Year 9 Home Learning Wright Robinson Mathematics Department

Year 9 Home Learning Wright Robinson Mathematics Department 29 th – 3 rd July 2020 Instructions There are 6 sheets to complete each week. Sets X 5, X 4, X 3 and Z 8 complete Foundation Sheets. Sets X 2, X 1, Z 7, Z 6, Z 5, Z 4, Z 3, Z 2 and Z 1 complete Higher Sheets. IMPORTANT: Cheat Sheets to all work found at the end of THIS file. Use them if you are stuck. Answers are provided. Mark your work once you have completed each sheet.

Top 2 Online Resources Use these online resources if you are stuck or want extra work. 1 www. vle. mathswatch. co. uk Amazing video tutorials on every single maths topics. Mathswatch also has a large supply of extra worksheets and answers to help you with your home learning. Username: 9 @wrightrobinson Password: SOHCAHTOA 2 www. mathsgenie. co. uk Lots of past papers and past exam questions for you to try. They have fully worked solutions to help you answer those tricky questions.

Foundation Questions X 5, X 4, X 3, Z 8

www. vle. mathswatch. com Collect like terms (33) Simplify basic expressions (34) Simplify i) t + p + p + t Basic index laws (34, 35 & 131) i) List the integers that satisfy the inequality Simplify i) g × 3 × p × 5 List and represent inequalities (138) i) x 2 × x 8 Expand a single bracket (93) Expand 6(7 x + 3) -1 < n ≤ 1 ………. . . ………………… ii) y 32 ÷ y 8 ………. . . ………………… ii) 3 e + 2 e + 5 f + f ………. . . ………………… ii) Represent the inequality on the number line. iii) (a 3)2 -5 -4 -3 -2 -1 0 1 2 3 4 5 0 ……. . . …… (R) (A) (G) Factorise a single bracket (94) Factorise fully 36 x + 48 y ……. . . …… (R) (A) (G) Simple substitution (95) Q = c - 2 d c=8 d=3 ……. . . …… (R) (A) (G) Solve equations – one side (135 a) (R) (A) (G) Solve inequalities – one side (139) Solve the inequality Solve 2 x - 5 = 11 3 x - 2 > 10 (R) (A) (G) Rearrange the formula (136) Make x the subject of the formula x + 2 c = t + 4 c Algebra 15 a Name Work out the value of Q. ……. . . . …… (R) (A) (G) ……. . . . . . . …… (R) (A) (G)

www. vle. mathswatch. com Numbers as words (1) Adding and subtracting (17) Write eight thousand thirty in numbers i) Round 153 to the nearest 10 Work out (Non calculator) i) 98 + 65 ……. . . . …… ……. . . …… (R) (A) (G) Order integers (2) Convert to 24 hour clock (6) Order the following from smallest to largest. Convert 2: 15 pm into the 24 hour clock 1 -12 -1 What is the value of the 6 in the number 21962? ……. . . . …… ……. . . …… (R) (A) (G) Shade fractions (24) ……. . . …… (R) (A) (G) Reading scales (4) Operations with negative numbers (68) Work out (Non calculator) i) -9 + 2 ……. . . . …… ii) -9 × -5 ……. . . …… (R) (A) (G) Calculations with money (22) Work out the cost of two yellow ties. 3 Name -11 Place value (1) ii) Round 1234 to the nearest 100 ii) 68 – 31 (R) (A) (G) Rounding to 10 s & 100 s (31) Red Tie 90 p Blue Tie 85 p Yellow Tie 66 p ……. . . …… (R) (A) (G) Basic multiplication (19) Work out (Non calculator) 7× 9 ……. . . …… (R) (A) (G) Basic division (20) Work out (Non calculator) Write the value shown Number 5 a 56 ÷ 8 7 ……. . . …… (R) (A) (G) 8 9 (R) (A) (G) ……. . . . …… (R) (A) (G) ……. . . …… (R) (A) (G)

www. vle. mathswatch. com Measure lengths Measure the length of the line. Give your answer to the nearest mm. Measure angles (46 a) Measure the angle. Name 2 D and 3 D shapes (10 & 43) Name the shapes Perimeter of basic shapes (52) Find the perimeter of the shape below. ………………………. . . …… ……. . . . …… (R) (A) (G) Area of basic shapes Lines of symmetry (11) Find the area of the shape below. Draw all the lines of symmetry on the shape below …………. . . …… (R) (A) (G) ……. . . …… Movement of a point (174) Congruent shapes (12 b) Write down the letters of 2 congruent shapes Name A C Geometry 15 a F ……. . . …… (R) (A) (G) E B D (R) (A) (G) …………. . . ……

www. vle. mathswatch. com List combinations Read from a table Find the median 7 6 2 7 Complete the pictogram. The UK has 12 astronauts, France has 10. Animal Frequency Leopard 62 USA Monkey 78 Russia Porcupine 11 UK Weasel 4 Pakistan 6 How many people are there in total? ……………. . How many fewer people like weasels than monkeys? ……. . . …… (R) (A) (G) ……. . . …… Nokia HTC 6 7 3 4 Statistics 5 a (A) (G) Malteser Bounty Mars Bounty =4 Choc astronauts Tally Total Mars Bounty Malteser ……. . . …… (R) (A) (G) Dual Bar charts Probability scale The dual bar chart shows some of the boys and girls in a year group. Key 5 Boys Using the scale: i) Mark with an A the probability that a fair dice will land on a 3. 4 Girls 3 2 1 0 (R) Key: ii) How many astronauts does Pakistan have? (R) (A) (G) Frequency Samsung Name i. Phone Complete the tally chart for the information below. Mars Bounty Mars Malteser Mars Bounty France Bar Charts Plot a bar chart for the information Tally charts Pictograms Year 8 Year 9 Year i)……. . . . . …………………………………. How many girls are there in total? ii) How many more girls than boys are there in year 8? ii) Mark with a B the probability of rolling an even number on a fair dice. Year 7 …………………………. . … (R) (A) (G)

www. vle. mathswatch. com Area of rectangles and parallelograms (53 & 55) Find the area of the rectangle. Perimeter of shapes (52) Find the perimeter of the triangle. 5 cm 6 cm (R) (A) (G) ……. . . …… Find angle d. Give reasons for your answer. d Find angle a. Give reasons for your answer. Find angle c. Give reasons for your answer. 46 o x 2 cm 113 o 34 o c 154 o (R) (A) (G) Angles in a quadrilateral Find angle f. Give reasons for your answer. (R) (A) (G) ……. . . …… 124 o 84 o (R) (A) (G) Angles in special triangles (122) (R) (A) (G) ……. . . …… Combined angle facts Find angle w. Give reasons for your answer. Find angle e. Give reasons for your answer. w 30 o f 45 o 44 o ……. . . …… e 65 o Geometry 5 b Name Find angle x. Give reasons for your answer. 3 cm Angles in a triangle (54) 84 o Angles around a point (45) a 13 cm ……. . . …… 4 cm Vertically opposite angles Angles on a straight line (45) ……. . . . …… (R) (A) (G) ……. . . . ……

www. vle. mathswatch. com Expand two single brackets (134 a) Expand simplify 3(4 x – 2) – 5(x + 3) Collect like terms (33) Solve equations – two sides (135 a) Solve Simplify 6 a 2 + 7 b 2 + a 2 + 11 b 2 2 x + 10 = 7 x - 15 Linear sequences (103) Find the nth term of the sequence 3 5 7 9 11 List and represent inequalities (138) List the integers that satisfy the inequality 15 ≤ 5 n < 30 ……. . . ……………. … Find the 50 th term of this sequence. ……. . . …… (R) (A) (G) Expand double brackets (134 b) Expand simplify Name (2 x + 3) (x + 5) ……. . . . …… (R) (A) (G) Factorise brackets (94 & 157) Index Laws (34) Factorise Simplify i) x 7 × x ……. . . …… (R) (A) (G) Solve inequalities – two sides (139) Solve the inequality 9 x + 6 ≤ 3(2 x + 11) i) 20 x – 8 y ……. . . …… (R) (A) (G) Substitution (95) Work out the value of Q. Q = 2 cd c = -3 d=5 ………………. . ………… ii) 8 y 7 ÷ 2 y ………………. . ………… ii) x 2 + 14 x + 24 Algebra 5 b ………………. . ………… iii) (5 a 3)2 ……. . . . . . . …… (R) (A) (G) ……. . . …… (R) (A) (G)

