LEVEL 6. Level 6. Page (iv)

Transcription

1 LEVEL 6 Number Page N9... Fractions, Decimals and Percentages N20... Improper Fractions and Mixed Numbers N2... Prime Numbers, HCF and LCM... 7 Calculating C22... Percentage of an Amount C2... Percentage Increase and Decrease... 7 C2... Addition and Subtraction of Fractions... 7 C2... Multiplication & Division of Integers by Fractions.. 7 Algebra A7... Substitution A8... Trial and Improvement A9... Algebraic Simplification A0... Linear Equations A... Generate a Number Sequence A2... Finding the nth Term... 8 A... Straight Line Graphs A... Distance - Time Graphs... 8 A... Real Life Graphs... 8 Shape, Space and Measure S7... Properties of Quadrilaterals... 8 S8... Nets of D Shapes... 86A, 86B S9... Constructions S20... Geometric Problems S2... Corresponding and Alternate Angles S22... Enlargement... 90A, 90B S2... Similar Shapes... 9 S2... Area of a Triangle... 92A, 92B S2... Area of a Parallelogram... 9 S26... Volume of a Cuboid... 9 S27... Surface Area of a Cuboid... 9 S28... Circumference of a Circle S29... Area of a Circle... 97A, 97B Handling Data D8... Bar Charts and Frequency Diagrams D9... Scatter Graphs D0... Pie Charts D... Two-Way Tables... 0 D2... Surveys D... Further Probability...0 N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D S8 Page (iv)

2 N9 Fractions, Decimals and Percentages ) Complete the tables. a) b) Fraction Decimal Percentage % 0% Fraction 68 Decimal Percentage 00 % % 2) Put these fractions, decimals and percentages in order, smallest to largest. a), 9%,, 0. 2 b) 27%, 0.2,, c) 0, 9%, 0.99, 00 d), 0.6, 2, 0% e) 0.2, 0%,, ) Chris says that is halfway between 0. and 00%. Is Chris correct? You must explain your answer. ) Emily says that 0.2 is halfway between 0% and. Is Emily correct? You must explain your answer. N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 69

3 N20 Improper Fractions and Mixed Numbers ) Convert the following improper fractions to mixed numbers. a) b) 8 f) g) c) 2 7 h) d) 20 9 i) e) 6 j) ) Convert the following mixed numbers to improper fractions. a) f) 0 9 b) g) c) 2 h) 9 d) i) 6 e) 2 j) 2 7 ) Put these numbers in order, lowest to highest. a).,, b) 7, 7., c), 98%,, 0 N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 70

4 N2 Prime Numbers, HCF and LCM ) Split up the following numbers into the product of their prime factors. a) 2 d) 20 b) e) 0 c) 72 f) 296 2) Find the Highest Common Factor (HCF) of the following numbers. a) and 6 d) 00 and 2 b) 8 and 6 e) 7 and 98 c) 6 and 8 f), 90 and 0 ) Find the Lowest Common Multiple (LCM) of the following numbers. a) 8 and 2 d), 6 and 8 b) 0 and e) 2 and 8 c) and 8 f) 72 and 96 ) The bells at Kings School ring every 6 minutes. At Queens School the bells ring every minutes. At Princess School the bells ring every 9 minutes. All three bells ring together at 8.0 am. When is the next time the bells of the three schools will ring together? N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 7

5 C22 Percentage of an Amount ) Work out the following: a) 0% of 80 b) 0% of 8 c) 0% of d) 2% of 20 e) 2% of 90 2) Work out the following: a) 0% of 0 b) 0% of 26 c) 0% of 2 d) 2% of 2 e) 7% of 2 ) Work out the following: a) 0% of 0 b) % of 0 c) % of 0 d) % of 70 e) % of 80 ) Work out the following: a) 20% of 0 b) % of 9 c) 80% of d) % of 6 e) 6% of 82 ) Jamie received 26 pocket money last week. He spent it as follows: 0% on sweets, 2% on magazines % on games How much did Jamie have left? Show your working. 6) Tony had 0 saved up and gave % of it to his younger sister, Ella. Ella gave 20% of what she was given to her younger brother, Ben. Ben gave 0% of what he was given to his younger brother, Tim. Tim spent 7% of what he was given on buying a toy for his hamster, Hammy. How much was the toy for Hammy? N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 72

