Answers. Cancelling Fractions - Page 15 Exercise 1
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1 Answers 0 s, 00 s and 000 s - Page 7 ) a) 0 0 c) 0 d),0 e) f). g). h) i). j).9 k) 0. l) 0. m) 0.0 n) 0.00 ) a) c),900 d),00 e) 90 f),70 g). h) 70 i) 0. j) 0. k) 0. l) 0.0 m) 0. n).00 ) a),000,000 c) 9,000 d) 900,000 e),70 f) 7,00 g),97 h) 00 i) 0 j) 0 k) l) 7. m) n) 0. ) a) 0.. c).9 d).9 e) 0. f) 0.7 g).7 h) 0.0 i) j) 0.0 k) 0.07 l) 0.00 m) n) ) a) c).7 d). e) 0.0 f) 0.7 g) h) i) j) k) l) m) n) ) a) c) 0. d). e) 0.00 f) 0.0 g) h) i) j) k) l) m) n) ) a) 7 c) d). e) 0 ) a) c) 0.07 d) 0.7 e) 0.7 9) From the top right - clockwise, 000,., 0., 0, 0.00, 00, 0.0 Rounding off Whole Numbers - Page ) a) Anything between 0 and c) Anything between 0 and 09 and between 00 and 0 ) a) 9,7 9,70 9,00,0,00,000,9,0,00,0,0,00 Anything between,0 and,0 c) Anything between,0 and,99 and between,00 and,9 d) 7,99 and,00 Negatives - Page 9 ), 0,,, 7, ) ºC, ºC, 7ºC, 0ºC, ºC ) 0, 0,, ) a) 7ºC ºC ) a) c) 0 d) 0 Number Cards - Page 0 a) 0 c) +7 d) 9 e) +7 f) 9 g) h) i) j) 9 k) 0 l) + Multiplication - Page ) a) 0 c) 9 d) 0 e) f) 0 g) h) i) j) k) 9 l) 99 m) 7 n) 7 o) 7 p) 00 q),0 r),0 s),0 t),700 u) v) 0 w) 9 x),0 y) 00 z),0 ) ) 0 ) 00 ) 99 ) 0 7) ) 9) 000 0) 70 Multiplying Decimals - Page ) a).. c) 0. d).7 e) 79. f).7 g). h) 7. i). j). k) l) m). n) 0 o). p). q) 9.7 r). s). t). u).0 v). w). x). y).9 ). ). ) a).0 c) 9.0 ) 00cm ) a) 7.kg 7.kg 7) 7.km ).g Division - Page ) a) c) d) e) f) g) 7 h) i) 7 j) 9 k) 09 l) m) 0 n) o) p) 9 q) r) 0 s) 09 t) ) a) r r c) r d) 0 r e) r f) r g) r h) r i) 7 r j) r7 k) 0 r l) r m) r n) 9 r o) 9 r ) a) c) 7 d) e) f) r7 g) r9 h) 7 i) r j) r k) 7 r9 l) 7 r7 m) r9 n) 9 r o) 0 r ) a) 0 c) 00 ) 0 ) a) rows with over 7) 9 ) 9) weeks Division with Decimals - Page ) a)..7 c). d) 7.7 e). f). g).0 h). i).7 j). k) 0. l). m). n). o). p) 0.0 q).0 r). s). t) 0. u). v).9 w). x) 7.9 y). ) 7. ). ) 9p ) a). miles 9. miles ) p 7) a).cm.cm c).cm ).cm 9).7 0).cm Cancelling Fractions - Page Exercise ) -- ) -- ) -- ) -- ) -- ) -- 7) -- ) -- 9) -- 0) -- 9 ) -- ) -- ) -- ) -- ) -- ) -- 7) -- ) -- 9) 9 0) -- ) -- ) -- ) -- ) -- ) -- ) -- 7) ) -- 9) -- 0) ) --, --, --, --, --, --, ) --, --, --, -- order is --, --, --, Exercise ) a) -- ) -- ) -- ) -- and ) a) c) Mixed Fractions - Page Exercise ) a) ) a) ) a) c) -- d) -- e) -- 9 ) a) c) Exercise ) no ) yes ) -- ) ) ) 7) --, --, --, --, --, --, ) -- 9) -- 0) a) ) -- ) a) c) Calculating a Fraction - Page 7 Exercise ) 0 ) ) ) 7 ) ) 7) ) 0 9) 0) ) ) ) ) 0 ) ) 7) ) 9) 0 0) Exercise ) ) ) 9 ) 9 ) ) 7) 0 ) 9) 0 0) ) ) ) 0 ) ) ) 7) ) Exercise ). ).7 ).7 ) 0. ). ) 0.0 7) 7.7 ) 7 9).0 0). ). ) 7. Exercise ) ) ) and ) a) -- 0 ) 7.0 ) 0 7) a),00 7,