Foundation Answers

www. vle. mathswatch. com Collect like terms (33) Simplify basic expressions (34) Simplify i) t + p + p + t i) g × 3 × p × 5 2 t + 3 p ii) 3 e + 2 e + 5 f + f i) x 2 × x 8 5 e or 6 f seen x 10 ………. . . ………………… 15 gp in any order ii) y 32 ÷ y 8 ………. . . ………………… (R) (A) (G) Factorise a single bracket (94) Factorise fully 36 x + 48 y Amber if not fully factorised e. g. 3(12 x + 16 y) 6(7 x + 3) 0, 1 ii) Represent the inequality on the number line. 42 x or 18 seen 42 x + 18 a 6 ……. . . …… (R) (A) (G) Simple substitution (95) Q = c - 2 d c=8 d=3 ……. . . …… -5 -4 -3 -2 -1 0 1 2 3 4 5 0 (R) (A) (G) Solve equations – one side (135 a) (R) (A) (G) Solve inequalities – one side (139) Solve the inequality Solve ……. . . …… (R) (A) (G) Rearrange the formula (136) Make x the subject of the formula 2 x - 5 = 11 3 x - 2 > 10 2 d = 6 2 x = 16 x = 4 x = t + 4 c - 2 c Q = 2 x = 8 x > 4 x = t + 2 c Work out the value of Q. x + 2 c = t + 4 c Algebra 15 a 12(3 x + 4 y) Expand iii) (a 3)2 5 e + 6 f ……. . . …… Expand a single bracket (93) -1 < n ≤ 1 ………. . . ………………… y 28 15 gp List and represent inequalities (138) i) List the integers that satisfy the inequality Simplify 2 t or 3 p seen ………. . . ………………… Name Basic index laws (34, 35 & 131) ……. . . . . . . …… (R) (A) (G) ……. . . …… (R) (A) (G)

www. vle. mathswatch. com Numbers as words (1) Adding and subtracting (17) Write eight thousand thirty in numbers 8030 i) Round 153 to the nearest 10 Work out (Non calculator) i) 98 + 65 163 150 ……. . . . . . . . …… ii) Round 1234 to the nearest 100 ii) 68 – 31 37 (R) (A) (G) Convert to 24 hour clock (6) Order the following from smallest to largest. Convert 2: 15 pm into the 24 hour clock 1 -12 -1 ……. . . …… (R) (A) (G) Shade fractions (24) ……. . . …… (R) (A) (G) Reading scales (4) -12, -11, -1, 1, 3 What is the value of the 6 in the number 21962? Operations with negative numbers (68) Work out (Non calculator) i) -9 + 2 -7 ……. . . . …… ii) -9 × -5 60 45 ……. . . …… (R) (A) (G) Calculations with money (22) Work out the cost of two yellow ties. 14: 15 3 Name Number 5 a ……. . . …… Place value (1) 1200 Order integers (2) -11 Rounding to 10 s & 100 s (31) Red Tie 90 p Blue Tie 85 p Yellow Tie 66 p ……. . . …… (R) (A) (G) Basic multiplication (19) Work out (Non calculator) 7× 9 63 ……. . . …… (R) (A) (G) Basic division (20) Work out (Non calculator) Write the value shown 56 ÷ 8 7 8 £ 1. 32 9 7 8. 9 ……. . . . . . . …… (R) (A) (G)

www. vle. mathswatch. com Measure lengths Measure the length of the line. Give your answer to the nearest mm. Measure angles (46 a) Measure the angle. Name 2 D and 3 D shapes (10 & 43) Name the shapes Perimeter of basic shapes (52) Find the perimeter of the shape below. Regular octagon ………………………. . . …… 35 mm or 3. 5 cm ……. . . …… (R) (A) (G) 342 - 344 o ……. . . …… (R) (A) (G) Area of basic shapes Lines of symmetry (11) Find the area of the shape below. Draw all the lines of symmetry on the shape below 26 cm (R) (A) (G) ……. . . …… Movement of a point (174) Write down the letters of 2 congruent shapes C F 32 cm 2 ……. . . …… (R) (A) (G) Congruent shapes (12 b) A Name Geometry 15 a Sphere …………. . . …… E B D A and D (R) (A) (G) …………. . . ……

www. vle. mathswatch. com List combinations Read from a table Find the median 7 6 2 7 Complete the pictogram. The UK has 12 astronauts, France has 10. Animal Frequency Leopard 62 USA Monkey 78 Russia Porcupine 11 UK Weasel 4 Pakistan 6 How many people are there in total? 155 ……………. . How many fewer people like weasels than monkeys? 6 ……. . . …… 74 (R) (A) (G) ……. . . …… i. Phone Samsung Nokia HTC 6 7 3 4 6 5 4 3 (R) i. Phone Samsung Nokia Phone HTC (A) (G) Malteser Bounty Mars Bounty =4 Choc astronauts 6 ……. . . …… Tally Total Mars |||| 5 Bounty |||| 5 Malteser ||| 3 (R) (A) (G) Dual Bar charts Probability scale The dual bar chart shows some of the boys and girls in a year group. Key 5 Boys Using the scale: i) Mark with an A the probability that a fair dice will land on a 3. 4 Girls 3 2 1 0 Key: ii) How many astronauts does Pakistan have? (R) (A) (G) Frequency Statistics 5 a Name 7 Complete the tally chart for the information below. Mars Bounty Mars Malteser Mars Bounty France Bar Charts Plot a bar chart for the information Tally charts Pictograms Year 7 Year 8 Year 9 Year 12 i)……. . . . . …………………………………. How many girls are there in total? ii) How many more girls than boys are there in year 8? 2 …………………………. . … (R) (A) (G) ii) Mark with a B the probability of rolling an even number on a fair dice. A B (R) (A) (G)

www. vle. mathswatch. com Area of rectangles and parallelograms Find the area of the rectangle. Perimeter of shapes Find the perimeter of the triangle. 5 cm 6 cm (R) (A) (G) ……. . . …… Find angle d. Give reasons for your answer. d Name Find angle a. Give reasons for your answer. Find angle c. Give reasons for your answer. 46 o x 2 cm 113 o 34 o x = 100 o, angles on a straight line add to 180 o 10 cm Angles in a triangle Geometry 5 b Find angle x. Give reasons for your answer. c 154 o 3 cm 78 cm 2 84 o Angles around a point a 13 cm ……. . . …… 4 cm Vertically opposite angles Angles on a straight line (R) (A) (G) Angles in a quadrilateral Find angle f. Give reasons for your answer. d = 52 o, angles in a triangle add to 180 o ……. . . …… (R) (A) (G) ……. . . …… 124 o 84 o f = 107 o, angles in a quadrilateral add to 360 o. ……. . . …… (R) (A) (G) Angles in special triangles c = 116 o, angles around a point add to 360 o (R) (A) (G) ……. . . …… Combined angle facts Find angle w. Give reasons for your answer. Find angle e. Give reasons for your answer. w 30 o f 45 o 44 o ……. . . …… a = 113 o vertically opposite angles are equal. e 65 o w = 50 o, base angles in an isosceles triangle are equal, angles in a triangle add to 180 o ……. . . …… (R) (A) (G) e = 105 o, base angles in an isosceles triangle are equal, angles on a straight line add to 180 o (R) (A) (G) ……. . . ……

