Revision exercise E2 (page 30) Stage 8. Revision exercise A2 (page 32) Answers to revision exercises STAGE

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1 A cm cm cm R B = to d.p. a),,,,,, c),,, d),,, e),,, 9 f),,, a) n + n c) n + d) n e) n a) c) a a d) b b + e) + f) p g) + + h) a) cm cm cm a) mm Answers to revision eercises mm R is the required region. a) c) d) e) f) a) c) d) e) f) 9 metres per minute $ 9 m cm a) c) d) e) f) 9 9 a) 9 c) = d) 9 e) f) 9 (or ) Revision eercise E (page ) litres, litres g, g cm, cm, m, m a) c) d) e) 9 f) g) h) i) a) a 9 b c) c d) d a) 9 c) d) 9 = to d.p. a) = 9, =, is between 9 and so one solution is between = and =. = to d.p. 9 mm a) cm cm 9 m cm a) cm m c) cm d) m e) cm f) 9m litres Stage Revision eercise A (page ) a) c) d) e) f) g) h) i) inches mm mm mm mm 9 mm mm mm mm mm mm mm mm 9 mm mm mm mm mm mm Graduated Assessment for OR GSE Mathematics Hodder Murra

2 a) Answers to revision eercises c) c) = to, or to. a) = a) (iii) (iv) c) (ii) d) (i) 9 a). F. F.. S.. F. S.. F S. S = (i) (ii) a) not not not not not not not c) = a) (i) (ii) = a) = 9 c) 9 = a) = = 9 c) = d) = e) = f) = g) = h) = i) = j) = 9 a) c) d) e) f) g) h) Graduated Assessment for OR GSE Mathematics Hodder Murra

3 a) = which simplifies to + = or + = =, angles are º, º, º = = metres a) +, + + > ( + ) c), so, Hassan s sister is less than ears old i.e. ma age ears and das Revision eercise B (page ) p 9 a) + a) Answers to revision eercises = + R = 9 R = + = Graduated Assessment for OR GSE Mathematics Hodder Murra

4 a) Answers to revision eercises umulative frequenc 9 West School East School 9 West School East School Height (cm) On average students at East School are taller than students at West School. The spread (IQR) is about the same but the range is greater at West School. Graduated Assessment for OR GSE Mathematics Hodder Murra

5 a) umulative frequencies: Bos:,, 9,,,, Girls:,,,, 9,, umulative frequenc 9 Girls Bos Sample B Length (Lcm) Frequenc umulative frequenc L L L L L 9 L L, c) Sample B Sample A Answers to revision eercises umulative frequenc Number of marbles Bos: median =, interquartile range = 9 = 9 Girls: median =, interquartile range = = 9 The median value for the girls is lower but the IQR is the same. c) Reading from the graph at marbles suggests that of the girls guessed this value or a value less so that 9 were overestimating while for the bos guessed this value or a value less so overestimated. Looking back at the figures, bos and girls guessed between and. Overall there is little difference between the sees. a) Sample A Length (Lcm) Frequenc umulative frequenc L L L L L L 9 L Length (cm) Sample B Sample A Sample A: median = cm interquartile range = 9 = 9cm Sample B: median = cm interquartile range = 9 = cm d) The fish in sample B are slightl longer and with less spread. 9 seconds Not quite doubled.. = 9 9 Graduated Assessment for OR GSE Mathematics Hodder Murra

6 Answers to revision eercises Revision eercise (page ) Rotation through 9º anticlockwise about (, ) a) to c) A 9 B d) Rotation through about (, ) a) to c) D F E 9 d) Enlargement, scale factor, centre (, ) Possible answers: Translation b ( )followed b reflection in the -ais Rotation through about (, ) followed b reflection in the line = a) to c) A B A B d) Enlargement centre (, ), scale factor Graduated Assessment for OR GSE Mathematics Hodder Murra

7 a) =, = =, = a) =, = =, = c) =, = d) =, = e) =, = f) =, = g) =, = h) =, = i) =, = + = 9 + = Pen costs p, ruler costs p 9 a) 9 c) d) 9 e) 9 f) g) h) a) c) d) e) f) g) h) 9 i) j) a) c) d) e) 9 f) g) 9 h) 9 i) j) a) 9 c) d) e) f) g) h) 9 i) a) c) d) e) f) g) h) i) 9 = = = + + = a) c) oordinates of B must satisf = + e.g. (, ) a), (, ), (, ) c), (, ) d), (, ) a) d (i) (ii) ost in per mile c) d) = d + Answers to revision eercises 9 a) = + k = + k c) = k d) + = k Graduated Assessment for OR GSE Mathematics Hodder Murra 9

