Answers to Homework Book 7

Transcription

1 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) e) (,, 0) f) (0,, ) a) (, 0, 0) (, 0, 0) c) (0, 0, 0) d) (,, 0) e) (,, ) a) (i) (,, 0) (ii) (,, ) (iii)(0,, ) (iv) (,, ) (v) (,, ) (i) B (ii) OCGD Percentages Exercise.H (page ) a) 0 c) d) a) 0 0 c) 0 0 d) 0 a) % % c) % d) % e) % Fraction Decimal Percentage % 0 0% 0 % 0 % 0 % a) 0 0 c) 0 d) 0 0 e) a) % % c) % d) 0% e) % Exercise.H (page ) % 0% 0 % Ratio and proportion Exercise.H (page ) a) : : c) : d) :: e) :: a) 0: : 00 c) :0 d) : e) : : : ::00 Exercise.H (page ) a) buckets buckets a) kg 00 g cm a) 0 a) 00 ml 0 ml a) 00 m cm a) cm cm a) 000 votes 000 votes Exercise.H (page ) Mrs Smith hours, Mrs Rogers hours a) litres litres Meat 00 g, onion g, carrot g hours 0 minutes 0 0 a) : Iain 000 euros, Stephen 000 euros Graduated ssessment for OCR GCSE Mathematics Hodder Murra 00

2 nswers to Homework Book Exercise.H (page ) In all these questions either cost per unit or number of units per pence can be used. Both are given in each answer. Where necessar, answers are rounded to decimal places, unless otherwise indicated. Cost per gram: 0 g bag = p, 00 g bag = 0p Grams per pence: 0 g bag = 0 0 g, 00 g bag = 0 g 00 g bag is better value Cost per litre: litre bottle = p, litre bottle = p Litres per pound: litre bottle = litres, litre bottle = litres litre bottle is the better value Cost per gram: 00 g tub = 0 p, 0 g packet = 0 p Grams per pence: 00 g tub = g, 0 g packet = g 0 g packet is the better value Cost per tub: tubs = p, tubs = p Tubs per pence: tubs = 0 0, tubs = 0 0 (to d.p.) Pack of tubs is the better value Cost per kilogram: kg pack =, kg pack = Kilograms per pound: kg pack = 0 kg, kg pack = 0 kg kg pack is the better value Cost per millilitre: ml bottle = p, 00 ml bottle = p Millilitres per pence: ml bottle = 0 ml, 00 ml bottle = 0 ml 00 ml bottle is the better value Cost per can: can pack = p, 0 can pack = p Cans per pound: can pack = cans, 0 can pack = cans can pack is the better value Cost per gram: 0 g pack = 0 p, kg pack = 0 0p, kg pack = 0 p Grams per pence: 0 g pack = g, kg pack = 0 g, kg pack = g kg pack is the best value Probabilit Exercise.H (page ) or 0 0 a) c) = 0 0 a) = BB, BG, GB, GG; a) H, H, H, H, H, H, T, T, T, T, T, T (i) (ii) = 0 = 0 Exercise.H (page 0) or a) 0 ellow, 0 blue, 00 green Exercise.H (page ) a) 0 Score Relative frequenc Yes. For a fair dice each score should have probabilit = 0... or 0. ll the relative frequencies for Pete s dice are close to this value. a) Win 0, draw 0, lose 0 No, there is onl a small number of trials. a) Flavour Relative frequenc Plain 0 Salt and vinegar 0 Cheese and onion 0 Other 0 There is a large number of trials. a) 0 0 a) Score Relative frequenc No. For a fair five-sided spinner, each score should have a probabilit of = 0. a) Yellow, green, white, blue You need to know whether or not the relative frequenc values were calculated from a large number of trials. Graduated ssessment for OCR GCSE Mathematics Hodder Murra 00

3 Using and generating formulae Exercise.H (page ) C = mq d s = t n = 0t + u p + q + r = p = hr t t = w r n = s = n d d f = + 0 C = 00 + s Exercise.H (page ) 0 mph Exercise.H (page ) 0 0 Solving angle problems Exercise.H (page ) a = 0 ngles on a straight line add up to 0 b = ngles on a straight line add up to 0 c = 0 ngles round a point add up to 0 d = ngles round a point add up to 0 e = 00 Verticall opposite angles f = 0 ngles on a straight line add up to 0 g = 0 Verticall opposite angles or ngles on a straight line add up to 0 h = ngles in a triangle add up to 0 i = ngles in a triangle add up to 0 j = k = ngles in a triangle add up to 0 and the angles of an isosceles triangle opposite the equal sides are equal. l = ngles in a quadrilateral add up to 0 0 m = 00 ngles on a straight line add up to 0 n = ngles in a quadrilateral add up to 0 Exercise.H (page ) a = 0º Corresponding angles b = º llied angles c = º lternate angles d = º Corresponding angles e = º lternate or opposite angles f = 0º llied angles g = 0º lternate angles or ngles on a straight line add up to 0 h = 00º Corresponding angles i = 0º llied angles or ngles on a straight line add up to 0 j = 0º lternate angles k = 0º ngles on a straight line add up to 0 l = º Corresponding angles m = º llied angles n = º lternate angles o = 0º lternate angles p = º llied angles 0 q = º Corresponding angles r = º ngles in a triangle add up to 0 s = º Corresponding angles or ngles in a triangle add up to 0 Exercise.H (page ) 0º 0º a) º º, 0º, º, º, º, º a) º 0º, 00º, º, 0º, º e = 0º, i = 0º e = º, i = º 0 nswers to Homework Book Graduated ssessment for OCR GCSE Mathematics Hodder Murra 00