www. vle. mathswatch. com Expand two single brackets (134 a) Expand simplify 3(4 x – 2) – 5(x + 3) 7 x – 21 Collect like terms (33) Solve equations – two sides (135 a) Solve Simplify 6 a 2 + 7 b 2 + a 2 + 11 b 2 2 x + 10 = 7 x - 15 x = 5 7 a 2 + 18 b 2 Linear sequences (103) Find the nth term of the sequence 3 5 7 9 11 2 n + 1 ……. . . ……………. … List and represent inequalities (138) List the integers that satisfy the inequality 15 ≤ 5 n < 30 3, 4, 5 Find the 50 th term of this sequence. 101 ……. . . …… (R) (A) (G) Expand double brackets (134 b) Expand simplify (2 x + 3) (x + 5) ……. . . . …… (R) (A) (G) Factorise brackets (94 & 157) Index Laws (34) Factorise Simplify i) x 7 × x ……. . . …… (R) (A) (G) Solve inequalities – two sides (139) Solve the inequality i) 20 x – 8 y Name (R) (A) (G) Substitution (95) Work out the value of Q. 9 x + 6 ≤ 3(2 x + 11) Q = 2 cd c = -3 d=5 x ≤ 9 -30 x 8 ………………. . ………… ……. . . …… 4(5 x – 2 y) ii) 8 y 7 ÷ 2 y ………………. . ………… 2 x 2 4 y 6 + 13 x + 15 ii) x 2 + 14 x + 24 Algebra 5 b ………………. . ………… iii) (5 a 3)2 25 a 6 ……. . . . …… (R) (A) (G) (x + 12)(x + 2) ……. . . . …… (R) (A) (G) ……. . . …… (R) (A) (G)

Higher Questions X 2, X 1, Z 7, Z 6, Z 5, Z 4, Z 3, Z 2, Z 1

www. vle. mathswatch. com Expand two single brackets (134 a) Expand simplify Collect like terms (33) Solve equations – two sides (135 a) Solve Simplify 6 x + 2 = 2 x + 18 3 a + 2 b + 9 a + 4 b 5(x + 2) + 2(3 x + 1) Linear sequences (103) Find the nth term of the sequence 3 7 11 15 19 List and represent inequalities (138) List the integers that satisfy the inequality -8 < 2 n ≤ 6 ……. . . ……………. … Find the 30 th term of this sequence. ……. . . …… (R) (A) (G) ……. . . …… Expand double brackets (134 b) Expand simplify Name (x + 3) (x + 7) (R) (A) (G) ……. . . …… (R) (A) (G) Factorise brackets (94 & 157) Index Laws (34) Factorise i) 15 x 2 - 20 xy Simplify i) x -5 × x 3 ……. . . …… (R) (A) (G) Solve inequalities – two sides (139) Solve the inequality 9 x – 2 < 4 x + 33 ……. . . …… (R) (A) (G) Substitution (95) Work out the value of Q. Q = 2 c + d c=5 d = -7 ………………. . ………… ii) y 6 ÷ y ………………. . ………… ii) x 2 + 4 x + 3 Algebra 15 b ………………. . ………… iii) ……. . . …… (R) (A) (G) (a 5)8 ……. . . . . . . …… (R) (A) (G)

www. vle. mathswatch. com Area of rectangles and parallelograms (53 & 55) Find the area of the rectangle. Perimeter of shapes (52) Find the perimeter of the triangle. 5 cm 6 cm (R) (A) (G) ……. . . …… Find angle d. Give reasons for your answer. d Find angle a. Give reasons for your answer. Find angle c. Give reasons for your answer. 46 o x 2 cm 113 o 34 o c 154 o (R) (A) (G) Angles in a quadrilateral Find angle f. Give reasons for your answer. (R) (A) (G) ……. . . …… 124 o 84 o (R) (A) (G) Angles in special triangles (122) (R) (A) (G) ……. . . …… Combined angle facts Find angle w. Give reasons for your answer. Find angle e. Give reasons for your answer. w 30 o f 45 o 44 o ……. . . …… e 65 o Geometry 5 b Name Find angle x. Give reasons for your answer. 3 cm Angles in a triangle (54) 84 o Angles around a point (45) a 13 cm ……. . . …… 4 cm Vertically opposite angles Angles on a straight line (45) ……. . . . …… (R) (A) (G) ……. . . . ……

www. vle. mathswatch. com Equations from shapes (137) Simultaneous Equations (162) Solve Plot straight line graphs Find x 7 x - 3 y = 11 2 x + 7 y = 11 5 x + 8 9 x - 20 y 5 4 3 ……. . . …… (R) (A) (G) Equation of a line (R) (A) (G) 2 Equations from words What is the equation of the line. Write it in the form y = mx + c y 5 4 Name ……. . . …… 1 Natalie is y years old. Amber is 2 years younger than Natalie. Richard is twice as old as Amber. Their ages total 102 years old. Work out how old each person is. -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 3 -3 2 1 -4 -5 -4 -3 -2 -1 -1 1 2 3 4 5 x -5 Algebra 15 c -2 -3 -4 -5 ……. . . . . …… (R) (A) (G) ……. . . …… (R) (A) (G) x

www. vle. mathswatch. com Decimal Multiplication (66) Work out (Non Calculator) 243 × 9. 1 Fractions of amounts (72) Work out 3 of 450 5 Increase & Decrease percentages (86&87) Fractions to percentages (89) Find the percentage change (88) Convert to percentages Decrease £ 160 by 85% A £ 1200 investment goes up in value by £ 123. What is the percentage increase? i) 56 out of 80 (Non calculator) ……. . . . …… Estimate (R) (A) (G) Long Division (20) 494. 4 ÷ 6 Estimate (91) . . . . ………………. . . …… ii) 207 out of 234 (With a calculator) (Non Calculator) (R) (A) (G) . . . . . . … . . . . … (R) (A) (G) Write the following as products of prime factors i) 24 ii) 64 Name 5. 2 has been rounded to 1 decimal place. Write the error interval for this number. (R) (A) (G) Standard form (83) Prime factors (78) Error Intervals (155) . . . …… Write the following in standard form. i) 1034000 . . …… (R) (A) (G) Best Value (41) Find the best value. Cesto 2 litre Dr Jalapeno is £ 1. 90 Sada 400 ml Dr Jalapeno is 60 p (R) (A) (G) ……. . . . ………………. . . …… HCF & LCM (79 & 80) ii) (1. 2 × 105) ÷ (4 × 103) Number 5 c Find the highest common factor of 24 and 64 ……. . . . . . . …… (R) (A) (G)

