# Algebra Number Data Shape.

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Algebra Number Data Shape

Algebra Home Brackets Two Brackets Solving Equations
Collecting like terms Simplifying 2 sided equations Simultaneous equations Solving simultaneous equations graphically Factorising Curved Graphs Sequences The Nth term Quadratic Sequences Substituting Formulae Quadratic Equation Factorising Quadratics Algebraic Fractions Trial and Improvement Inequalities Laws of Indices Parallel and Perpendicular lines Finding the Gradient Writing Expressions y=m x + c Home

Shape Home Area of Circles Area of triangles
Circumference Area of triangles Circle theory Double angle Circle theory triangles Circle theory angles connected by a chord Circle theory cyclic quads Circle theory tangents Perimeter Sin and Cos Sin, cos and tan Sin, cos and tan 2 Sine rule Angles in a triangle Cosine rule Sine and cosine rules Trig- missing angles Angles on a straight line and around a point Angles on parallel lines Angles in Polygons Interior and Exterior angles Polygons- finding sides Construction Worded Pythagoras ago Reflection 1 Reflection 2 Translation Rotation 3D Pythagoras Pythagoras Plans and Elevations Home

Data Home Mean Mean, Mode, Median and Range Median and range
Mean from tables Mean from group tables Tree Diagrams Sampling Mutually Exclusive Events Listing Outcomes Histograms Cumulative frequency Reading Pie Charts Reading Pie Charts 2 Drawing Pie Charts 1 Drawing Pie Charts 2 Scatter Graphs Box and Whisker plots Sample Space Diagrams The Probability Scale Probability as Fractions Stem and Leaf Diagrams Relative Frequency Reading Bar Charts Drawing Bar Charts Home

Number Home Adding, subtracting decimals BIDMAS
Adding and subtracting fractions Direct Proportion Factors Factor Trees Directed Numbers Directed Numbers 2 Equivalent Fractions FDP Finding % Ratio HCF and LCM Indirect Proportion Limits Multiplying and dividing decimals Multiplying and Dividing Fractions Multiples Ordering Decimals Ordering Fractions Percentage Increase Reverse Percentage Rounding dp Rounding sig fig Standard form Home

ANSWERS 0.5 1.2 0.8 1.3 1.5 1.47 1.28 1.66 0.97 1.68 31.44 70.81 39.46 34.15 50.8 0.45 0.54 0.49 0.71 0.7 2.94 39.02 67.25 77.03 54.11 Home

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

Answers 0.5 1.2 0.8 1.3 1.5 1.47 1.28 1.66 0.97 1.68 31.44 70.81 39.46 34.15 50.8 0.45 0.54 0.49 0.71 0.7 2.94 39.02 67.25 77.03 54.11 Adding and Subtracting Decimals Home

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

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

1,2,4,5,10,20 1,2,3,4,6,8,12,24 1,3,9,27 1,2,4,8,16,32 1,2,4,5,8,10,20,40 1,2,5,10,25,50 1,2,4,6,7,8,14,28,56 1,2,3,4,5,6,10,12,20,24,30,40,60,120 1,2,4,5,10,20,40,50,100,200 2,3,5,7,11,13,17,19,23,29 (10 of them) 18 5 6 27 15 90 96 39 Find all the factors of the following numbers: 20 24 27 32 40 50 56 120 200 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) Find the highest common factors of the following pairs of numbers: 18 and 54 25 and 45 12 and 18 27 and 108 30 and 75 Find the HCF of these pairs of numbers: 90 and 450 96 and 480 39 and 195 Home

Factor Trees Home Answers 22x5 3 x 23 3 x 24 2 x 32 x 5 34 2 x 52
Draw factor trees for the following numbers: 20 24 48 90 81 50 75 120 200 1800 2. Using your factor trees from question 1, write the numbers as products of their prime factors . Home

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

Directed Numbers 2 285 23 -28 66 Home
I am £250 into my overdraft () but then I get paid £535, how much will I have in my bank account? 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? 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? 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? 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? 285 23 -28 66 Home

Equivalent Fractions 2. Home 4 15 12 20 60 8 26 32 120 64 154 125 400
615 9720 Equivalent Fractions Home

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

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

Equivalent Fractions Home Answers 2. 4 15 12 20 60 8 26 32 120 64 154
125 400 615 9720 Home