2 Calculating Percentages - Page Exercise ).0 ) 9p ).00 ) 7.0 ). ) 0p 7) 9p ) p Exercise ) ) ) ) 0 ) ) 0 7) 0 ) 9). 0) 7. ). ) p ). ). ).9 ).77 Exercise ).kg ).0kg ) 7.kg ) 7. metres ).9 metres ).9 metres 7). litres ). litres 9) 7. litres 0) 9.9 litres ).kg ).0metres ) 0.kg Exercise ) ) 00 ) a) ) a) 70. c).0 ) a).0.0 c) 90p d).0 e).0 Ratio and Proportion - Page 9 ) :9 ) 0, 0 and 0 ) a) 90cm 0cm ) a) Second school : c) 0 and 00 ) a) :::0 0 Checking - Page 0 ) a) 0 0 = = 00 c) 0 0 = 00 d) 0 0 = 000 e) 00 0 =,000 f) 00 0 =,000 g) 00 0 =,000 h) 0 00 =,000 i) 0 00 =,000 j) 00 0 =,000 k) 00 0 = 0,000 l) = 0,000 m) = 0,000 n) =,000 o) = 0,000 (ii) (iii) (v) (vi) (viii) ) These are suggested estimates. Others are acceptable. a) = 0 c) 00 = 00 0 = 0 d) 900 = e) 00 9 f) 0 = = 0 g) 0 0 = h) 700 i) = 70 = 0 j) 00 7 k) = l) = = 0 m) = n) 00 0 = 0 o) = ) (i), (ii), (v), (ix) Inverse Operations - Page ) a, b, d, g, h, k and l are wrong ) b, e, f, h and j ) = 0 ) = 7 ).0 7 =.0 ) 99 or ) centimetres Adding Letters - Page ) a) g + f or f + g w + v or v + w c) x ) a) r + s + t w + x c) f + e + g + h Adding Letters and Numbers - Page ) a) a + b + w + y + 7 c) h + k + n ) a) d d c) d d) d g) c + h) 9d i) t + 0s ) a) n and n n + c) n n d) -- e) n n f) n g) n n and n h) n and n i) n n ) a) n n and n and n n c) n + and + n d) n n and -- e) n and n + n f) n n and n Brackets - Page ) a) 7 c) d) e) f) g) h) i) j) 0 k) 0 l) ) a and g b and f c and d e and k h and l i and j ) a) x 0n 0 c) x d) 9n e) x + f) y + y g) b b h) c + c i) x + x j) f f k) y y l) x x ) a) x + x + c) 7y + d) 7a e) b + f) 0a 0 g) 0d + x h) 7x 7 i) y + x j) x 7 k) 7y l) x + m) + a n) b + a o) b + a + ) a) 9 9 c) d) 0 e) x f) 0y g) 0a h) 9b i) a + j) 9 + b k) 7 + b l) + y ) a) ( ) = ( ) = c) 7 ( 7) = d) e) f) g) 0 h) i) j) = k) l) ( ) = 7) a) a x + c) y d) b + 7 e) y + 7 f) x + 7 g) b + 7 h) y i) a j) + y k) + b l) + y or y Number Rules - Page 7 a) n +, n +, n + 0,, n +, n +, n +, n + 0 c),, n, n, n, n, 7n(in centre) d),, 9, n, n, n, n e) 7,,, n, n +, n + Number Grids - Page ) n n + n + 0 n + n + ) n n 0 n 9 n n 0 Number Patterns - Page 9 ) a) c) multiply the number of squares by then add d) m = s + e) 0 f) 0 g) with over ) a) 7 c) subtract from the number of pots then multiply by d) r = (p ) e) 7 f) Negative Co-ordinates - page 0 ) a) Perimeters of Tiles - Page ) a) x x = c) x = cm ) a) y y = 0 c) y = 0cm d) 0cm by 0cm Simplifying Expressions - Page ) a) 7a 9y c) x d) n e) n f) p g) 9y h) 0 i) s j) 0 k) a l) m) p n) r o) z p) n ) a) p + r + c) a + d) b e) n + f) k Hexagon c) The y axis or x = 0
