Answers to Homework Book 9

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1 Answers to Homework ook Checking answers Eercise.H (page ) a) = 7, 7 b) (7 ) 0 = 0 (or, better, (7 ) 0 = 00), c) 0 = 00, d) 0 = 0, 0 e) =, 7 f) 0 0 = 00, g) 70 0 = 00, h) = 00, 0 a) 0 7 =, 7 b) (0 + 70) (0 ) = 0 (or, better, (0 + 70) ( ) = ), c) 0 0 =, d) 0 70 = 7; e) 0 0 = 0 0, 0 07 f) =, 0 g) = 0 =, 07 a) 0, 0 b) 0 0, 7 0 c) 0, 0 d) 0, 0 0 e) 0, 0 f) 0, 0 g) 7 0, 0 h) 0, 7 0 i) 0, 0 Algebraic manipulation Eercise.H (page ) a + ab + b m mn n 0p pq + q a + 7ab b + a b Eercise.H (page ) a a b Cannot be simplified 0a b c 7 0 p q p 0 p mn pq p a b b Eercise.H (page ) ( + ) (a b) a( + 7a) ( ) a(a b + c) ( + ) 7 ( + ) a(a + b) ab( b) 0 a (a + b) ( ) ( ) ab(a + b) a(bc + b ac) z( + + ) Eercise.H (page ) ( )( + ) (7 )(7 + ) ( )( + ) ( )( + ) ( t)( + t) ( )( + ) 7 (a b)(a + b) (a b)(a + b) (0 7)(0 + 7) 0 ( )( + ) Graduated Assessment for OCR GCSE Mathematics Hodder Murra 007 0

2 Answers to Homework ook Eercise.H (page ) ( + )( + ) ( + )( + ) ( )( ) ( )( ) ( )( ) ( + )( + ) 7 ( + )( + ) ( + )( + ) ( )( ) 0 ( )( ) Eercise.H (page 7) ( )( + ) ( + )( ) ( + )( ) ( )( + ) ( )( + ) ( )( + ) 7 ( )( + ) ( + )( ) ( + )( ) 0 ( )( + ) Eercise.7H (page 7) ab Eercise.H (page ) = or = or = or 7 = or = or = or 7 = or = or = or 0 = or Proportion and variation Eercise.H (page ) a) b) t c) d t d) r d e) p a) b) c) d) e) Eercise.H (page 0) a) = or = 0 b) = or = t = 0 0 = Graduated Assessment for OCR GCSE Mathematics Hodder Murra 007

3 c) 0 = or = 0 0 = d) = or = 0 7 a) b) c) d) e) Eercise.H (page ) = Answers to Homework ook 0 = e) = 00 or = = 0 0 = 0 = 0 0 = 00 = 0 0 a) PV = 000 b) P = Eercise.H (page 0) 70 = 0 Graduated Assessment for OCR GCSE Mathematics Hodder Murra 007

4 Answers to Homework ook = = = 0 b) = c) = 00 =. 0 = =. 0. = d) = a) = 0 00 = 0. 0 e) = 0 0 = 00 = 0. = Graduated Assessment for OCR GCSE Mathematics Hodder Murra 007

5 Eercise.H (page ) a) (i) (ii) = 0 (iii) b) (i) (ii) = (iii) c) (i) (ii) = (iii) 0 d) (i) 0 (ii) = (iii) 0 e) (i) (ii) = 0 (iii) 0 0 a) It is of its value at the Earth s surface. b) 00 km G Indices Eercise.H (page ) a) n b) n a) b) c) d) e) a) b) 00 c) d) e) a) b) 0 c) d) e) 7 a) b) c) 0 0 d) 7 7 e) a) b) c) d) e) 0 7 Eercise.H (page ) a) b) c) d) 0 7 e) f) n+ a) b) c) d) e) n n f) n n 7 a) b) 7 c) a) b) c) d) e) f) n n Rearranging formulae Eercise.H (page ) r = V π = z = (tv) or t v = f r = V π = m 7 = p q + = p + q + = 0 = = p aq f b a π T g = L ( ) or πl T Arcs, sectors and volumes Eercise.H (page 7) a) 0 cm b) cm c) cm d) 7 cm e) 7 cm a) cm b) cm c) cm d) cm e) cm a) cm b) cm c) cm a) 7 b) c) 7 d) e) 0 f) a) 0 7 cm b) cm c) cm d) cm e) 7 cm f) cm a) 7 b) 0 cm 7 a) cm b) 7 Answers to Homework ook Graduated Assessment for OCR GCSE Mathematics Hodder Murra 007