HCF and LCM Home Find the Highest Common Factor of these numbers:
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 6 5 8 12 10 14 13 19 42 12 40 20 80 55 14 Home

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

Fractions, Decimals and Percentages
75% 10% 20% 35% 42% 0.7 0.25 0.3 0.15 0.05 60% 70% 8% 27% 80% 33/100 51/100 4/5 1/5 0.4 0.9 0.74 0.03 7/10 3/5 11/50 7/20 21/50 Home

Limits These numbers have been rounded to the nearest 10, write down the largest and smallest values they could be: 50 80 110 These numbers have been rounded to the nearest whole number, write down the upper and lower limits: 3 17 23 100 -3 These lengths have been rounded to the nearest 10th of a cm, write the upper and lower limits: 12.5cm 21.7cm 35.8cm 52.1cm 80.4cm 4) A field is 100m wide and 120m long, both lengths have been rounded to the nearest metre. a) Find the perimeter and area of the field if these measurements are accurate b) Find the largest and smallest possible perimeter c) Find the largest and smallest possible area. 5) A rectangle has it’s area rounded to the nearest whole number, it becomes 40cm2. One side of the rectangle is exactly 10cm; find the maximum and minimum lengths the other length could have. 6) Two lengths of wood are stuck together and their combined length is rounded to the nearest mm and it is 14.9cm, one length is rounded to the nearest mm and is 7.1cm. Find the minimum and maximum length of the other length. Answers 45 and 75 and 105 and 2.5 and 16.5 and 22.5 and 99.5 and and -2.5 12.45 and 12.55 21.65 and 21.75 35.75 and 38.5 52.05 and 52.15 80.35 and 80.45 p=44om and area= 12000m2 largest= 442m smallest=438m largest= m2 smallest= m2 smallest- 3.95cm largest- 4.05cm 6. largest- 7.9cm smallest- 7.7cm Home

Multiples Home C. List 3 numbers which are in: 3 and 4 times tables
A. List the first 5 multiples of: 5 7 12 14 19 B. What is the: 9th multiple of 8 7th multiple of 6 12th multiple of 12 11th multiple of 10 13th multiple of 5 5th multiple of 13 5,10,15,20,25 12,24, 36, 48, 60 14,28,42,56,70 19,38,57,76,95 72 42 144 110 65 12,24,36 15,30,45 20,40,60 18,36,54 60,120,180 30 56 8 18 60 80 210 D. What is the lowest common multiple of: 5 and 6 7 and 8 4 and 8 9 and 6 10 and 6 E. What is the lowest common multiple of: 13 and 5 15 and 12 16 and 10 14 and 21 21 and 70 Home

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

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

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

Ordering Decimals Home
< > For each pair of numbers say which is bigger by adding > or <. Try these: 3. These are trickier: 4. Put these decimals in ascending order (smallest to biggest): a b c d e Home

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

Rounding to Significant Figures
Main 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 4.7 0.058 0.19 540 Home

Rounding to Decimal Places
ANSWERS 18.43 26.37 2.30 219.15 3.67 Round the following numbers to a) 1 decimal place b) 2 decimals places c) 3 decimal places a) b) c) d) e) f) g) h) i) j) Work out the following on a calculator and give the answer to 2 decimal places; 3.104 x 5.938 2.99 x 8.82 7.1537÷ 3.111 14.772 Home

Reverse Percentages Home
Answers 1.15 1.25 1.04 1.005 1.135 45 65 50 80 240 0.85 0.75 0.96 0.995 0.865 110 60 15 150 3450 What would you multiply an amount by to increase it by: 15% 25% 4% 0.5% 13.5% Find the original prices of these prices that have been increased by the given percentage: Cost= £49.5 after 10% increase Cost= £74.75 after 15% increase Cost= £61 after 22% increase Cost= £104 after 30% increase Cost= £120 after 50% increase 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: 15% 25% 4% 0.5% 13.5% 5. Find the original prices of these items that have been decreased by the given percentage: Cost= £72 after 10% decrease Cost= £93.5 after 15% decrease Cost= £39 after 35% decrease Cost= £4 9fter 40% decrease Cost= £67.50 after 55% decrease 6. A Cars value has dropped by 11.5% it is now worth £ , what was it worth when it was new? Home