3 ) a) ) a) c) d) e) (,) (,) (,) (,) c) (, ) (, ) (, ) (, ) ) a) y f) g) x h) i) j) (, 7) (, ) (, ) (, 7) (, 7) (, ) (, ) (, 7) ) a) k) l) Triangles - Page a) 7º 7º c) 9º d) 9º e) º f) 9º g) 7º h) 9º i) º (, ) ) a) c) e) Angles at a Point - Page a) 7º 0º c) 9º d) º e) 99º f) 0º g) º h) º i) 70º j) 7º k) º l) 77º m) º Drawings - Page See separate sheet Making Shapes - Page ) a, c, e and f ) a, b, d and e ) f and c a, j and m n, e and b l and i (,) and (, ) d) 9 Angles - page ) A = 7º B = 0 º C = º D = º E = º F = º G = 7º H = 0º I = º Packages - Page ) a) Hexagon a, b, c, d, e, f and g ) a) 9 d c) ) b and c
4 Missing Blocks - Page 7 Enlargements - Page 9 a) c) d) e) f) g) h) i) j) -D Shapes - Page a) l) k) c) d) e) f) g) h)
5 Rotational Symmetry - Page 0 a) c) d) e) f) g) h) i) j) Rainfall - Page a) Sydney July c) April c) Sydney - its total rainfall for the year is greater than that of New York. e) cm f) Approx..cm g) March, April and May h) July, August and September i) September, October and November j) April, May and June. Youth Club - Page a) Tuesday c) d) e) f) years (from the beginning of age to the end of age is years) g) h) Ranges remain the same. The mode of the Tuesday club changes from to Moving - Page 7 ) a) : (approx) (i) :00 and 0:00 (ii) 0mins and mins c) 0 miles and miles (approx) ) a) Martin Simon takes the lead c) 0 seconds d) Martin, seconds k) l) m) n) o) p) Percentage Bars - Page ) a) Labour Conservative c) Labour and Liberal Democrat d) % e) Labour share went down by about %. The actual Labour vote went down by about % ) a) Helen Jane c) % d) % e) Jane gives about sq m and Helen gives about sq m Reading Pie Charts - Page 9 ) a) Crisps Juice c) Sweets and Chocolate d) Crisps ) a) D A - red or black, B - white, C - black or red, E - blue c) 0 d) 0 Metric and Imperial Measure - Page ) a) litres. litres ) 0g of butter 0g of sugar 00g of flour eggs ml using oz = g and pint = 0. litre ),,, using mile =.km ) a) lbs.lbs ) a) 0cm.cms c) 0cms ) kg 7) litres Estimating Measures - Page ) a) miles, kilometres cm c) kg d) seconds e) grams f) gallons, litres g) cms h) millimetres i) ml ) a) c) - d) 0-00kg, 0-0kg e) 0-0litres f) 0-0 minutes, - minutes g) - h) - 0 metres i) hrs - hrs Area and Perimeter - Page ) a) 0cm, 9cm cm, cm c) cm, 0.cm d) 0cm, cm e) cm, 0cm f) 9cm, cm g) 0cm, 0cm ) a) 0, ) 0 ) ) 00 Mean - Page ) a),.,.9 c), 0 ) a) Mean = Mean = 0.9 ) a) c) ) a), and Comparing Pie Charts - Page 0 ) a) Oak The diagram shows only the proportion of Ash trees on each farm. If there are more trees on farmer Williams farm there could be a larger number of Ash trees than on farmer Jones farm. A small proportion of a large number can be bigger than a large proportion of a small number. c) Farmer Williams has more trees on his land. ) a) More