www. vle. mathswatch. com Two way tables (61) Venn Diagrams (127 a) Experimental Probability (125) Henry asks 90 people whether they travel to work by car, bus or train. 40 of the students are female. 17 of these females travel by car. 23 males travel by bus. 9 out of the 23 people who travel by train are female. Work out the number of males who travel by car. The table show the probability of getting a colour on a spinner. i) Complete the table. Purple 0. 16 Pink 0. 18 Orange 0. 32 There are 110 students in a college. 35 study both P. E and Media Studies. 26 study P. E but not Media Studies. A total of 56 students study Media Studies. i) Complete the Venn diagram. P. E Media Blue ii) The spinner is spun 500 times. Estimate the number of blues you would expect. ……. . . …… ε = {odd numbers less than 30} A = {3, 9, 15, 21, 27} B = {5, 15, 25} A (R) (A) (G) Estimate the mean for the information given in the table. Time (t seconds) Frequency B Name Statistics 5 c & d ……. . . . …… ……. . . …… Estimate the mean (130 b) Sets (127 b) ε (R) (A) (G) ii) A person is picked at random. What is the probability that this person doesn’t study either P. E or Media Studies? 0<t≤ 3 3<t≤ 6 7 19 6<t≤ 9 22 9 < t ≤ 12 11 12 < t ≤ 15 5 (R) (A) (G) Replacement Tree Diagrams (151) George plays a game of pool and a game of snooker. The probability he wins the pool game is 0. 74. The probability he wins the snooker game is 0. 42. What is the probability the George wins at least one game? Pool Snooker Win. . . . Lose Win What is the probability of picking a number at random from the set A U B ……. . . …… (R) (A) (G) ……. . . . … ii) What is the modal class width ……. . . …… (R) (A) (G) . . . . Lose (R) (A) (G)

www. vle. mathswatch. com SOHCAHTOA – Angles (168) Find the size of angle ABC. Answer to 3 significant figures. C 6. 5 cm A 12 cm ……. . . …… SOHCAHTOA – Sides (168) Find the length of AB. Answer to 3 significant figures. B C 28 o Mass Density Volume (142) Tony leaves his home at 8: 00 and arrives at his friends house at 8: 36. His friend lives 9 miles away. What was Tony’s average speed for the journey? The mass of 5 m 3 of copper is 44800 kg. Work out the density of the copper. 9 cm B (R) (A) (G) Distance Speed Time (142) A ……. . . . …… (R) (A) (G) Sectors (167) Interior & Exterior angles (123) The diagram shows a regular polygon. Find x. For the sector find: Find the length of x. 40 m x i) The area x (R) (A) (G) Similar Triangles (144) 75 o 3 cm Name ……. . . …… 3 m 12 m Geometry 5 e ……………. . … ii) The arc length ……. . . . …… (R) (A) (G) ……. . . …… (R) (A) (G)

Higher Answers

www. vle. mathswatch. com Expand two single brackets (134 a) Expand simplify Collect like terms (33) Solve equations – two sides (135 a) Solve Simplify 6 x + 2 = 2 x + 18 3 a + 2 b + 9 a + 4 b 5(x + 2) + 2(3 x + 1) Linear sequences (103) Find the nth term of the sequence 3 x = 4 12 a + 6 b 11 x + 12 7 11 15 19 List and represent inequalities (138) List the integers that satisfy the inequality -8 < 2 n ≤ 6 4 n - 1 ……. . . ……………. … Find the 30 th term of this sequence. -3, -2, -1, 0, 1, 2, 3 119 ……. . . …… (R) (A) (G) ……. . . …… Expand double brackets (134 b) Expand simplify (x + 3) (x + 7) (R) (A) (G) ……. . . …… Factorise brackets (94 & 157) Index Laws (34) Factorise i) 15 x 2 - 20 xy Simplify i) x-5 × x 3 x-2 Name (R) (A) (G) ……. . . …… (R) (A) (G) Solve inequalities – two sides (139) Solve the inequality 9 x – 2 < 4 x + 33 5 x(3 x-4 y) ………………. . ………… ii) y 6 ÷ y x 2 + 10 x + 21 y 5 ii) (R) (A) (G) Substitution (95) Work out the value of Q. Q = 2 c + d c=5 d = -7 3 ………………. . ………… x 2 ……. . . …… + 4 x + 3 Algebra 15 b ………………. . ………… iii) (a 5)8 a 40 ……. . . . …… (R) (A) (G) (x+3)(x+1) ……. . . . …… (R) (A) (G) ……. . . …… (R) (A) (G)

www. vle. mathswatch. com Area of rectangles and parallelograms Find the area of the rectangle. Perimeter of shapes Find the perimeter of the triangle. 5 cm 6 cm (R) (A) (G) ……. . . …… Find angle d. Give reasons for your answer. d Name Find angle a. Give reasons for your answer. Find angle c. Give reasons for your answer. 46 o x 2 cm 113 o 34 o x = 100 o, angles on a straight line add to 180 o 10 cm Angles in a triangle Geometry 5 b Find angle x. Give reasons for your answer. c 154 o 3 cm 78 cm 2 84 o Angles around a point a 13 cm ……. . . …… 4 cm Vertically opposite angles Angles on a straight line (R) (A) (G) Angles in a quadrilateral Find angle f. Give reasons for your answer. d = 52 o, angles in a triangle add to 180 o ……. . . …… (R) (A) (G) ……. . . …… 124 o 84 o f = 107 o, angles in a quadrilateral add to 360 o. ……. . . …… (R) (A) (G) Angles in special triangles c = 116 o, angles around a point add to 360 o (R) (A) (G) ……. . . …… Combined angle facts Find angle w. Give reasons for your answer. Find angle e. Give reasons for your answer. w 30 o f 45 o 44 o ……. . . …… a = 113 o vertically opposite angles are equal. e 65 o w = 50 o, base angles in an isosceles triangle are equal, angles in a triangle add to 180 o ……. . . …… (R) (A) (G) e = 105 o, base angles in an isosceles triangle are equal, angles on a straight line add to 180 o (R) (A) (G) ……. . . ……

www. vle. mathswatch. com Equations from shapes (137) Simultaneous Equations (162) Solve Plot straight line graphs Find x 7 x - 3 y = 11 2 x + 7 y = 11 5 x + 8 9 x - 20 x = 2 x -3 -2 -1 0 y -3 0 3 6 y x = 7 5 y = 1 4 3 ……. . . …… (R) (A) (G) Equation of a line y 5 4 Name (R) (A) (G) 2 Equations from words What is the equation of the line. Write it in the form y = mx + c 1 Natalie is y years old. Amber is 2 years younger than Natalie. Richard is twice as old as Amber. Their ages total 102 years old. Work out how old each person is. -5 -4 -3 -2 -1 1 2 3 4 5 -1 -2 3 -3 2 Natalie: y = 27 Amber: 25 Richard: 50 1 -5 -4 -3 -2 -1 -1 1 2 3 4 5 x -2 Algebra 15 c ……. . . …… -3 -4 -5 y = 3 x + 3 ……. . . . . …… (R) (A) (G) ……. . . …… (R) (A) (G) x