6 C2 Percentage Increase and Decrease ) Describe how you would increase a number by 0%. 2) Describe how you would decrease a number by 0%. ) Increase the following numbers by 0% a) 0 e) 7 b) 0 f) 0 c) 80 g) 2 d) 20 h) 2 ) Decrease the following numbers by 0% a) 20 e) 2 b) 60 f) c) 80 g) d) 90 h) 7 ) Work out the following: a) Increase 00 by % e) Increase 20 m by 0% b) Decrease 20 by % f) Decrease 820 by 7% c) Decrease 00 km by 20% g) Increase 60 kg by 60% d) Increase 96 kg by 0% h) Decrease 26 by % 6) A shop is having a sale and all prices are reduced by 2%. a) Work out the sale price of an item normally priced at 8.0 b) Work out the sale price of an item normally priced at 99 N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 7

7 C2 Addition and Subtraction of Fractions ) Work out the following, simplifying your answers where possible. a) 2 + = e) b) = f) c) = 9 g) d) 0 0 = h) = 2 + = 2 = = + = = 6 6 = 2) Work out the following, simplifying your answers where possible. a) f) + = b) 9 g) = 2 c) + = h) 2 d) i) 7 = 8 e) 2 + = j) = + = 6 0 = + = 2 6 = 2) Write the missing numbers in each of these fraction sums. a) b) c) d) + 6 = = 8 = = N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 7

8 C2 Multiplication and Division of Integers by Fractions ) Work out the following, giving your answers in their simplest forms a) e) 9 b) 7 f) c) 2 g) d) 2 9 h) 2) Work out the following, giving your answers in their simplest forms a) of 0 e) 2 2 of 0 cm b) of 20 km f) 7 8 of 6 c) of 20 kg g) 7 of 7000 g d) of 99 h) 9 of 00 ) Work out the following, giving your answers in their simplest forms a) e) 0 b) 7 2 f) 8 c) 2 g) d) 9 h) ) An industrial machine takes of an hour to produce a very special tool. How long would it take the machine to produce 2 of the tools? ) A road is 20 km long. Road signs are to be installed every 2 of a kilometre. How many signs will be needed? N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 7

9 A7 Substitution ) Using a =, work out a) a + d) 2a + b) 7 a e) a c) 6a f) a 2 + 2a 20 2) Using x = and y = 2, work out a) x y d) y x b) y x e) x 2 + y c) x + 2y f) x xy y ) Using a =, b = and c = -2, work out a) a + b + c d) ab c b) 2b + c e) ac + b c) c a + b f) c 2 2ab ) Using x =, work out a) x 2 2x b) 2x 2 + x + c) x 2x 2 ) If =.2 and r = 9, work out a) 2 r b) r 2 N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 76

10 A8 Trial and Improvement ) Using a trial and improvement method, solve the equation x 2 x = 6 You must show ALL your working. 2) Using a trial and improvement method, solve the equation x 2 + x = 2 You must show ALL your working. ) Using a trial and improvement method, solve the equation x + 2x = 72 You must show ALL your working. ) Using a trial and improvement method, solve the equation x x = 0 You must show ALL your working. N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 77

11 A9 Algebraic Simplification ) Simplify these expressions a) a + a = f) r 2r + r = b) b + b = g) t t + t + 2t = c) x x = h) 7p p + 2p p = d) 6d + d 2d = i) -y + 2y y + y = e) 2k + k + k k = j) -2c + c c c = 2) Simplify these expressions a) a + b + a + b = f) 6x y + 7y 2x = b) a + 2a + b + b = g) 2k l k + 0l = c) 7x + 2y + x + y = h) m + n + 7m 7n = d) r + 6p 2r p = i) v w v 2w = e) c + 8d c + d = j) -x y y x = ) Simplify these expressions a) 7xy 2xy = f) 6m + 2pr m + rp = b) cd + dc = g) 0a 2 d + 2y da 2 + y 2 = c) x 2 + x 2 + 2x 2 = h) bz 2 + t t zb 2 = d) 9y + y 2y = i) 2r 2 b + r 2 r + 6br 2 = e) ab + 7ab 2a = j) 8x y + 2w w yx = N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 78

12 A0 Linear Equations ) Solve a) x + = 8 f) 2x = b) x + 7 = 9 g) x = 0 c) x = 2 h) x 2 = 8 d) x 6 = 0 i) x = 7 e) 2 + x = j) x = 8 2) Solve a) x + 2 = 7 f) x 2 + = 7 b) x = 7 g) x 2 = c) 2x + 0 = 20 h) 2x = 9 d) x 7 = 29 i) x + = 2 e) + 2x = j) x + 6 = 8 ) Using the statement: I think of a number, double it, and subtract. I get 7. a) Form an equation. b) Solve the equation to find the number that was thought of. ) Using the statement: I think of a number, multiply it by 7, and add. I get 80. a) Form an equation. b) Solve the equation to find the number that was thought of. ) Using the statement: I think of a number, multiply it by 2, divide the result by and then subtract. I get. a) Form an equation. b) Solve the equation to find the number that was thought of. N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 79