people went to the cinema on Saturday than on Monday. Lots more on Saturday. This is probably because children are off school on Saturday and not on Monday Chances - Page ) Impossible Poor Even Good Certain ) -, 0., 0% ) No. It is expected that over a large number of tosses there would be about the same number of heads and tails. Sometimes it happens with a small number of tosses but not always. ) a) Car. There have been more cars passing than any other vehicle. Bus. There have been fewer buses passing than any other vehicle. ) a) or 0. or 0% - or 0. or 0% 0 Taking a Chance - Page 7 7 ) a) White c) d) ) a) 7 - c) Because there are the same number of s and s on the dice. i.e. of each. d) - ) a) - - c) - d) - e) -
6 Spinners - Page ) - - c) Getting a on spinner is more likely. There are fewer numbers on spinner than on spinner thereby increasing the probability ) The spinner has fours, threes, twos and one. ) a) 9 c) d) Take a Card - Page ) a) - - c) - d) e) f) Because there are not an equal number of outcomes for each total. ) a) - - c) - Different Outcomes - Page ) a) - 0 times c) by dividing the number of times the 9 number occurs by 0 d) = e) 00 f) g) One way 0 0 is to compare fractions like this:- 00 Theoretical is - = Damian s is = Dawn s is = 00 Dawn s is closer to the theoretical value than Damian s. ) a) He divides the number of lorries by the number of vehicles. 0.0, 0., 0., 0.0 c) She divides the total number of lorries by the total number of vehicles. d) Yes is very close to 0.. It is therefore a very good approximation. Trial and Improvement - Page ) a) cm mm (When the areas are the same, the length of the side is between. and., so mm is the nearest) ) When the difference is 0, the value of x will be between.7 and.. therefore. is the nearest value correct to decimal place. Negatives - Page 7 ) ) ) and ) and ) 7 ) a) + + c) + d) + e) 0 f) g) 7 Fraction Problems - Page ) a) ) a) - - c) 0 d) 00 ) a) 7 ) a) - 0 ) a),00km c) d) e) 00, 00, 00km ) a),00 litres - c),00 litres Percentage Calculations - Page 9 ) a) % ) a) c) % d) 7.% ) a) % % c) 0 d) 70 ) a) 00km 0% c) 0% d) 7% e) 0,, ) a) 0 % c) 900 Fractions, Decimals and Percentages - Page 0 ) a) 0% 0% c) 70% d) % e) 7% f) 9% g).% h) % i).% j).% k).% l) % m).% n) 90.% 9 7 ) a) - - c) - d) - e) - f) - g) h) i) j) k) l) m) n) - o) 00 0 ) a) c) 0. d) 0. e) 0. f) 0.0 g) 0.00 h) 0.0 ) a) 0., 0% 0., 0% c) 0.7, 7% d) 0., 0% e) 0.0, % f) 0., % g) 0.0,.% h) 0., 0% i) 0.7, 70% j) 0., % k) 0., % l) 0.7, 7.% m) 0.07, 7.