6 Answers to Homework ook Eercise.H (page ) a) 7 cm b) 0 cm c) cm d) cm a) cm b) 7 cm c) cm d) 7 cm a) 0 cm b) 0 mm cm cm 0 cm 7 cm 7 Upper and lower bounds Eercise 7.H (page ) a) 0 cm b) seconds a) cm b) 7 seconds a) m b) 0 kg a) m b) 0 7 kg hours minute, hours minutes 0 mm, mm 7 0 m Yes. The upper bound of the combined weight of the parcels is 00 g, so the weight will be less than this. Eercise 7.H (page ) a) 7 7 m b) 7 7 m a) 7 m b) 7 m a) km/h b) 7 7 cm/s a) 7 km/h b) 7 7 cm/s a) cm, 7 cm b) cm, cm a) 7 cm, cm b) m, 7 m 7 a) cm b) 70 7 cm 00 seconds Similarit and enlargement Eercise.H (page 7) a) b) a) b) 000 a) b) cm 7 cm 0 m 7 7 cm a) 0 7 m b) litres c) 000 kg a) 7 cm b) cm c) cm 0 a) cm b) 7 cm c) cm Eercise.H (page ) a) (, ) b) a) (, 7) b) 0 D D A C A Probabilit Eercise.H (page ) 0 7 a) 0 b) A C 0 C A 0 a) 0 0 b) 0 a) 0 b) a) 0 b) P(stop once) = P(stop at lights, don t stop at level crossing) + P(don t stop at lights, stop at level crossing) = (0 0 7) + (0 0 ) = = 0 Rami has onl calculated the probabilit that she has to stop at the lights and not at the level crossing. She has forgotten to add the probabilit that she doesn t have to stop at the lights but does have to stop at the level crossing. a) 0 b) 0 77 c) 0 7 C Graduated Assessment for OCR GCSE Mathematics Hodder Murra 007

7 Eercise.H (page ) a) b) (i) (ii) a) b) (i) (ii) a) Student Student 7 G b) (i) 0 (ii) 0 G First card R Year Year 0. M M L G Second card R R L M L 0 Working in two and three dimensions Eercise 0.H (page ) a) 7 units b) 0 units c) 7 units d) 0 units e) 7 units a) units b) 0 units c) 0 units d) units e) units f) 7 units Eercise 0.H (page ) a) (i) 7 cm (ii) 7 (iii) 7 cm (iv) b) A(0, 0, ), (0,, ), C(,, ), D(, 0, ), E(0, 0, 0), F(0,, 0), G(,, 0), H(, 0, 0) a) 7 0 cm b) c) 7 cm d) a) 7 cm b) c) cm d) 0 cm Eercise 0.H (page ) a) 0 units b) 0 0 units c) units d) 7 7 units e) 0 units or Answers to Homework ook a) Saturda Rain No rain b) 0 b) (i) 0 (ii) Sunda Rain No rain Rain No rain Eercise 0.H (page ) a) G A C b) C E F a) 0 b) ; all cubes are similar. a) b) a) 0 cm b) cm 7 a) cm b) (i) (ii) 0 Graduated Assessment for OCR GCSE Mathematics Hodder Murra 007

8 Histograms Answers to Homework ook Eercise.H (page ).. 0 Frequenc densit Height (cm) Men Frequenc densit Age (ears) Women Frequenc densit Age (ears) Graduated Assessment for OCR GCSE Mathematics Hodder Murra 007

9 0. Frequenc densit (people per ) Mone raised ( ) Answers to Homework ook Frequenc / Amount earned ( ) Graduated Assessment for OCR GCSE Mathematics Hodder Murra 007 7

10 Answers to Homework ook Eercise.H (page ) a) Time (t hours) b) hours a) b) ears a) Amount raised ( ) b) 00 c) More people took part in the second race: in the second race compared with in the first. The distributions were similarl shaped. oth distributions were positivel skewed with just over half the people in each race raising less than 00, about one third raising between 00 and 00 and around % raising more than 00. a) Waiting time Frequenc (w minutes) b) 0 minutes Frequenc 0 t t t t 0 0 t t 0 Frequenc w w 0 0 w w 0 0 w 0 0 w 0 Circle properties Other reasons ma be possible in some cases. Eercise.H (page ) a = 0 (angle at centre = angle at b = (angle at centre = angle at c = (angle sum of a triangle = 0 and base angles of an isosceles triangle are equal) d = (base angles of an isosceles triangle are equal) e = 70 (angle at centre = angle at circumference or eterior angle of a triangle = sum of interior opposite angles) f = (angle at centre = angle at g = 0 (angle in a semicircle and eterior angle of a triangle) h = (angle at centre = angle at circumference and angles on a straight line) 7 k = (angle sum of a triangle and base angles of an isosceles triangles give angle at centre as 0 ; angle at centre = angle at w = (angle at the centre = angle at = 0 (angles at a point) = 0 (angle at the centre = angle at Eercise.H (page ) a = (angles in the same segment) b = c = 0 (angles at centre = angle at circumference and angles in the same segment) d = 70 (opposite angles of a cclic quadrilateral) e = 0 (angle in a semicircle) f = (angles in the same segment) g = (angle sum of a triangle) j = 0 (opposite angles of a cclic k = quadrilateral) (opposite angles of a cclic quadrilateral) m = (angle at centre = angle at circumference and angles in the same segment) p = (angles in the same segment) q = (angle at centre = angle at circumference and isosceles triangle) Eercise.H (page ) a = (angles in the same segment) b = (angle AC = angle DC =, angles in the same segment; angle sum of a triangle) angle AC = (base angles of an isosceles triangle) angle AC = (angle sum of a triangle) refle angle AOC = (angle at centre = angle at c = (angles at a point) Graduated Assessment for OCR GCSE Mathematics Hodder Murra 007