4 nswers to Homework Book Exercise.H (page ) a = º b = º c = º d = º e = º f = º g = 0º h = 0º Direct proportion Exercise.H (page ) a) Yes, is proportional to x. There is a constant multiplier of. = 0 x a) x 0 = x x x 0 x 0 0 = x a) a) 0 hours 0 0 a) 0 No, he can onl bu enough for miles. Checking solutions and calculations Exercise.H (page ) Check student s answers. Possible answers include the following. a) Positive negative = negative Multipling b number greater than should make answer larger c) 00 = 00 and answer should be less than this d) = and answer should be more than this e) 0 = 0 f) Negative negative = positive g) 0. = 0 0 h) = so last digit should be a) 0 00 = = 0 c) 0 + = a) 0 = 0 0 = 0 c) + = a) = = 0 c) 0 = or 0 = d) =, = or = Exercise.H (page ) Exercise.H (page ) = = = = 0 0 = 0 = 0 0 = = = = 00 = = = 0 = = 0 0 = 00 = = = = = 00 0 Graduated ssessment for OCR GCSE Mathematics Hodder Murra 00

5 = = = = = = = = 0 00 = cm 0 = cm Scatter diagrams and correlation Exercise.H (page ) a), c) Strong positive correlation d) bout kg a), c) Price ( 000s) Mileage (thousands) Weight (kg) mount of fertiliser (g/m ) Strong negative correlation d) (i) bout 00 (ii) bout 000 miles 0 a), c) Height of daughter (cm) Height of father (cm) Strong positive correlation d) bout cm 0 Pthagoras theorem Exercise 0.H (page ) cm 0 cm cm cm Exercise 0.H (page ) cm 0 cm cm cm Exercise 0.H (page ) cm m cm cm cm 0 m cm cm Exercise 0.H (page ) m (to the nearest metre) cm (to the nearest centimetre) m cm 0 km Exercise 0.H (page ) Yes + 0 = (This is the,, triangle) No + No + Yes + = 0 (This is the,, triangle) No + No + Yes + = 0 (This is the,, triangle) No + 0 nswers to Homework Book Graduated ssessment for OCR GCSE Mathematics Hodder Murra 00

6 nswers to Homework Book Quadratic graphs Exercise.H (page 0) x 0 x 0 + x 0 = x + x a) x 0 x 0 + x 0 = x + x 0 0 x 0 x 0 x = x x = x x + = x + x 0 x 0 x 0 + x 0 x 0 = + x x x = + x x 0 x 0 Graduated ssessment for OCR GCSE Mathematics Hodder Murra 00

7 x 0 x 0 x 0 = x x a) 0 = x x x nswers to Homework Book 0 = x x x = 0 or x = c) x = 0 or x = a) = x x + 0 x 0 x Exercise.H (page ) a) 0 = x + x x = or x = c) x = 0 or x = a) 0 = x x 0 x 0 x 0 x = or x = c) x = or x = d) x = or x = x = to or x = to Graduated ssessment for OCR GCSE Mathematics Hodder Murra 00

8 nswers to Homework Book Finding the mean of grouped data Exercise.H (page ) 0 0 Exercise.H (page ) cm grams mm minutes 0 m grams minutes mph 0 0 seconds Equations and inequalities Exercise.H (page ),,,,, 0,, x 0 x 0 x 0 x 0 x x x x 0 x x x x x x Exercise.H (page ) a) 0x 00 x so the maximum number of pens she can bu is. a) x + x = x = so the numbers are and. a) x + = x = + x 0, x, so Bob can make sandwiches. a) 0 + x 0 + x =, x =, so the job took hours. x +, x, so licia must bu fence panels. Compound measures Exercise.H (page 0) mph g/cm people per km people per km 0 m seconds 0 cm kg a) g/cm g 0 a) 0 km/h km/h Reciprocals, factors and multiples Exercise.H (page ) a) c) d) e) 0 a) c) d) e) 000 a) c) d) e) 00 0 a) 0 c) 0 00 d) e) 0 Graduated ssessment for OCR GCSE Mathematics Hodder Murra 00