% n) 0., % o) 0.0, % p) 0.9, 9% ) a) 0.7, -, 7 -%, , 0.00, 0%, c) 0.7,, 7%, d) %,, 0., ) a) - c) d) Ratios - Page ) a) ::: ::7: c) % ) a) :: :: c) 0% ) a) :::0 9 c) ::: Adding and Subtracting Fractions - Page ) a) - - c) - d) - e) - f) g) - h) - i) j) - k) - l) m) - n) - o) - p) ) a) - c) - d) - e) f) g) h) i) j) k) l) m) n) o) p) 7 0 ) a) - - c) - d) - e) - f) - g) - h) - i) - j) k) 0 ) a) and and c) and d) and e) and f) and g) and h) and 0 0 i) and j) and k) and l) and ) a) - c) - d) e) f) - g) h) i) j) ) a) - c) - d) e) f) g) h) i) - j) 0 0 More Fractions - Page ) a) c) d) e) f) g) h) i) j) k) l) - m) n) o) p) - q) r) - s) t) ) a) c) d) - e) f) g) h) i) j) k) - l) m) n) - o) p) q) r) - s) 7 - t) ) From the top, clockwise -, -, -,, -,, -, Numbers for Letters - Page ) a) 0 0 c) d) ) a) c) d) e) f) g) h) ) a) c) d) 0 e) f) 0 g) h) ) a) to d.p. c) d). She has used π =. instead of. Multiplying a Bracket by a Bracket - Page ) a) n, n and 0 n + 7n +0 c) n + 7n +0 ) a) n, 7n, n, n + n + c) n + n + ) a) n + 9n + n + n + 0 c) n + 7n + d) n + n + Finding the Missing Expression - Page ) a) c) a d) 0 e) y f) g) 7p h) r i) 7f j) 9 k) k l) m ) b + c) y + 7 d) x + e) y f) c g) w h) c i) w + 7 j) s k) x l) y m) a ) a) p, d + d 7, a c) y, x d) m, n +
7 Making Magic Squares - Page 7 ) a) n + n + n + = n n + + n + + n = n n + + n + n = n n + n + + n = n n + n + n + = n n + + n + n + = n n + n + n + = n Drawing T s - Page 7 T Y T T Y ) a) T n+ n+ n T n n n+ n+ n n X X T Tiling Patterns - Page ) a) c) d) n ) a) c) 0 d) 0n e) ) a) c) d) e) n + f) n g) n + Equations of Parallel Lines - Page 9 ) B y = x +, C y = x, D y = x, E y = x ) B y = -x +, C y = -x, D y = -x, E y = -x 9 Graphs of Equations - Page ) a) D E c) C d) B e) A f) F ) a) x = 7, x =, y =, y = y = x c) y Properties of Quadrilaterals - Page 7 ) 90º ) 0º ) a) º 7 -º ) a) 0º 70º ) a) º 7º ) a) 9º º 7) a) 0º 0º Angles of Polygons - Page 7 ) Triangle Quadrilateral Pentagon Hexagon Heptagon Octagon Nonagon 7 9 n 7 n 0º 0º 0º 70º 900º 00º 0º 0(n ) ) a) Divide by the number of sides 0( n ) - c) (i) 0º (ii) º (iii) º n 0º 0º 0º 70º 900º 00º 0º 0(n ) X d) y = x Viewing Shapes - Page 7 ) a) C D c) A d) B ) a) C, D,and B c) (ii) and (iii) x Symmetry of Polygons - Page 7 ) Hexagon Square Equilateral Triangle Octagon Heptagon 7 7 Pentagon ) a) (i) º (ii) 0º (iii) 0º (i) Exterior angle 0º º = º Interior angle is half of º = 7 -º Centre angle is 0º = 90º (ii) Exterior angle 0º 0º = 0º Interior angle is half of 0º = 0º Centre angle is 0º = 0º (iii) Exterior angle 0º 0º = 7º Interior angle is half of 0º = º Centre angle is 0º = 7º 7