www. vle. mathswatch. com Decimal Multiplication (66) Work out (Non Calculator) 243 × 9. 1 Fractions of amounts (72) Increase & Decrease percentages (86&87) Work out 3 of 450 5 (R) (A) (G) Long Division (20) £ 160 by 85% (Non calculator) 270 £ 24 Name 70, 000 10. 25% . . . . ………………. . . …… ii) 207 out of 234 (With a calculator) 88. 5%. . . . . . … . . . . … (R) (A) (G) Write the following as products of prime factors i) 24 ii) 64 23 x 3 . . . …… (R) (A) (G) Standard form (83) Prime factors (78) Error Intervals (155) 5. 2 has been rounded to 1 decimal place. Write the error interval for this number. Estimate 70% 82. 4 (R) (A) (G) Estimate (91) A £ 1200 investment goes up in value by £ 123. What is the percentage increase? i) 56 out of 80 494. 4 ÷ 6 ……. . . …… Find the percentage change (88) Convert to percentages Decrease 2211. 3 ……. . . …… Fractions to percentages (89) Write the following in standard form. i) 1034000 26 . . …… (R) (A) (G) Best Value (41) Find the best value. Cesto 2 litre Dr Jalapeno is £ 1. 90 Sada 400 ml Dr Jalapeno is 60 p 1. 034 × 106 (R) (A) (G) 5. 15 ≤ n < 5. 25 ……. . . . ………………. . . …… HCF & LCM (79 & 80) ii) (1. 2 × 105) ÷ (4 × 103) Number 5 c Find the highest common factor of 24 and 64 3 × 101 8 ……. . . . …… (R) (A) (G) ……. . . …… (R) (A) (G) Cesto is the cheapest: 1 l for £ 0. 95 ……. . . …… (R) (A) (G)

www. vle. mathswatch. com Two way tables (61) Venn Diagrams (127 a) Experimental Probability (125) Henry asks 90 people whether they travel to work by car, bus or train. 40 of the students are female. 17 of these females travel by car. 23 males travel by bus. 9 out of the 23 people who travel by train are female. Work out the number of males who travel by car. 13 The table shows the probability of getting a colour on a spinner. i) Complete the table. Purple 0. 16 Pink 0. 18 Orange 0. 32 Blue 0. 34 ii) The spinner is spun 500 times. Estimate the number of blues you would expect. There are 110 students in a college. 35 study both P. E and Media Studies. 26 study P. E but not Media Studies. A total of 56 students study Media Studies. i) Complete the Venn diagram. P. E 26 500 x 0. 34 = 170 ……. . . …… ε = {odd numbers less than 30} A = {3, 9, 15, 21, 27} B = {5, 15, 25} Name A Statistics 5 c 21 27 15 5 25 1 7 11 13 17 19 23 29 What is the probability of picking a number at random from the set A U B 7 15 (R) (A) (G) ……. . . …… Estimate the mean for the information given in the table. Time (t seconds) Frequency B 3 9 ……. . . . …… (R) (A) (G) 0<t≤ 3 3<t≤ 6 7 19 6<t≤ 9 22 9 < t ≤ 12 11 12 < t ≤ 15 5 Media 35 21 ii) A person is picked at random. What is the probability that this person doesn’t 28 study either P. E or Media Studies? 110 ……. . . …… Estimate the mean (130 b) Sets (127 b) ε (R) (A) (G) 28 Replacement Tree Diagrams (151) George plays a game of pool and a game of snooker. The probability he wins the pool game is 0. 74. The probability he wins the snooker game is 0. 42. What is the probability the George wins at least one game? Pool Snooker Win 0. 42. . 0. 74. . 0. 58. . P(WL): 0. 4292 Win 0. 42. . P(LW): 0. 1092 0. 26. . Lose ……. . . …… (R) (A) (G) P(WW): 0. 3108 Win Lose 444 ÷ 64 = 6. 94 (R) (A) (G) 0. 58. . Lose = 0. 8492 (R) (A) (G)

www. vle. mathswatch. com SOHCAHTOA – Angles (168) Find the size of angle ABC. Answer to 3 significant figures. C 6. 5 cm A 12 cm SOHCAHTOA – Sides (168) Find the length of AB. Answer to 3 significant figures. B C 28 o Mass Density Volume (142) Tony leaves his home at 8: 00 and arrives at his friends house at 8: 36. His friend lives 9 miles away. What was Tony’s average speed for the journey? The mass of 5 m 3 of copper is 44800 kg. Work out the density of the copper. 15 m/h 8960 kg/m 3 9 cm B A 4. 23 cm 28. 4 o ……. . . …… Distance Speed Time (142) (R) (A) (G) ……. . . . …… (R) (A) (G) Sectors (167) Interior & Exterior angles (123) The diagram shows a regular polygon. Find x. For the sector find: Find the length of x. 40 m x i) The area x 22. 4 cm 2 126 o 3 m ……………. . … Geometry 5 e (R) (A) (G) Similar Triangles (144) 75 o 3 cm Name ……. . . …… ii) The arc length 12 m 32 m 14. 9 cm ……. . . . …… (R) (A) (G) ……. . . …… (R) (A) (G)

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www. vle. mathswatch. com Collect like terms (33) Simplify i) a + a Count up the letters Three a’s so the answer is 3 a ………. . . ………………… ii) 3 a + b + 2 a + 2 b Collect like terms 3 a + 2 a = 5 a b + 2 b = 3 b Cheat Sheet Simplify basic expressions (34) 5 a + 3 b (R) (A) (G) Factorise a single bracket (94) Factorise fully 4 x + 14 4 x ÷ 2 = 2 x i) 5 × b × 2 × e Times the numbers together 5 x 2 = 10 10 x b x e Remove the multiplication signs and put everything side by side (in alphabetical order) ……. . . …… (R) (A) (G) Simple substitution (95) Q = d - 3 c c=2 d = 10 Algebra A The biggest factor of 4 and 14 Sub in values 2(2 x + 7) (R) (A) (G) x 4 + 3 = x 7 ………. . . ………………… Subtract the powers ii) y 9 ÷ y 7 y 9 -7 =y 2 ………. . . ………………… Multiply the powers iii) (a 2)5 a 2 x 5 =a ……. . . …… 10 Use BIDMAS Q = 10 − 6 Q = 4 ……. . . …… (R) (A) (G) List and represent inequalities (138) i) List the integers that satisfy the inequality -5 < n ≤ 1 List the whole numbers between -5 and 1 (including 1) -4, -3, -2, -1, 0, 1 ………. . . ………………… ii) Represent the inequality on the number line. For draw -5 -4 -3 -2 -1 0 1 2 3 4 5 0 (R) (A) (G) Solve equations – one side (135 a) (R) (A) (G) Solve inequalities – one side (139) Solve the inequality Solve 5 y - 20 = 5 2 x + 5 < 13 Use the balance method and keep the inequality sign throughout +20 -5 +20 ÷ 5 (R) (A) (G) 3(5 x + 6) Set up the box and multiply inside × 5 x +6 3 15 x +18 3 x 5 x = 15 x Write out your answer 15 x + 18 ……. . . …… (R) (A) (G) Rearrange the formula (136) Make x the subject of the formula 2 x + 3 c = 4 t Use the balance method to get by itself x - 3 c -3 c 2 x = 4 t – 3 c ÷ 2 ÷ 2 x= y=5 ……. . . …… Expand -5 5 y = 25 ÷ 5 Expand a single bracket (93) 2 x + 3 c = 4 t 5 y – 20 = 5 Q = 10 − 3 x 2 Write in a bracket ……. . . …… i) x 4 × x 3 Work out the value of Q. Q = d− 3 xc × 2 x +7 2 4 x +14 Add the powers Simplify 10 be ……. . . …… Basic index laws (34, 35 & 131) ……. . . …… (R) (A) (G) ÷ 2 4 t – 3 c 2 ……. . . …… (R) (A) (G)