9 Exercise.H (page ) a) (i) (ii) (iii) (iv) (v) (i) (ii) (iii) (iv) 0 a) (i) (ii) (iii) (iv) (v) (i) (ii) 0 (iii) (iv) 00 a) = ; = ; HCF = ; LCM = = ; = ; HCF = ; LCM = a) HCF = ; LCM = 0 HCF = ; LCM = c) HCF = ; LCM = 0 Circles and tangents Exercise.H (page ) a) π π c) π d) π e) π a) π π c) π d) π e) 0π cm : (π ) cm Exercise.H (page ) a) 0 a) cm Changing the subject of a formula Exercise.H (page ) a) b = 0 a c x z = c) h = b a d) n = a + 0 or n = p c e) t = f) pr q = or q = P r p g) g = p + f h) n = Ft m a) 0 F C = (F + 0) 0 c) C a) 0 cm (to the nearest whole number) r = π c) cm (to d.p.) Equations and inequalities Exercise.H (page ) x = x = x = x = x = x = x = x = x = 0 x = x = x = x = x = 0 x = x = x = 0 x = x = 0 x = nswers to Homework Book Graduated ssessment for OCR GCSE Mathematics Hodder Murra 00

10 Exercise.H (page ) nswers to Homework Book x x x x x x x x x 0 x x x x x x cm cm cm ll three bisectors go through the same point. cm B cm Exercise.H (page ) x =, x = x = 0, x = 0x + =, x = x =, x = x =, x = x = 0, x = 0 so the angles of the triangle are 0, 0 and 0. x + = x, x = x + (x ) =, x = so the dimensions of the rectangle are cm and cm. D cm C cm 0 cm cm cm C B Loci Check students drawings. The diagrams in these answers are shown half-size but the dimensions given are those students should have used. Exercise.H (page ) cm cm cm Exercise.H (page ) C cm cm 0 D B cm cm B cm O cm Graduated ssessment for OCR GCSE Mathematics Hodder Murra 00

11 C cm cm cm C cm cm 0 cm cm cm 0 cm cm Required locus. cm B cm D B B ,,,,, Exercise 0.H (page 0) nswers to Homework Book R cm ccurac D 0 Decimals Exercise 0.H (page 0) a) c) 0 d) e) f) g) h) i) 0 j) k) 0 l) a) c) d) e) f) g) h) i) j) k) l) Exercise 0.H (page 0) C Exercise.H (page ) a) Continuous Continuous c) Discrete d) Discrete e) Continuous Discrete Continuous GCSEs m 0 kg friends km passengers 0 minutes litres 0 km/h Exercise.H (page ) a) (i) cm, cm (ii) cm, 0 cm (iii) cm, 00 cm (iv) m, m (i) 0 cm, 0 cm (ii) cm, cm (iii) cm, 0 cm (iv) m, m c) (i) cm, cm (ii) cm, 0 cm (iii) m, m (iv) 0 mm, 0 mm Graduated ssessment for OCR GCSE Mathematics Hodder Murra 00

12 nswers to Homework Book d) (i) seconds, seconds (ii) 0 seconds, 0 seconds (iii) seconds, 0 seconds a) cm, cm ml, ml c) 0 seconds, 0 seconds d) kg, kg e) m, m f) cm, cm g) cm, 0 cm h) mm, mm Indices Exercise.H (page ) a) c) a a) c) d) a) c) d) a) 0 or c) d) or a) a a c) a d) a Exercise.H (page ) a) 00 c) a) 0 c) a) c) a) 00 c) cm a) 00 c) 0 d) 00 e) 0 a) 0 c) d) e) 0 a) c) 0 d) 000 e) a) c) d) e) 0 cm Trial and improvement Exercise.H (page ) 0 is between and so one solution is between and. x = 0 is between and so one solution is between 0 and. x = 0 0 is between 0 and so one solution is between and. x = 0 is between and so another solution is between 0 and. x = 0 Sequences Exercise.H (page ) Linear; 0, Not linear;, 0 Linear;, Not linear;, Linear;, Exercise.H (page ) Exercise.H (page ) n n + n n + 0 n n + n 0 n or n + 0 n or n + 0 n or n + Graduated ssessment for OCR GCSE Mathematics Hodder Murra 00

13 Multipling out two brackets Exercise.H (page ) x + x + x + x + x + x x + x x x + x x x x + x + x x + 0 x x + 0 Prisms and units Exercise.H (page ) a) cm 0 cm c) cm d) 0 cm e) cm f) cm cm a) cm cm cm cm cm Exercise.H (page ) cm cm cm cm Exercise.H (page 0) a) 0 mm 00 cm c) mm d) mm e) mm a) cm 00 mm c) 00 cm d) mm e) mm a) 0 cm 0 cm c) 00 m d) 00 m e) m a) 000 mm cm c) 00 mm d) cm e) 0 mm a) m 0 cm c) m d) mm e) 0 cm a) 000 cm litres c) 00 ml d) 0 0 litres e) litres 0 cm or 0 nswers to Homework Book Graduated ssessment for OCR GCSE Mathematics Hodder Murra 00