8 Intersecting and Parallel Lines - Page 7 a, b, c, d, e, f, g, h, i, j, k, l 7, m 7, n 09, o 09, p, q 9, r 9, s 9, t. g) (i) ACB (ii) ABC (iii) They are equal h) (i) c (ii) they are equal (iii) j (iv) They are equal Computer Instructions - Page 77 ) a) 0, Forward Turn Right 0 Forward 0 Turn Right 9 Forward Turn Right 0 Forward ) a) 0º and 0º Forward Turn Right 0 Forward 9.9 Turn Right 0 Forward 7. c) Forward Turn Right 0 Forward Turn Right 0 Forward Drawing an Octagon - Page 7 a) º FORWARD 0 TURN RIGHT FORWARD 0 TURN RIGHT FORWARD 0 TURN RIGHT FORWARD 0 TURN RIGHT FORWARD 0 TURN RIGHT FORWARD 0 TURN RIGHT FORWARD 0 TURN RIGHT FORWARD 0 c) REPEAT [FORWARD 0, TURN RIGHT ] d) A regular hexagon e) REPEAT [FORWARD 0, TURN RIGHT 0] f) REPEAT [FORWARD 0, TURN RIGHT 90] Enlarging Letters - Page Enlarging Through a Point - Page Area and Circumferance of a Circle - Page 79 ) a) 7.cm.cm c).cm times c) times d) :: e).cm,.cm,. f) :: ) a).m Approximately. revolutions ) a) Approximately.cm Approximately cm ) a) 7m m c) 0m d) m Areas of Rectangles - Page 0 ) n + n ) a) n and n + n + n ) a) n + and n n + n ) a) n + n n + n c) n + n Volumes - Page ) (i) a) 0cm 0cm c) cm d) 0cm e) 00cm f) 90cm (ii) b, c, e and f. ) litres ) a) 0.m and.m.97m Continuous Data - Page a) 9 is less than c) is less than or equal to d) h lies between 0 and, and includes 0 but does not include e) h < 0 f) g) h) 9
9 Pupils Weights - Page a) c) 7 d) e) Constructing a Pie Chart - Page a) º ) a) 0 7 ) a) º Weight Tally Frequency 0 w < 0 0 w < 0 0 w < 0 0 w < w < 0 Other White Red Silver Department Percentage Angle needed Fruit and Vegetables Delicatessen Frozen Foods Household Goods Butcher General Groceries 0% % 0% % 0% 0% 7º º º º º º GG B F&V D FF HG Distance and Time - Page 7 ) a) rd, st and th 0 seconds c) seconds ) a) minutes 9 minutes c) after minutes d) About minutes and 0 seconds Scatter Diagrams - Page ) a) (ii) (iii) c) (i) ) a) The more bedrooms a house has, the more windows it has. or c) Dice - Page 9 ) a) c),,, and, d) - e) - f) 7 9 ) a) - c) - Blue Dice Second Dice Children Choosing - Page 90 ) a) First Ball 0 c) d) V eos Non Fiction Fiction Red Dice,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,,, First Dice Second Ball,,,,,,,,,,,,,,,,,,,, 9
10 ) a) R,W R,B B,W - c) - ) a) - c) d) e) On the Road - Page 9 ) a) egg, bacon, beans egg, bacon, tomatoes bacon, beans, tomatoes egg, beans, tomatoes egg, egg, bacon bacon, bacon, egg egg, egg, beans bacon, bacon, beans egg, egg, tomatoes bacon, bacon, tomatoes tomatoes, tomatoes, egg beans, beans, egg tomatoes, tomatoes, bacon beans, beans, bacon tomatoes, tomatoes, beans beans, beans, tomatoes c) 0 (with the addition of lots of of the same) ) bacon, beans, tomatoes bacon, toast, tomatoes beans, toast, tomatoes egg, toast, tomatoes ) year old car year old car year old car ) a) Probability of breaking down Probability of not breaking down
11 Drawings - Page
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