www. vle. mathswatch. com Measure lengths Measure angles (46 a) Measure the length of the line. Give your answer to the nearest mm. Measure the angle. Name 2 D and 3 D shapes (10 & 43) Name the shapes Rectangle Triangle Circle Perimeter of basic shapes (52) Find the perimeter of the shape below. Count the sides using the square paper! Place your ruler at the end on zero and measure using the numbers. Check the units! 13 Sphere Cylinder Cuboid 12 11 10 14 16 15 Hexagon Octagon Pentago n ………………………. . . …… 9 8 17 7 18 cm Use a protractor to measure the angle. Remember to start from zero! 5 cm = 50 mm ……. . . …… (R) (A) (G) Area of basic shapes Find the area of the shape below. 45˚ ……. . . …… (R) (A) (G) Lines of symmetry (11) Name 3 4 5 6 7 8 4 Triangular-Based Cube Triangular Prism Pyramid …………. . . …… 18 cm (R) (A) (G) ……. . . …… Movement of a point (174) Draw the lines of symmetry 5 to the RIGHT and 1 DOWN (R) (A) (G) Congruent shapes (12 b) Write down the letters of 2 congruent shapes Congruent means exactly same shape and size! A 9 10 Geometry a 2 3 6 Start Count the squares inside the shape! 1 2 1 Stop 5 12 cm 2 ……. . . …… 1 1 12 (R) (A) (G) Lines of Symmetry create a reflection (mirror image). The shape would also fold in half on a line of symmetry! (R) (A) (G) C B In a vector: • The top number means RIGHT (+) or LEFT (-) • The bottom number means UP (+) or DOWN (-) E D A and B F (R) (A) (G) …………. . . ……

www. vle. mathswatch. com Area of rectangles and parallelograms (53 & 55) Find the area of the parallelogram. 7 cm Perimeter of shapes (52) Find the perimeter of the triangle. 12 cm 8 cm 10 cm Cheat Sheet 10 cm 49 o = 10 + 12 + 9 = 31 cm (R) (A) (G) ……. . . …… Angles in a triangle (54) Find angle d. Give reasons for your answer. d (R) (A) (G) 84 o Angles in a triangle add up to 180˚ 39˚ + 84˚ + d = 180˚ 123˚ + d = 180˚ - 123˚ = 57˚ ……. . . …… (R) (A) (G) 145 o c 62 o 102 o o Vertically Opposite angles are equal Angles around a point add up to 360˚ a = 102˚ 145˚ + 62˚ + c = 360˚ 207˚ + c = 360˚ - 207˚ = 153˚ x = 180˚ - 139˚ = 41˚ ……. . . …… (R) (A) (G) ……. . . …… f = 360˚ - 252˚ = 108˚ (R) (A) (G) ……. . . …… Combined angle facts Find angle w. Give reasons for your answer. Find angle e. Give reasons for your answer. w 34 o 62 o 60˚ + 111˚ + 81˚+ f = 360˚ 252˚ + f = 360˚ (R) (A) (G) Angles in special triangles (122) 81 o Angles in a quadrilateral add up to 360˚ ……. . . …… Find angle c. Give reasons for your answer. 49˚ + 90˚ + x = 180˚ 139˚ + x = 180˚ Find angle f. Give reasons for your answer. f 60 o 111 o Find angle a. Give reasons for your answer. a Angles on a straight line add up to 180˚ Angles in a quadrilateral 39 o Angles around a point (45) x Right-Angle = 90 Perimeter is the outside lengths added together = 10 × 7 = 70 cm 2 Geometry B Find angle x. Give reasons for your answer. 9 cm Area =b × h ……. . . …… 2 cm Vertically opposite angles Angles on a straight line (45) 62 o Base angles in an isosceles triangle are equal Angles in a triangle add up to 180˚ 62˚ + w = 180˚ 124˚ + w = 180˚ - 124˚ = 56˚ ……. . . …… (R) (A) (G) 73 o e Base angles in an isosceles triangle are equal 180˚- 34˚ = 146˚ ÷ 2 = 73˚ Angles on a straight line add up to 180˚ 73˚ + e = 180˚ - 73˚ = 107˚ (R) (A) (G) ……. . . ……

www. vle. mathswatch. com Expand two single brackets (134 a) Expand simplify 5 a 2 – 7 a 3 + 3 a 2 + 9 a 3 5 x +6 3 15 x +18 + = 5 x + 38 Expand double brackets (134 b) Expand simplify (3 x + 1) (x – 2) 3 x 3 x 2 +1 +x -3 y Linear sequences (103) Find the nth term of the sequence 3 5 7 9 11 List and represent inequalities (138) List the integers that satisfy the inequality -3 < 3 n ≤ 9 -2 -6 x + x = -5 x – 5 x - 2 8 10 Divide by 3 3 5 9 -1 < n ≤ 3 2 = 8 a 2 + 2 a 3 Multiply powers Square numbers 36 a 2 b 6 ………………. ………… DO NOT include -1 i) 5 ax 3 – 15 bx Two terms = one bracket 5 x ax 2 -3 b 5 ax 3 -15 bx = 5 x(ax 2 – 3 b) ………………. ………… Two terms = one bracket ii) x 2 + 5 x – 36 Factors of -36 1 2 3 -4 6 36 18 12 +9 6 Multiply Add (x - 4) (x + 9) ………………. ………… Include 3 List the WHOLE NUMBERS that are between -1 and 3 = 0, 1, 2, 3 Solve inequalities – two sides (139) Substitution (95) 2 x + 10 ≤ 6 x + 33 Work out the value of Q. Q = 5 d + c 2 c = -3 d=6 Balance method Work out the value of Q. Solve the inequality ………………. ………… iii) (6 ab 3)2 2 = 2 n + 1 ÷ 5 Factorise brackets (94 & 157) i) 2 a 4 x 5 × 3 ax 2 Subtract powers Divide numbers 2 2 11 y=3 Index Laws (34) ii) 8 x 6 y 8 2 x 2 y 7 +20 5 y = 15 ÷ 5 6 a 5 x 7 4 6 5 y – 20 = - 5 Do not add powers Add powers Multiply numbers 2 -3 y +20 2 x 4 y 7 = 8 y – 20 = 3 y - 5 5 a 2 – 7 a 3 + 3 a 2 + 9 a 3 ………………. ………… 3 x 2 Solve 8 y – 20 = 3 y – 5 Signs attached to numbers after 15 x + 18 – 10 x + 20 x Solve equations – two sides (135 a) Collect like terms Cheat Sheet Simplify 3(5 x + 6) – 5(2 x – 4) 2 x -4 -5 -10 x +20 Algebra B Collect like terms (33) 2 x + 10 ≤ 6 x + 33 -2 x 10 ≤ 4 x + 33 -33 Squaring a minus becomes positive -33 – 27 ≤ 4 x ÷ 4 = 5 × 6 + (-3) ÷ 4 -27 ≤x 4 = 30+ 9 = 39 2