11 d = (eterior angle of a triangle and isosceles triangle) e = (angle at centre = angle at f = (angle in a semicircle and angle sum of a triangle) g = 7 (opposite angles of a cclic quadrilateral) h = (h + h = 0, angle in a semicircle and angle sum of a triangle) k = (isosceles triangle and angles in the same segment) Eercise.H (page 0) a = (angle between radius and tangent and angle sum of a triangle) b = 0 (perpendicular from centre to chord and angle sum of a triangle) c = 0 (angle between radius and tangent and angle sum of a triangle) d = (isosceles triangle and angle between radius and tangent) e = (angle in a semicircle and angle sum of a triangle) f = (angle at centre = angle at g = (angle between radius and tangent) n = cm (perpendicular from chord to centre and Pthagoras) OM = cm (perpendicular from chord to centre and Pthagoras) ON = cm k = 7 cm (perpendicular from chord to centre and Pthagoras) Eercise.H (page ) a = 0 (angle in the alternate segment) b = 0 (angle in the alternate segment) c = (angle in the alternate segment) d = (angle in the alternate segment) e = (angle between radius and tangent) f = (angle in the alternate segment) g = (angle in the alternate segment) h = (angle in the alternate segment) n = 77 (opposite angles of a cclic quadrilateral) p = (angle in the alternate segment) q = (angles on a straight line) u = (angles in the alternate segment) v = (angles on a straight line) Straight-line graphs Eercise.H (page ) = + = + + = + = = + + = 7 = + = + = 0 a) v 00 Velocit (m/s) t Time (seconds) b) Gradient = and represents acceleration in m/s ; Intercept = 0 and represents the initial velocit in m/s c) v = 0 + t Eercise.H (page ) a) b) c) = + = or + = 7 a) b) = + = + = 7 = 7 a) None of them b) = + and + = + = 7 0 a) + = 7 b) = + c) (, ) and (0, ) Answers to Homework ook Graduated Assessment for OCR GCSE Mathematics Hodder Murra 007

12 Answers to Homework ook Surves and sampling Eercise.H (page ) For eample: How old are ou? or What school ear are ou in? together with an appropriate tick bo list. How often do ou visit the cinema? together with an appropriate tick bo list. a) Give a list of programme tpes e.g. pop, rock, eas listening, classical and so on. b) What time of da? e.g. breakfast, morning, afternoon, evening, night. c) What tpe of competition? Would ou take part? d) Irrelevant? Other possible questions: Age. How long do ou listen for? Do ou listen to other stations? Wh? Eercise.H (page ) a) Would be random but ecludes those without phones and those who are e-director. Response depends on who answers the phone. b) Ma not be from our town. Ecludes those who do not travel b train. c) Will onl include those who do go to restaurants. a) Sstematic random sampling or stratified random sampling b) Simple random sampling or sstematic random sampling c) Sstematic random sampling Eercise.H (page ) a) Select three from each class at random. b) Choose one bo and two girls from each class at random. 0 out of 00 is in. Select the following number of emploees from each department. Eercise.H (page 7) 0 Check students work. The actual total number of nests is 77. a) and b) Start at (st value): mean = 0 cm Start at (nd value): mean = 0 0 cm Start at 77 (rd value): mean = 0 cm Start at 0 (th value): mean = 0 cm Start at 0 (th value): mean = 0 cm c) Students own sample. d) Approimatel the same. e) Average of all 00 is 0 cm Eercise.H (page 0) a) Likel to involve bias as onl football supporters will be chosen. Also a ver small sample. b) Satisfactor as the cars are likel to have been parked randoml. c) Could be biased as qualit could alter during the shift. a) Not random and likel to be biased as mainl car owners use car parks. b) Satisfactor as register is arranged in house order, which is not a relevant attribute. Onl bias is that under-s are not included. c) Likel to be biased as man use the bus because the do not own a car. Department Number of emploees A C D 0 0 Graduated Assessment for OCR GCSE Mathematics Hodder Murra 007

Answers to Homework Book 7

Answers to Homework Book 7 nswers to Homework Book Coordinates Exercise.H (page ) a) (, ) (, 0 ) c) (, ) d) (, ) e) (, ) a) (, ) (, ) c) (, ) d) (, ) e) (, ) f) (, ) Exercise.H (page ) a) (, 0, 0) (, 0, ) c) (0, 0, ) d) (0,, 0)