Book 14. Surds O1 1. (c), (d), (e) and (i). 2. (c) 3, (d) 1, (e) 4 and (i) (a) 2 6 (b) 3 2 (c) 3 5 (d) 3 6. (e) 4 2 (f) 2 5 (g) 4 6 (h) 7 5

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1 Book 14 Surds O1 1., (d), (e) and (i). 2. 3, (d) 1, (e) 4 and (i) O2 1. (a) (d) 3 6 (e) 4 2 (f) 2 5 (g) 4 6 (h) 7 5 (i) 3 10 (j) 2 2 (k) 5 (l) (a) (d) 2 5 (e) 9 2 (f) 3 3 (g) 7 2 (h) 4 (i) (a) (d) 2 O3 1. (a) (d) (e) 6 2 (f) 2 7 (g) 10 5 (h) (i) Proof. 3. Yes (supported by working). O4 1. (a) (d) (e) 2 (f) 3 (g) 5 (h) 6 (i) (j) 9 2. Proof. 3. Proof.

2 Cumulative Revision Section # million (two sig fig based on information given) million kg bikes 5.(a) trips 7. No, he is 20km short ml (a) (d) 15 (e) 8 (f) 13 (g) 7 (h) 21 (i) 8 (j) 9 (k) 20 (l) Second year as 460 is more than First recipe as 250g is more than 240g. 15. (a) Accurate as 2 in 5 is 40% and 36% is nearly 40%. Not accurate as half is 50% and 47% is less than a half. Accurate as 9 out of 10 is 90% and 92% is more than 90%. Indices O5 1. (a) x 7 y 5a 5 (d) 18p 8 (e) 10h 2 (f) x 4 (g) a 2 (h) x 1 (i) 2y 2 2. (a) x 6 y 8 z 10 (d) 9a 6 (e) 32b 5 (f) 125y 6 3. (a) 1 y 5 1 a (e) 5p 7 (f) (i) 1 7d 2 2p 7 5 (g) 3 x4 (d) t3 1 4b 3 (h) 5 2c

3 4. (a) y 4 y 7 a 2 (d) 1 p (e) q (f) 10 (g) f 2 (h) 2s 3 (i) 16 3a 3 5. Proof 6. b 2 4ac 7. (a) 256 n = 2 O6 1. (a) a 1 2 b 1 3 (e) x 7 3 (f) (i) b 1 6 (j) 1 x a2 3 c (d) x 3 5 (g) x 7 6 (h) 3m 4 3 (k) 4p 5 3 (i) p (a) (d) 5 (e) 8 3. (a) (d) 125 O7 (e) 2 (f) 3 (g) 2 (h) 5 1. (a) x 3 x 1 p + p 6 a 3 + a 4 (d) 10x + 15x 2 (e) 8a + 12 (f) a + 1 (g) 3t 4 1 (h) 6m m 2 2. Statement correct (supported by working). Cumulative Revision Section #2 1. (a) 1905 metres Yes as is less than 22 metres stock cubes. 3. $ % % 7.

4 8. (a) 76 km/hr 36 mph miles hours 45 mins 11.(a) 1.15 p.m p.m p.m. Scientific Notation O8 1. (a) (d) (e) (f) (g) (h) (i) (a) (d) (e) (f) (g) 134 (h) (i) (a) (d) (e) (f) (g) (h) (a) (d) (e) (f) (g) (f) (a) (d) (e) (f) (a) (d) (e) (f) O9 1. (a) (d) (e) (f) (g) (h) (a) (d) seconds grams km metres atoms metres per second

5 Cumulative Revision Section #3 1. (a) (d) Gross Pay Total Deductions Net Pay (a) weeks each 6. (a) weeks 7. She spent 5 more than she hoped, she came back with 70 not She should buy it in France as it is to fill her tank compared to in the UK : 150: grams Book 15 Multiplying Out Brackets O1 1. (a) 20x x + 2 2x 2 + 5x 3 4x 2 12x + 9 (d) 25x x (a) 10x 2 31x x x + 4 3x 2 19x + 6 (d) 4x 2 3x (a) 3x 2 12x x x 20 3x x 8 (d) 20x x (a) 6x 2 7x + 2 2x 2 5x + 3 2x x 98 (d) 14x 2 11x 2 5. (a) 3x 2 11x 20 45x 2 120x 80 10x x + 15 (d) 16x x x 6. (a) 5x 2 + 6x + 1 2x (a) x x 4 8x 2 + 3x 2 8. Gillian is correct (support with working) 9. Proof. 10. x + x x or x + x + 1 x Proof. 12. (a) 2x x + 8 Proof 13. 2