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www. vle. mathswatch. com Expand two single brackets (134 a) Expand simplify 5 a 2 – 7 a 3 + 3 a 2 + 9 a 3 5 x +6 3 15 x +18 + = 5 x + 38 Expand double brackets (134 b) Expand simplify (3 x + 1) (x – 2) 3 x 3 x 2 +1 +x 8 y – 20 = 3 y - 5 -3 y -2 -6 x + x = -5 x – 5 x - 2 8 10 Divide by 3 3 5 9 -1 < n ≤ 3 2 iii) (6 ab 3)2 Multiply powers Square numbers 36 a 2 b 6 ………………. ………… 2 DO NOT include -1 i) 5 ax 3 – 15 bx Two terms = one bracket 5 x ax 2 -3 b 5 ax 3 -15 bx = 5 x(ax 2 – 3 b) ………………. ………… Two terms = one bracket ii) x 2 + 5 x – 36 Factors of -36 1 2 3 -4 6 36 18 12 +9 6 Multiply Add (x - 4) (x + 9) ………………. ………… Include 3 List the WHOLE NUMBERS that are between -1 and 3 = 2 n + 1 ÷ 5 = 0, 1, 2, 3 Solve inequalities – two sides (139) Substitution (95) Expand brackets Work out the value of Q. Q = 5 d + c 2 c = -3 d=6 Balance method Work out the value of Q. Solve the inequality 2(x + 5) ≤ 3(2 x + 11) ………………. ………… Subtract powers Divide numbers 2 2 11 +20 Factorise brackets (94 & 157) i) 2 a 4 x 5 × 3 ax 2 ii) 8 x 6 y 8 2 x 2 y 7 y=3 Index Laws (34) List the integers that satisfy the inequality -3 < 3 n ≤ 9 4 6 5 y = 15 = 8 a 2 + 2 a 3 List and represent inequalities (138) 2 -3 y ÷ 5 6 a 5 x 7 Find the nth term of the sequence 3 5 7 9 11 5 y – 20 = - 5 Do not add powers Add powers Multiply numbers Linear sequences (103) × 4 +20 2 x 4 y 7 = × 4 5 a 2 – 7 a 3 + 3 a 2 + 9 a 3 ………………. ………… 3 x 2 Solve 2 y – 5 = 3 y – 5 4 Signs attached to numbers after 15 x + 18 – 10 x + 20 x Solve equations – two sides (135 a) Collect like terms Cheat Sheet Simplify 3(5 x + 6) – 5(2 x – 4) 2 x -4 -5 -10 x +20 Algebra B Collect like terms (33) 2 x + 10 ≤ 6 x + 33 -2 x 10 ≤ 4 x + 33 -33 Squaring a minus becomes positive -33 – 27 ≤ 4 x ÷ 4 = 5 × 6 + (-3) ÷ 4 -27 ≤x 4 = 30+ 9 = 39 2

www. vle. mathswatch. com Area of rectangles and parallelograms (53 & 55) Find the area of the parallelogram. 7 cm Perimeter of shapes (52) Find the perimeter of the triangle. 12 cm 8 cm 10 cm Cheat Sheet 10 cm 49 o = 10 + 12 + 9 = 31 cm (R) (A) (G) ……. . . …… Angles in a triangle (54) Find angle d. Give reasons for your answer. d (R) (A) (G) 84 o Angles in a triangle add up to 180˚ 39˚ + 84˚ + d = 180˚ 123˚ + d = 180˚ - 123˚ = 57˚ ……. . . …… (R) (A) (G) 145 o c 62 o 102 o o Vertically Opposite angles are equal Angles around a point add up to 360˚ a = 102˚ 145˚ + 62˚ + c = 360˚ 207˚ + c = 360˚ - 207˚ = 153˚ x = 180˚ - 139˚ = 41˚ ……. . . …… (R) (A) (G) ……. . . …… f = 360˚ - 252˚ = 108˚ (R) (A) (G) ……. . . …… Combined angle facts Find angle w. Give reasons for your answer. Find angle e. Give reasons for your answer. w 34 o 62 o 60˚ + 111˚ + 81˚+ f = 360˚ 252˚ + f = 360˚ (R) (A) (G) Angles in special triangles (122) 81 o Angles in a quadrilateral add up to 360˚ ……. . . …… Find angle c. Give reasons for your answer. 49˚ + 90˚ + x = 180˚ 139˚ + x = 180˚ Find angle f. Give reasons for your answer. f 60 o 111 o Find angle a. Give reasons for your answer. a Angles on a straight line add up to 180˚ Angles in a quadrilateral 39 o Angles around a point (45) x Right-Angle = 90 Perimeter is the outside lengths added together = 10 × 7 = 70 cm 2 Geometry B Find angle x. Give reasons for your answer. 9 cm Area =b × h ……. . . …… 2 cm Vertically opposite angles Angles on a straight line (45) 62 o Base angles in an isosceles triangle are equal Angles in a triangle add up to 180˚ 62˚ + w = 180˚ 124˚ + w = 180˚ - 124˚ = 56˚ ……. . . …… (R) (A) (G) 73 o e Base angles in an isosceles triangle are equal 180˚- 34˚ = 146˚ ÷ 2 = 73˚ Angles on a straight line add up to 180˚ 73˚ + e = 180˚ - 73˚ = 107˚ (R) (A) (G) ……. . . ……

www. vle. mathswatch. com Solve 2 x *When signs are the same *Subtract equations 3 *Keep the x value positive 4 20 x + 12 y = 52 6 x + 12 y = 24 - 4 x=2 Substitute x=2 into 6 x+ 50 2 x + 6 x + 50 + 4 x + 10 = 12 x + 60 5 x + 3 y = 13 5 × 2 + 3 y = 13 10 + 3 y = 13 - 10 3 y = 3 e. g. 5 x + 3 y = 26 3 x - 2 y = 8 ÷ 3 Angles in a triangle equal 180 12 x + 60 = 180 -60 ÷ 10 ……. . . …… Equation of a line) *Pick two sensible points on the graph 5 2 4 3 1 -5 -4 -3 -2 -1 -1 1 2 3 4 -2 -1 0 1 2 3 y -9 -7 -5 -3 -1 1 3 Substitute each x value into the e. g. x = 3 y=2× 3– 3 equation to find the y value = 6 – 3= 3 (R) (A) (G) Jamie is x years old. Peter is five years older than Jamie. Mohamed is 3 times the age of Peter. The total of their ages is 60 years. Work out the age of Jamie. *Draw a triangle 2 2 -3 Equations from words What is the equation of the line. Write it in the form y = mx + c m = gradient (steepness of y ÷ 10 x……. . . …… = 10 (R) (A) (G) x Plot all the coordinates onto the graph and join up with a straight line. -60 12 x = 120 ÷ 3 y=1 *Add equations 4 x + 10 Collect like terms 1 Plot straight line graphs Draw the graph of y = 2 x – 3 for values of x from – 3 to 3 *Make ys the same *When signs are the different Cheat Sheet Find x 5 x + 3 y = 13 1 × 4 2 x + 4 y = 8 2 × 3 3 Algebra C Equations from shapes (137) Simultaneous Equations (162) 5 *Cancel fraction where needed dy 2 = m= =1 dx 2 x -2 c = y intercept -3 (where the line crosses the y axis) -4 -5 Finally, substitute your y = mx + c values for m and c into y= x+2 ……. . . . . …… the equation c = +2 Create an equation Jamie x Peter x+5 Mohame 3(x d+ 5) = 3 x + 15 Total of their age is 60 x + 5 + 3 x + 15 = 60 5 x + 20 = 60 -20 5 x = 40 ÷ 5 (R) (A) (G) ÷ 5 x =……. . . …… 8 (R) (A) (G)