13 A Generate a Number Sequence ) Write the first five terms of each sequence a) Start at and add d) Start at 8 and subtract b) Start at 0 and subtract e) Start at -0 and add 6 c) Start at and add 9 f) Start at and subtract 2) For each sequence, describe the rule and find the next two terms a), 7, 9,,, d) -, 2,, 8,, b), 6, 2, 26,, e) 6, 2, -2, -6,, c) 22, 9, 6,,, f) -2, -, -28, -2,, ) Here is a pattern made up of sticks a) Write the pattern as a number sequence. b) Describe the rule. c) Find the next five terms of the sequence. ) For each sequence, find the first terms and the 0th term. a) n b) n + 2 c) n + 2 d) n 7 e) 0n + 9 N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 80

14 A2 Finding the nth Term ) Pattern Pattern 2 Pattern a) Draw pattern b) How many lines would be in Pattern 6? c) How many lines would be in Pattern n? 2) Work out the nth term of the following number patterns. a) 2,, 6, 8,.... b),, 7, 9,.... c), 8,,,.... d),, 9,,.... e) 2, 22, 2, 2,.... f) 2, 8,, 20,.... g),., 6, 7.,.... ) Write down the first four terms and the 0th term of the following number patterns. a) n n b) n n + 2 c) n n d) n 2n + e) n n 7 f) n n + g) n n N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 8

15 A x y Straight Line Graphs ) a) Complete the table of values for y = x y 8 b) Plot the graph of y = x 2 c) Use your graph to estimate the value of x when y = 2 d) Use the graph to estimate the value of x when y = O x 2) a) Plot the graph of y = 2x y b) Plot the graph of x + y = O x N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page

16 A Distance - Time Graphs Distance in miles Time pm pm pm pm pm pm The graph, above, shows Jade s journey by scooter from her house to university with some stops along the way. a) How long did the journey take? b) How many breaks did Jade take throughout her journey? c) At what time did Jade take her first break? d) How long did the first break last? e) What was Jade s average speed between pm and pm? f) What was Jade s average speed between.0 pm and pm? g) What was Jade s average speed between.0 pm and 7 pm? N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 8

17 A Real Life Graphs ) Use the conversion graph below to convert : a) 80 km to miles b) miles to km c) 0 km to miles d) 60 miles to km Miles e) 00 miles to km f) 0 km to miles Kilometres 2) The graph below shows three different mobile phone tariffs. Cost Tariff in Pay as you go C B 60 0p per minute. Tariff 2 0 per month and A 0p per minute Tariff 0 0 per month, 00 free minutes then 0 0p per minute 20 a) Match each tariff with its graph, A, B or C 0 b) Every month, James needs about 90 mins 0 talk time Monthly used minutes Work out which tariff would be best for him. Explain your answer. c) Tariff is announced. This is 0 per month, 0 free minutes then 0p per minute. Draw a line on the graph to show this tariff. N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 8

18 S7 Properties of Quadrilaterals ) Write down the names of the quadrilaterals a) to g) a) b) c) d) e) f) g) 2) Fill in the table for quadrilaterals A, B and C. Shape Number of lines of symmetry Order of rotational symmetry Area A B C A 0 cm 9 cm 8 cm B 8 cm C cm 9 cm 6 cm 2 cm N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 8

19 S8 Nets of D Shapes a) Draw a net of this cube. b) Draw a net of this cuboid. squares squares squares squares square 2 squares N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 86A

20 S8 Nets of D Shapes Draw a net of this triangular prism. squares squares 2 squares squares N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 86B

21 S9 Constructions ) Using only a ruler, protractor and pencil, draw the following diagrams accurately. For each diagram measure and write down the side you are asked for. a) Measure length AC C b) Measure length AC C A cm B A 2 6 cm 20 B c) Measure length CD D 80. cm 0 A cm C B d) E cm D cm F 20 cm A cm B Measure length CD C cm 2) Using only a ruler, pencil, compasses and protractor as needed, draw the following diagrams accurately. For each diagram, measure and write down the angle you are asked for. a) 7 cm r C Measure angle r. cm cm b) C Measure angle s cm A c) Measure angle t A 6 cm 7. cm t cm B B cm C A 8 cm d) cm D Measure u cm angle u E C cm 2 cm A 7 cm B s B N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 87