8 Answers to revision eercises Revision eercise D (page ) cm, cm, cm, 9 cm No, the sides are not proportional,. a) º (9º + º) = º so the angles are the same in both triangles. cm cm BDA, AD, BA (If the order of the letters in the first is different then the others must correspond.) cm Breed B give more milk on average but with a wider spread of amounts. Both have a mean of which suggests that, on average, there are the same number of peas per pod for the two tpes. Alternativel, the median of Biggapeas is and and of WondaP is so WondaP have slightl more peas per pod. Ranges: Biggapeas, WondaP ; there is a much wider spread for WondaP. 9 A longer time is spent, on average, on English but with a wider spread of times. Modes: lass A =, lass B =, which suggest, on average, that the students in lass B own more pets. Although the range is the same (), the shape of the distribution suggests a wider spread of numbers in lass A. a) Upper quartile umulative frequenc Median Lower quartile Time (seconds) Median, lower quartile, upper quartile 9 c) st nd Time (seconds) d) If second bank s claim is true then the average response time is far less and the spread of times is also much less. a) c) d) 9 cm e) cm f) cm g) cm h) 9 cm 9 North km, east km 9 m Angle = 9, just legal a) Volume Area c) Area a) c) Graduated Assessment for OR GSE Mathematics Hodder Murra

9 Revision eercise E (page ) a) + + a + a c) + d) + e) a + a f) p g) + + h) + a) ( + )( + ) ( )( ) c) ( )( ) d) ( + )( + 9) e) ( + )( ) f) ( )( + ) g) ( )( ) h) ( )( + ) i) ( 9)( + ) j) ( )( + ) k) ( )( + ) l) ( + )( + ) a) (p + )(p ) ( + )( ) c) ( + )( ) d) (s + )(s ) a), c) Graph not full-size Answers to revision eercises Number of people 9 M Tu W Th F M Tu W Th F M Tu W Th F M Tu W Th F Moving averages:,,,,,,,,, 9,,,,,, d) There is a general downward trend. Monda is alwas highest, Wednesda is alwas lowest. a), c) Graph shown half-size. Week Week Week Week 9 Number of people M Tu W Th Week F Sa M Tu W Th F Sa M Tu W Th F Sa M Tu W Th F Sa Week Week Week Graduated Assessment for OR GSE Mathematics Hodder Murra

10 Answers to revision eercises 9 Moving averages:,,,,,, 9,,,,,,, 9,, 9, 9,, d) There is a slight downward trend towards the end of the weeks. Saturda is alwas highest, Tuesda is alwas lowest. a) = or = or c) = or d) = or e) = or f) = 9 or g) = or h) = or i) = or j) = or k) = 9 or l) = or a) = or = or c) = ±9 d) = ± e) = or f) = or g) = or h) = or a) = b = d a + c c) = z + a a d) = a e) a = V + b c f) = A + h bc b g) a = c gt h) l = π P i) T = V T P V a a j) b = + k) r = l) R = V V πa + πb RR R R s 9 a) t = g seconds Stage 9 Revision eercise A (page ) a) =, 9 =, 9 c) + =, d) ( + ) = ( + 9) = = a) a) c) + d) + e) a ab b f) + g) h) + i) + a) a a c) a d) a b e) z f) a bc a) (a + b c) a(c + c) ab(a d) Will not factorise e) ab(c + a f) a( + b bc) g) (pq ) h) a( a + a ) i) ac(b + ) a) ( )( + ) Will not factorise c) ( )( + ) d) ( cd)( + cd) e) ( )( + ) a) ( 9)( ) ( + )( ) c) ( )( ) d) ( + )( ) e) ( )( + ) f) ( )( ) g) ( )( + ) h) ( + )( + ) i) ( )( ) j) ( + )( ) a) + c) + d) + ( e) + ) + 9 a) = or = or c) = or d) = or e) = or, L = 9h Graduated Assessment for OR GSE Mathematics Hodder Murra