6 O2 1. (a) x 3 + 6x 2 + 3x 20 3x 3 7x x 16 3x 3 4x 2 5x + 2 (d) 2x 3 + 7x 2 8x (a) 6x 3 + x x 4 4x 3 7x 2 5x 14 6x 3 2x 2 11x + 4 (d) 2x 3 12x x 4 3. (a) 20x 3 47x x 6 6x 3 x 2 x4 3x 3 5x 2 4x + 4 (d) x 3 + 9x x (a) 2x 3 + 5x 2 + x 2 3x 3 7x 2 18x 8 6x x 2 4 (d) 2x 3 + 5x 2 9x Proof. Cumulative Revision Section #4 1. (i) (ii) (iii) 2. (i) (ii) (iii) 3. (i) (ii) (iii)

7 4. (a) 45º 123º 61º 146º 5. Angles drawn accurately using a protractor. 6. (a) 70 km/h 2hours 30mins 7. (a) 50 mph 224 mph 40 kmph (d) 152 kmph gallons 9.(a) (a) 50 kmph 50 kmph 11. (a) Add 75 ml Remove 225 ml Remove 75 ml Factorisation O3 1. (a) 4(2x + 3y) 5(2a + 3b) 7(3p + 5q) (d) m(2n + p) (e) r(5s + t) (f) y(7x + 2z) (g) 3p(3q 4r) (h) 4x(2y 5z) (i) 5p(p 3q) 2. (a) x(3x 2y + 6) 4x(2x 4t + a) x(3x 2y) (d) 5x 2 (5 y) (e) 5a 3 (2 7b) (f) 3t(8 tr) (g) 3x(3x 2 5x + 7) (h) 16ab(b b) (i) 5x 2 (5a + 8x) (j) 3qx 2 (9p + 4x) O4 1. (a) (k 5)(k + 5) (t 7)(t + 7) (2 m)(2 + m) (d) (4 n)(4 + n) (e) (a 10)(a + 10) (f) (b 8)(b + 8) (g) (11 x)(11 + x) (h) (20 y)(20 + y) (i) (z 1)(z + 1) (j) (13 u)(13 + u) (k) (v 12)(v + 12) (l) (3 w)(3 + w) 2. (a) (5x 9)(5x + 9) (6p 5q)(6p + 5q) (2x 9)(2x + 9) (d) (11 6x)(11 + 6x) (e) (3x 20y)(3x + 20y) (f) (8k l)(8k + l)

8 3. (a) 2(7 2x)(7 + 2x) 5(s t)(s + t) 2(7 2x)(7 + 2x) (d) 3(5x 9)(5x + 9) (e) 18(2 x)(2 + x) (f) 3x(2 x)(2 + x) (g) (3 x)(3 + x)(9 + x 2 ) (h) 3w(3 2w)(3 + 2w) (i) 2x(5x 1)(5x + 1) (k) 5r(r 2)(r + 2) (l) 2p(2p 2 1)(2p 2 + 1) 4. (a) (a b)(a + b) 3 2 O5 1. (a) (x + 3)(x + 2) (x + 10)(x + 1) (x + 7)(x + 3) (d) (x + 4)(x + 4) (e) (x + 6)(x + 1) (f) (x + 5)(x + 3) 2. (a) (2x 1)(x 3) (2x + 3)(x + 4) (3x + 4)(x + 2) (d) (x + 3)(x 2) (e) (2x + 1)(3x + 2) (f) (x 2)(x 1) (g) (5x 1)(x + 1) (h) (7x + 2)(x + 2) (i) (2x 3)(x + 5) (j) (x 5)(x + 3) (k) (4x + 1)(x + 3) (l) (6x + 1)(2x 1) (m) (4x + 3)(2x 1) (n) (4x 3)(2x + 3) (o) (3x + 4)(3x + 1) 3. (a) (3 + x)(2 x) (5 x)(4 + 3x) (1 + x)(3 2x) (d) (5 + x)(3 2x) (e) (4 + x)(1 2x) (f) 4(3 + x)(1 2x) 4. x = 2 and x = 1 O6 1. (a) 3(x + 4)(x 2) 5x(3xy + 1) 2(x 4)(x + 4) (d) 5x(x 3)(x + 3) (e) 6(3x + 2)(x 1) (f) 4xy(3x + 2y 2 ) (g) 5(2x 1)(x + 3) (h) 6x(x + 3)(x + 2) (i) 7(x 2)(x + 4) (j) 2(x 3)(x 2) (k) 3x(x + 9)(x 2) (l) 3x(2x 2 21) 2. (a) (d) -5