22 S20 Geometric Problems ) a In every question below, calculate the missing angles indicated by the letters. None of the diagrams are drawn accurately. d b c 7 f g 0 l 6 e h i j k 2) 8 b a c d 72 ) a 0 e 2 f g c h 2 6 b 68 d e f 2 72 g 20 2 h 6 8 N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 88

23 S2 Corresponding and Alternate Angles ) In every question below, calculate the missing angles indicated by the letters. None of the diagrams are drawn accurately. a 7 28 b 2 c 0 e 7 f d 2) 8 c a b d g e f 79 h i j k l m o n p t r s q 6 70 ) a 72 0 c 6 b e d ) a 6 e 2 b 7 c 80 d N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 89

24 S22 Enlargement Enlarge the following shapes with scale factor 2, using the dot as the centre of enlargement. a) b) c) d) e) f) N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 90A

25 S22 Enlargement ) Enlarge the following shapes using the dots as the centres of enlargement. Scale factor Scale factor a) b) Scale factor Scale factor 0. c) d) A ) Use dots to mark on the grids the positions of the centres of enlargement. a) b) C B D N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 90B

26 S2 Similar Shapes ) In each of the following questions, the two shapes are mathematically similar. Work out the lengths of the missing sides. a) b) 7 cm?? cm 0 cm cm 2 cm 8 cm c) d) 0 cm? 8.2 cm? 2 cm 6.6 cm?.2 cm 7 cm 9.8 cm 2) a) Work out the length of CD. A b) Work out the length of AE. cm 0 cm E. cm B cm D C N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 9

27 S2 Area of a Triangle ) Find the areas of the following triangles 0.6 cm a) b) c) d) cm cm 6 cm 7 cm cm 8 cm cm 2) Find the areas of the following triangles c) a) b) cm 2.8 cm 0 cm 2 cm. cm 2. cm 0 cm cm 0 cm ) Find the areas of the following triangles a) b) c) 26. cm 8 cm 6. cm 8.6 cm 8.2 cm cm d) e) 6 cm cm 28 cm 20 cm N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 92A

28 S2 Area of a Triangle ) Find the lengths w, x, y and z a) b) c) cm d) w Area = 2 cm 2 6 cm Area = 8 cm 2 x 8 cm Area = 2. cm 2 y z Area = 0. cm 2 z 2) Find the areas of the following shaded parts of rectangles a) b) 6 cm c) cm 20 cm 9 cm 6 cm 22 cm cm 6 cm cm 26 cm cm cm cm 7 cm cm 7 cm cm 8 cm ) The two squares are drawn on cm square grids. Find the areas of the squares. a) b) N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 92B

29 S2 Area of a Parallelogram ) Find the areas of the five parallelograms on this cm square grid a) b) d) c) e) ) Find the areas of these four parallelograms a) b).6 cm 9.8 cm 8. cm c) 9 cm cm d) 2. cm 22 cm 20 cm 8 cm N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 9

30 S26 Volume of a Cuboid ) Find the volume of the following: a) b) cm cm 20 cm 0 cm 7 cm 9 cm c) d) 6 cm cm 8 cm 22 cm 2. cm cm.2 cm.6 cm 0 cm 2) Find the height of this cuboid Volume = 0 cm ) The cuboid below is made out of steel and has a rectangular hole all the way through it. If cm of steel has a mass of 8 g, what is the mass of the cuboid?? cm 8 cm 9 cm 9 cm 6 cm 7 cm 20 cm N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 9

31 S27 Surface Area of a Cuboid ) Find the surface area of the following: a) b) cm cm 20 cm 0 cm 7 cm 9 cm c) d) 9. cm 2. cm 8 cm 2 cm.2 cm.6 cm 2) The cuboid below is made out of steel and has a rectangular hole all the way through it. All the surfaces are painted including the base and the sides of the rectangular hole. Work out the area which will be painted. ) The shape below consists of a cuboid glued onto another cuboid. If the whole shape - including the base - is painted, work out the area which will be painted. cm 6 cm cm 8 cm 9 cm 7 cm 6 cm 20 cm cm 0 cm 22 cm N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 9