Standard Form Home Answers a,e,f,g 474000000 190 8620000 64000 35000
6000 8.3 x 103 4.4 x 105 1.35 x 107 9.87 x 107 3.4 x 10-5 9.301 x 10-5 4.3 x 10-4 Home

Two Brackets Home Answers x2+12x+35 x2+10x + 21 x2 + 5x + 6

Home Find x Answers 2x + 4 = 3x + 1 1. 10x + 8 = 4x + 38 a)x=3
Solve these equations 2(3x+4)= 2(4x-1) 2(3x-4)= 4(x + 3) 4(3x + 2) = 8(2x -1) 2(4x+2) = 4(3x-1) 4(3x+2)=10(x+4) Solve these equations by multiplying out brackets and simplifying: 3(x +2) + 5(x-1)= 25 2(2x + 1) + 6(x + 3)= 70 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. c)x=9 Home

c)x=11 4. x=10 x=5 x=2 x=7 x=6 x=4 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 Home

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

Collecting like terms Answers Home Simplify 10a + 4a 2b + 7b
3a + a + 4a 11b – 4b 14b – 5b + 4b 3a – 6a + a 10a + 4b –a +5b 8a + 5a +5b – 3b 12b – 7a + 3b +a 2b – 8b –a + 9a -13b + 4a -5b -4a 11a + 8b + 2c + 6a + 3b -2c 6b + 4b –a +6c + 5a – 4c 7c + 4b- 3b + a + 10c – 5a 10a + 4b + 7a + 10b – 17a – 14b 5b + 4c + 18c – 22a + z Answers 14a 9b 8a 7b 13b -2a 9a + 9b 13a + 2b 15b – 6a 8a – 6b -18b 17a + 11b 4a + 10b + 2c -4a + b + 17c 5b + 22c -22a + z Home

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

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

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

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

Inequalities Home ANSWERS x>6 x>9 x≥11 x≥2 x<12 x≤20 x<20

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

Parallel and Perpendicular lines
ANSWERS y=3x-7 y=5x-10 y=2x+16 y=131-9x y=-3x-15 ANSWERS y=-1/2x+9 y=-1/4x+17.75 y=2x-1 y=(2/3)x-2.67 Home

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

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

Factorise and solve: X2 + 8X + 12= 0 X2 + 7X + 10= 0 X2 + 13X + 12= 0 X2 + 17X + 70=0 X2 + X – 20=0 X2 - 4X- 12=0 X2 - 12X + 20=0 Rearrange, factorise and solve X2 + 21X + 32=12 X2 + 8X -5 = 15 X2 + 6X + 23 = 5 – 3X Solve 3X2 + 21X + 51=15 2X =-6 4X2 -8X -4= x ANSWERS -6 and -2 -5 and -2 -12 and -1 -7 and -10 -5 and 4 6 and -2 10 and 2 -20 and -1 -10 and 2 -6 and -3 -4 and -3 -8 and -1 5 and -2 Home

Sequences Home Answers 18,21,24 27,32,37 32,36,40

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

Simplifying Expressions
Answers 20a4 18a7 63a8 20a2b4 18a2b7 63a2b8 8a2b2c5 60a2b2c14 36a8b8c 12a5b4c4 4a 3a4 7a2 6a3b3 9a4/b5 10a2 10ab2 ab6/10 ab2 119a3b8 Home

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

Solving Equations Answers Home 8 6 3 10 7 12 5 16 27 4 Find x if:
How did you answer these questions? X + 10 = 17 X + 15 = 27 X + 25 = 30 X- 9 = 15 X – 13 = 40 Find x if 3x + 6 =21 7x + 11 = 67 5x + 4 = 24 9x – 2 =25 11x – 14= 30 10x - 7= 53 12x + 11= 155 15x - 14= 61 13x + 25 = 90 Answers 8 6 3 10 7 12 5 16 27 4 Home

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

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

Trial and Improvement Home
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). X2 + 3x -30=0 X2 + 2x -20=0 X2 + 4x -10=0 X2 -2x -5=0 Use trial and improvement to find the positive solution to these quadratic equations to 2dp (all answers are between 1 and 5) 3X2 - 5x -10=0 2X2 + 2x -25=0 x X2 +3x -30 Big or small? ANSWERS x=4.2 x=3.6 x=1.7 x=3.4 x=2.84 x=3.07 Home