9 Cumulative Revision Section # boxes 2. (a) 18 cans 2 x 18 cans and 1 x 10 cans. Total cost = Not set correctly as 64 4 is less than (a) 3 size A and 1 size B 730 Book 16 Completing the Square O1 1. (a) (x + 4) 2 13 (x + 2) 2 6 (x 3) 2 5 (d) (x + 2) 2 2 (e) (x 1) 2 8 (f) (x + 4) 2 21 (g) (x ) (h) (x ) (a) (x + 4) (a) (x + 2) 2 3, minimum of 3 when x = 2. (x 1) 2 6, minimum of 6 when x = 1. (x + 4) 2 19, minimum of 19 when x = 4. (d) (x 3) 2 8, minimum of 8 when x = 3. (e) (x ) , minimum of, when x = (f) (x ) , minimum of, when x = (i) (x ) (a) False True False (d) False Cumulative Revision Section #6 1. (a) % (d) 44% 2. (a) (d) (a) 33, 36, 37, 39 28, 28, 29, 30 33, 36, 37, 39, 43, 44 (d) 5, 9, 13, 15, 28, 28, Don t know 23, Enough 1127, More than enough 184, Not enough (a) (d)

10 Quadratic Graphs O1 1. (a) Proof ICT Activity Yes 2. (a) ICT Activity (3, 1) y = (x + a) 2 + b has a turning point of ( a, b). 3. (a) ( 2, 3) Learners reply based on 2 4. (a) ( 2, 3) (6, 5) ( 3, 6) (d) (4, 2) (e) (5, 4) (f) ( 1, 1) 5. Parabola 6. (a) ICT Activity minimum 7. (a) ICT Activity maximum y = (x + a) 2 + b has a minimum turning point, y = (x + a) 2 + b has a maximum turning point. 8. (a) Minimum Maximum Maximum (d) Minimum (e) Minimum (f) Maximum (g) Minimum (h) Minimum (i) Minimum (j) Maximum (k) Maximum (l) Minimum 9. (a) Proof ICT Activity Yes 10. (a) ICT Activity x = 4, x = 2 y = (x a)(x b) has roots at x = a and x = b. 11. (a) Correct response is x = 1 and x = 2. Learners reply based on 11(a). 12. (a) x = 5 and x = 3. x = 7 and x = 1. x = 3 and x = 1. (d) x = 8 and x = 2. (e) x = 0 and x = 4. (f) x = 0 and x = (a) ICT Activity ICT Activity plot x = 2 and confirm it is the axis of symmetry. 14. (a) ICT Activity ICT Activity plot x = 3 and confirm it is the axis of symmetry. y = (x + a) 2 + b has an axis of symmetry of x = a.

11 15. (a) x = 2 x = 6 x = 3 (d) x = 4 (e) x = 5 (f) x = (a) ( 3, 1) and x = 3 (8, 3) and x = 8 ( 1, 8) and x = 1 (d) (6, 0) and x = 6 (e) ( 3, 2) and x = 3 (f) ( 1, 0) and x = (a) ICT Activity ICT Activity plot x = 1 and confirm it is the axis of symmetry. 18. (a) ICT Activity ICT Activity plot x = 3 and confirm it is the axis of symmetry. y = (x a)(x b) has an axis of symmetry of x = ( a+( b) ). 19. (a) x = 4 x = 3 x = 1 (d) x = 5 2 (e) x = 2 (f) x = (a) Roots x = 3 and x = 1. Line of symmetry x = 2. Turning Point ( 2, 1) Roots x = 2 and x = 2. Line of symmetry x = 0 (the y-axis). Turning Point (0, 4) Roots x = 5 and x = 3. Line of symmetry x = 1. Turning Point ( 1, 16) (d) Roots x = 2 and x = 3. Line of symmetry x = 1 2. Turning Point ( 1 2, 25 4 ) (e) Roots x = 6 and x = 0. Line of symmetry x = 3. Turning Point ( 3, 9) (f) Roots x = 0 and x = 3. Line of symmetry x = 3 2. Turning Point ( 3 2, 9 4 )

12 O2 1. Sketch a quadratic graph, when in factorised form, using the following procedure. (a) Find the roots and annotate them onto the x axis. Find the axis of symmetry and indicate on your diagram. x = 1 y -3 1 x (d) (e) Now substitute the value of x from the line of symmetry to find the ycoordinate of the turning point and annotate this onto your graph. Sketch the parabola ensuring the correct nature of the turning point (maximum or minimum). Substitute x = 0 to find the y-intercept and annotate onto your graph. x = 1 y -3 O 1 x ( 1, 4) -3

