040 145 271 406 1442 1547 1722 354 3831 1713 182 2713 Hours spent on internet Score on ICT test 1314 3339 2737 3845 1318 3962 1019 3054 1936 2934 1622 2542 2833

103 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

104 Box and Whisker plots

105 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

106 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

107 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

108 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 100.5 51 155 302.5 604 15

109 Drawing Cumulative Frequency Graphs

110 Pie Charts 40 people 100 people 40 people36 people 48 people 320 people640 people720 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

111 Find the number of people represented by these slices of pie charts Pie Charts 2 Favourite ColourAngle Blue60 Green30 Turqoise120 Purple120 Black30 Favourite CountryAngle USA20 Mexico20 Turkey40 France100 Spain180 How do you get to schoolAngle Bus10 Train80 Walk140 Car90 Metro40 Favourite SportAngle Football36 Hockey108 Swimming36 Water polo108 Basket Ball72 Favourite foodAngle Pizza6 Chinese54 Roast Dinner96 Curry186 Mexican18 Favourite Maths TopicAngle Fractions18 Area90 Algebra54 Percentages72 Pie Charts126 156 people were asked 180 people were asked 240 people were asked 72 people were asked 400 people were asked 160 people were asked people 26 13 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

112 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 BartHomerMargeLisaMaggie Heavy Metal PunkRnBRap 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


Download ppt "Algebra Shape Data Number 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."

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