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

y=mx +c Answers Home bottom / top top / bottom

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

Area of Triangles Home Answers: 6m2 24m2 3m2 20m2 12m2 35m2
1. Find the area of the triangles on the left 2. Find the missing lengths of the triangles on the right Answers: 10m 14m 6m 3m 20m Home

Circumference Home Answers: 34.6cm 72.3 25.1cm 44.0cm 77.1cm 51.4cm
8 5cm 30cm 20cm 3cm 9 10 11 12 6cm 5cm 9cm 4cm 14cm 8cm 30cm 6cm 12cm 18cm Home

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

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

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

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

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

Construction Home

Trigonometry- Sin and Cos

Trigonometry- finding angles
24cm 29cm Answers: 41.4 76.2 49.3 51.4 70.6 53.1 32cm Home

Cosine rule Home Answers: 32cm 3.5cm 45.4c˚ 139.5 ˚ 25.2 or 11.1cm

The Sine rule Answers: 10cm 3.0cm 3.4 cm 25.7cm 50.2cm 26.7cm Home

Trigonometry- Sin, Cos and Tan
Answers: 15.7 46.7 32.2 30.6 21.9 63.5 6.1 11.9 69.3 15.6 2.1 7.7 15.7cm Home

Sine and Cosine Rule Home 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 10cm 14cm 8cm 22cm 19cm 15cm Home

Sin, cos and tan 2 Home Home Answers: 3.1cm 6.1cm 5.1cm 17.1cm 4.5cm

Translation Home

Reflection 2 Home

Reflection 1 Reflect these shapes in the mirror lines Home

3D Pythagoras Find the length of the longest diagonal of these cuboids Answers 11.2cm 12.0cm 12.2cm 9.4cm 13.4cm 15.2cm Home

Rotation Home

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

Worded Pythagoras Home Answers 44.7m 74miles 27.7m 8m 10.7m 52.9m
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? A boat travels 45 miles east then 60 miles north, how far is it from where it started? A swimming pool is 25m by 12m, if someone swam from one corner to the other, how far would they have swum? 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? 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? 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 44.7m 74miles 27.7m 8m 10.7m 52.9m Home

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

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

Angles in a triangle Home ANSWERS 50 65 60 ANSWERS 100 80 90 60 72 71
93 85 ANSWERS 80 130 40 75 Home

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

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

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

Regular polygons – finding number of sides
ANSWERS 8 9 12 16 18 120 1. How many sides does a regular polygon have if it’s exterior angles are: 45 40 30 22.5 20 3 ANSWERS 2. 8 9 12 16 18 120 2. How many sides does a regular polygon have if it’s interior angles are: 150 156 157.5 162 165 168.75 Home

Pythagoras ANSWERS 5m 10m 13m 10.8m 6.3m 3.3m 6.9m 8.7m 5.8 1.9m Home

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

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

Median and Range Home ANSWERS Median-6, range-10 Median-17, range-8
2. Median=21, range=34 Median=35, range=55 Median=574, range=669 Median=-50, range=97 Median=-18, range=83 3. Median=22, range-36 Median=18.5, range=80 Median=223.5, range=336 Median=7.5, range=17 Median=-32, range=96 Home

Mean from grouped tables
ANSWERS 40 18.25 Midpoints are an approximation of the scores 9.05 Home

Mean from tables ANSWERS 18 24 1.3 30 44 1.5 47 107 2.3 Home

Drawing Pie charts 1 Home 1. 8 dog=1/8, cat=1/4, fish=5/8 2.
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 Home

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

Probability as Fractions
ANSWERS 3/10 1/5 4/5 7/10 1/20 1/13 4/13 5/13 1/26 5/52 I have some counters in a bag. There are 3 blue, 5 red and 2 green. What is the probability I pick out: A blue A red A green A purple A blue or red A red or green 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: Spotty socks Clown socks Maths Socks Clown or spotty socks Maths or stripe socks 3. I have a pack of card (without jokers) what is the probability I pick: A Red card A heart A Club A heart or a club A 2 A King A picture card A number card smaller than 6 A number card greater than 6 An even number An odd number A red number 3 A black Queen or red Jack A King of Hearts or a 5 Home