32 S28 Circumference of a Circle In all questions, take to be.2 ) Find the circumference of the following circles a) b) c) π 8 cm 6. cm 9. cm d) e) f) cm 6.7 cm 9.6 cm 2) Find the perimeter of the following cm a) 8 cm b) c) 2 cm d). 0 cm 60 ) The circumference of the earth is approximately 0000 km. If you had a piece of string which was 6. m longer than 0000 km and put it around the earth, how far away from the earth, all the way round, would the extra 6. m allow it to be? a) 0. mm b) mm c) cm d) m N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 96

33 S29 Area of a Circle In all questions, take π to be.2 ) Find the areas of the following circles a) b) c) 8 cm 6. cm 9. cm d) e) f) cm 6.7 cm 9.6 cm 2) Find the areas of the following cm a) 8 cm b) c) 2 cm d) 0 cm 60 e).. 0 cm N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 97A

34 S29 Area of a Circle In all questions, take π to be.2 In each question, find the area of the shaded section. a) b) 6 cm 2 cm c) cm d) cm 8 cm e) = 2 cm f) A square touching a circle at four points 2 cm N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 97B

35 D8 Bar Charts and Frequency Diagrams ) A group of pupils were asked for their favourite colour. Here are the results. Draw a suitable chart to show this information. Colour Frequency Red 8 Blue 0 Purple 9 Green Yellow 7 2) A group of people were given a puzzle to solve. The time taken by each individual to complete the puzzle was recorded in the table below. Draw a suitable chart to show this information. Time in mins 0 < t < 0 0 < t < < t < 0 0 < t < 0 0 < t < 0 Frequency N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 98

36 D9 Scatter Graphs ) The heights and weights of some children are shown in the table, below. Height (cm) Weight (kg) a) Plot the information from the table. b) Describe the correlation between height and weight. 0 0 c) Draw a line of best fit. d) Estimate the weight of a child of similar age to the group above with a height of cm Height (cm) 2) The scatter graph below relates car engine sizes to their fuel consumption in mpg. mpg 60 a) Describe the correlation shown by the data Engine size (litres) b) A car has an mpg of 2. Estimate the engine size. N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 99

37 D0 Pie Charts ) The table on the right shows how far 90 visitors to a museum have travelled. Draw a pie chart to show this information.. Distance Within the city Within 0 miles of the city Over 0 miles from the city Overseas Frequency ) The table shows the land usage of a farm. Draw a pie chart to show this information. Land usage Arable Pasture Woodland Waste Area (hectares) N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 00

38 D Two-Way Tables ) 60 pupils in a school are asked to choose a new colour for the school tie. They can only choose from Blue, Green or Red. Some of the results are shown in this two-way table. Blue Green Red Total Male Female Total Complete the two-way table. 2) A survey was done by a school to find out how people travel to the school. Altogether, 00 people were asked and the results can be seen below. Male pupils Female pupils Male teachers Female teachers Total Walk Car Cycle Taxi Bus Total a) Complete the two-way table. b) How many people cycle to school? c) How many female pupils go to school by taxi? N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 0

39 D2 Surveys ) Lesley wants to find out the types of food people like best. She is going to ask people to choose between Italian Food, French Food, Indian Food and Chinese Food. Design a suitable table for a data collection sheet she could use to collect this information. 2) Beth wants to find out two things: the types of books people prefer to read how much time, on average, they spend reading books a) Design two suitable questions for Beth to use in her questionnaire. b) She decides to ask her questions to the first ten people going into the public library on a Saturday morning. Give one reason why this might not be a good way to carry out the survey. N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 02

40 D Further Probability ) A counter is taken at random from set followed by another counter at random from set 2. B D 2 A C Set Set 2 a) Write down all the possible pairs of counters that may be chosen. b) What is the probability that B will be picked? c) What is the probability that any pair of counters will be chosen except B? d) What is the probability that the pair of counters chosen will include an odd number? 2) The two spinners on the right are spun and their scores added together to give a total. a) Draw a possibility space to show all the totals. 2 6 b) What is the probability of scoring a total which is bigger than? ) Every Tuesday the main school dinner is either Sausages, Chicken, Pizza or Tuna. Use the table below to work out the probability that the main dinner will be Pizza next Tuesday. School dinner Sausages Chicken Pizza Tuna Probability ? 0.7 N9 N20 N2 C22 C2 C2 C2 A7 A8 A9 A0 A A2 A A A S7 S8 S9 S20 S2 S22 S2 S2 S2 S26 S27 S28 S29 D8 D9 D0 D D2 D Page 0