www. vle. mathswatch. com Decimal Multiplication (66) 3 2 1 2. 3× 4. 51 4 5 1 2 0 1 1 8 0 2 0 3 0 12 1 5 3 3 7 3 3 2 1 =10. 373 Long Division (20) Fractions of amounts (72) Increase & Decrease percentages (86&87) Cheat Sheet 5 1. 5 2 0 6. 20 × 4 77 ÷ 11 = 7 ÷ 2 Number C Write as an inequality 2. 25 ≤ n < 2. 35 40% = £ 220 ÷ 3 × 10 (With a calculator) 37 ÷ 55 × 100 67. 2727 = 67. 3% £ 550 + £ 247. 50 Write the following as products of prime factors 30 5 42 6 2 2 3 21 =2 × 3 × 5 7 =2 × 3 × 7 ………. . . ……………. . . . …… HCF & LCM (79 & 80) 30 42 5 2 3 7 Highest common factor (HCF) – Multiply middle HCF: 2 × 3 = 6 Decimal numbers have negative powers 0. 0 0 0 6 5 = 6. 5 × 10 -4 ………. . . ……………. . . . …… Large numbers have positive powers 5 4 3 2 1 7 3 2000 = 7. 32 × 10 5 ………. . . ……………. . . . …… Swap numbers and powers Round numbers to 1 significant figure 20 × 60 0. 5 6 × 10 8 ………. . . ……………. . . . …… 1200 0. 5 = ÷ 0. 5 ÷ 0. 2 ÷ 0. 1 × 2 × 5 × 10 = 1200 × 2 = 2400 Best Value (41) Spar 1. 5 litre Coke is £ 1. 40 Nisa 330 ml Coke is 45 p *Check units match *Change if needed *1 litre = 1000 ml Spar 1500 ml 140 p Nisa 330 ml 45 p *Money ÷ Amount value is best (2 × 10 5 ) × (3 × 10 3 ) *Smallest (2 × 3) × (10 5 × 10 3 ) 140 ÷ 1500 Lowest common multiple Multiply numbers, Add powers (LCM) – Multiply all LCM: 5 × 2 × 3 × 7 = Estimate 23. 2 × 57. 72 0. 518 Original value £ 13, 000 Change in value £ 13, 000 - £ 6, 200 = £ 6, 800 Percentage change £ 6, 800 × 100 = 52. 3% £ 13, 000 -1 -2 -3 -4 3 ………. . . ……………. . . . …… A car costs £ 13, 000 new. After 4 years it costs £ 6, 200. Work out the percentage loss. Standard form (83) Prime factors (78) Estimate (91) Change in value × 100 Original value ii) 37 out of 55 Increase means add to original amount 7 × 5 = 35 × 10 = 60% ÷ 2 45% = £ 247. 50 2. 30 2. 25 and 2. 35 10% = £ 55 ÷ 1 0 × 4 5% = £ 27. 50 Times by top ‘Add a zero’ ‘ 5 higher and 5 lower’ ÷ 3 18 6 60 = = 30 10 100% = £ 550 ÷ 10 Error Intervals (155) 2. 3 has been rounded to 1 decimal place. Write the error interval for this number. (Non calculator) Find 45% of £ 550 Divide by bottom Find the percentage change (88) i) 18 out of 30 Increase £ 550 by 45% 5 of 77 11 206 ÷ 4 0 4 2 Fractions to percentages (89) = 0. 093 45 ÷ 330 = 0. 136 Spar has the best

www. vle. mathswatch. com Cheat Sheet Two way tables (61) John asks 150 students in his class whether they like tea, hot chocolate or coffee best. 56 of the students are girls. 15 of these girls like coffee the best. 35 boys like tea the best. 15 out of the 28 students who like hot chocolate best are girls. How many students like coffee best. Tea Choc Coffe e Total Girls 26 15 15 56 Boys 35 13 46 94 Total 61 28 A 6 9 8 10 2 Yellow 0. 5 Green 0. 2 0. 15 Blue 0. 15 *Probability adds to 1 Red 0. 5 + 0. 2 = 0. 7 1 – 0. 7 = 0. 3 ÷ 2 = 0. 15 The spinner is spun 500 times. Estimate the amount of reds you would expect. (G) 500 × 0. 15 = 75 70 people are asked about Saturday night TV. 13 like both Strictly and X factor. *Middle 29 like Strictly but not X factor. *Right side A total of 30 people like X factor. *Subtract numbers i) Complete the Venn diagram. X-Factor 17 B 3 5 7 *Intersection –middle Time (t seconds) Frequency 0 < t ≤ 20 20 < t ≤ 40 4 6 40 < t ≤ 60 5 60 < t ≤ 80 7 80 < t ≤ 100 3 Total 25 Midpoint Freq x Mid 10 30 50 70 90 11 Strictly 13 29 ii) What is the probability that this person doesn’t like either TV show? 11 70 ……. . . …… *Outside the Venn Diagram (R) (A) (G) Replacement Tree Diagrams (151) *Add two columns *’Midpoint’ and ‘Frequency x Midpoint A = {Even Numbers} B = {Prime Numbers} 1 The probability of getting a red and blue are the same Estimate the mean (130 b) ε = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} 4 Statistics C & D 61 150 61 ……. . . …… (R) (A) Sets (127 b) ε Venn Diagrams (127 a) Experimental Probability (125) 40 180 250 490 270 1230 There are blue and red counters in a bag. One is picked and then replaced before a second is picked. Complete the tree Pick two diagram. *Multiply along branches Blue Pick one 0. 6 0. 4. . 0. 6. . 0. 4. . Blue P(BB): 0. 6 × 0. 6 = 0. 36 Red P(BR): 0. 6 × 0. 4 = 0. 24 P(RB): 0. 4 × 0. 6 = 0. 24 Blue Red 2 i) A ∩ B. . . . . . *Union - Everything in both circles 2, 3, 4, 5, 6, 7, 8, 10 ii) A U B ……. . . . . … 1230 ÷ 25 = 49. 2 P(RR): 0. 4 × 0. 4 = 0. 16 What is the probability of getting two blues? P(BB) = 0. 36 *Branches add to 1 . . 0. 4 Red

www. vle. mathswatch. com SOHCAHTOA – Angles (168) SOHCAHTOA – Sides (168) Find the angle x. Find the length of BC. x A H 7 cm S O 5 cm *Label sides O A H H O Sin θ = H 5 Sinx = 7 C T OA Cheat Sheet *shift function for angles x =sin -1 (5 ÷ 7) x =45. 6 o ……. . . . . … x. A 34 o B O A S H C × 7 Tobias drives 15 km in 5 hours. Work out Tobias’ average speed. T Mass Density Volume (142) Find the density of an object if it has a mass of 12 kg and a volume of 300 cm 3. *Draw and fill in the triangle *Include units 7 cm *Label sides O A O H H A A Cos θ = H x Cos 34 = 7 C Distance Speed Time (142) M D S 15 km 5 S hours = T D V = 3 km/hour = 0. 04 kg/cm Sectors (167) Find the length of x. 220 o Geometry E * Divide 360 o by number of sides 360 o ÷ 8 = 45 x o *Subtract exterior angle from 180 o – 45 o = 135 o Draw out both shapes separately 7 cm y y is an interior angle 3 Similar Triangles (144) 5 cm *Exterior angles always add to 360 o 3 × 7 7 × cos 34 = 5. 8 cm For the sector find: X is an exterior angle 300 cm 3 D D = 12 kg ÷ 300 cm S = 15 km ÷ 5 hours Interior & Exterior angles (123) x 12 kg = (Small) i) The area Fraction of circle = 220 360 220 = 360 220 Area = 360 × πr 2 220 Area = 360 × π× 5 2 = 48. 0 cm ii) The arc length Fraction of circle 2 220 Arc = 360 × πD 4 cm (Big) 16 cm Find the scale factor Big shape s ide Scale factor = Small shape side Big shape side: 16 + 4 = 20 cm Small side: 16 cm Diameter = 5 × 2 Scale factor = 20 = 1. 25 16 = 10 cm Finding a larger side: Multiply 220 Arc = 360 × π× 10 7 cm × 1. 25 = 8. 75 cm = 19. 2 cm