Relative Frequency Home ANSWERS 75 37.5 125
Blue-0.25, red -0.5, yellow – 0.1, black 0.15 Blue-20,red-40,yellow-8, black-12 0.1,0.25,0.15,0.05, 0.45 50,125, 75,25, 225 Home

Listing Outcomes ANSWERS H1,H2,H3,H4,H5,H6,T1,T2,T3,T4,T5,T6 1+1=2 1+2=3 1+3=4 2+1=3 2+2=4 2+3=5 3+1=4 3+2=5 3+3=6 Tb,Tt,Tc,Cb,Ct,Cc,Jb,Jt,Jc 4 8 64 2x 6 24 If I flip a coin and roll a dice, list all the possible outcomes I could get. I spin two fair spinners number 1 to 3. Copy and complete the table to show all the possible outcomes. 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. If I toss 1 coin there are 2 possible outcomes, find the number of outcomes for: 2 coins b. 3 coins c. 4 coins d. X coins Lucy, Amy and George are going to have their photo taken so they sit in a line: How many different ways could they order themselves? Andy joins them, how many different ways could they order themselves now? Spinner 1 Spinner 2 Total Home

Drawing Bar Charts Home

Tree Diagrams Home ANSWERS 2. 169/400 49/400 91/400 0.4 0.8 3. a)0.12
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. Draw a tree diagram showing all possible outcomes Use your tree diagram to find the probability of getting: 2 pink 2 orange, 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 What is the probability I will NOT: Have toast for breakfast Miss my bus Use your tree diagram to find the probability of: Having toast and missing my bus Not having toast and missing my bus Not having toast and not missing my bus C) I am tossing a coin and rolling a dice: Draw a tree diagram to show all possible outcomes. A head a 3 A tails and a number bigger than 4 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) Draw a tree diagram to show all the possible outcomes, Find the probability that I will listen to: Hip Hop then Pop Rock twice A Rock song and a pop song in any order 2 songs which are the same style (rock and rock or pop and pop ect.) ANSWERS 2. 169/400 49/400 91/400 0.4 0.8 3. a)0.12 b)0.08 c)0.32 1/12 1/6 7/44 4/121 14/121 93/242 Home

Stem and Leaf Diagrams Home ANSWERS 2. Range-42 , median-34, mode-22

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

The Probability Line ANSWERS 2. 0.1 0.5 0.2 1 0.4 0.6 Home

Box and Whisker plots Home

Mutually Exclusive Events
ANSWERS 0.7 0.6 0.48 0.79 75% 2% 3/5 4/10 3/15 Mutually exclusive Not mutually exclusive 0.1 0.2 0.23 0.24 Home

Sample Space Diagrams Home ANSWERS 1/36 1/12 1/9
7, it appears the most 6/25 19/25 9/25 8/25 Home

Sampling Home ANSWERS Year 7- 20 Year 8-18 Year9 -24 Year 10- 15
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 Home

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

Drawing Cumulative Frequency Graphs
Home

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

Pie Charts 2 Home Find the number of people represented by these slices of pie charts 156 people were asked 72 people were asked Favourite Colour Angle Blue 60 Green 30 Turqoise 120 Purple Black people 26 13 52 Favourite Country Angle USA 20 Mexico Turkey 40 France 100 Spain 180 people 4 8 20 36 180 people were asked 400 people were asked How do you get to school Angle Bus 10 Train 80 Walk 140 Car 90 Metro 40 people 5 40 70 45 20 Favourite Sport Angle Football 36 Hockey 108 Swimming Water polo Basket Ball 72 people 40 120 80 240 people were asked 160 people were asked Favourite food Angle Pizza 6 Chinese 54 Roast Dinner 96 Curry 186 Mexican 18 people 4 36 64 124 12 Favourite Maths Topic Angle Fractions 18 Area 90 Algebra 54 Percentages 72 Pie Charts 126 people 8 40 24 32 56

Home Reading Bar Charts Presentation Courtesy- TES ANSWERS 5 3 39 Punk
14 12 10 8 ANSWERS 5 3 39 Punk RnB 51 Punk, RnB, Metal/Rap, Pop/Reggae 6 4 2 Bart Homer Marge Lisa Maggie 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 Home Heavy Metal Punk RnB Rap Pop Reggae Favourite Music Style Presentation Courtesy- TES

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