13 2. y x = 1-3 O 5 x -15 (1, 16) 3. Sketch a quadratic graph, when in completed square form, using the following procedure. (a) (d) (e) The roots (if real roots exist) are not readily accessible when the quadratic is in this form. Find the axis of symmetry and indicate on your diagram. Find the turning point and mark on the line of symmetry. Substitute x = 0 to find the y-intercept and annotate onto your graph. Sketch the parabola ensuring the correct nature of the turning point (maximum or minimum). x = 3 y 15 ( 3, 6) O x

14 4. (a) a = 3 (5, 0) 5. (a) A (2, 0) and B (6, 0) x = 4 6. (a) x = 2 y = (x + 2) 2 1 (0, 3) 7. k = 9 8. (a) a = 5 and b = 1 x = 5 P (0, 26) and Q (10, 26) Cumulative Revision Section #6 1. (a) Yes as = 1775 to the nearest person. Taking 2009 as the base year (100%) Killed or seriously injured 2014 (91% after a 9% fall) = (from table). Therefore one percent = Killed or seriously injured 2009 (100%) = 100 ( ) = Difference = = The ministers claim is not true as 2431 is less than (a) Pedestrians Overall trend is a reduction in fatalities from 2000 to However, there was a slight increase in Cyclist Overall trend is very constant from 2000 to 2013 will little change from year to year. In 2000 the percentage of cyclist fatalities was approximately 12% In 2013 the percentage of cyclist fatalities was approximately 22% Yes the claim is true as 22% is greater than 12%. 3. (a) Yes as 7 out of 14 is equal to one half. 5AL = 21%, 5BL = 15% so claim only true for 5AL. 4. (a) 25% is equal to one quarter so claim is true. 19% = 019 and one fifth is 02. Claim is not true as 19% is less than one fifth (019 < 02). 5. Bag B as 029 is greater than School raffle as 0030 is greater than 0025

15 Book 17 Percentages O O2 1. $ The shares are now worth which is 6 72 less O million miles tonnes Cumulative Revision Exercise #8 1. (a) 5a x t + 6 (d) 22p (a) 9a x + 9 7b + 13 (d) 8h + 15 (e) 13x + 39y (f) 10c + 38d 3. (a) (d) 18 (e) 0 (f) (a) (a) p(q + 4) b(5a 2d) h(10g + 3) (d) y(x 2) (e) t(8v + 7) (f) m(n 6) 6. (a) 7x(y + 3) 4b(4a 3) 5m(2 + 5n) (d) 2g(15 + h) (e) 3s(2t 9) (f) 8qr(p + 4s) (g) 6b(2z + 3q) (h) 10w(3v 2e) (i) 4p(t + 3r)

16 7. (a) 8, 10, 12, 14 p = 2d + 2 (d) (i) 72 (ii) 158 (iii) 212 (e) 38 desks. 8. (a) 4n 2n 1 5n 1 (d) 4n 1 9. (a) Yes, as 1 is less than 1 or Yes, as is less than Yes as 05m = 50cm = 500mm which is less than 760mm. Fractions O1 1. (a) (d) (e) (f) (g) (j) (h) (k) (i) (l) (a) (d) (e) 2 15 (f) (g) (h) (i) (j) (k) (l) with some left over m with a bit left over cm kg km

17 Cumulative Revision Exercise # metres complete metres mm 2 4. (a) cm 2 19 pizzas m cm cm cm m (a) Algebraic Fractions O1 1. (a) b 3 3x 2 2p 5 3 (d) a 2 b 4 (e) x 3 y 5 (f) p 4 q 4 (g) (j) 1 (h) 2 (i) 3 b 4 x 5 2a 2 b 2 (k) 3x 3 5p 5y 2 (l) q 2 2p 2 2. (a) 3 x 5 5 x 2 x + 3 (d) 2x+5 2x 1 (e) 2 x+4 (f) 3(x+2) 3x 1 (g) x 1 3 (h) x+2 x 1 (i) 5 2x 1 (j) 7 2x+3 (k) 3x+1 x 2 (l) x+1 5x+1 O2 1. (a) a 2 b 2 ab x 2 +y 2 xy a 2 +2 a (d) 4a 2 3b 2 6ab (e) 2x 2 +15y 2 10xy (f) a a (g) a 2 ab (h) 3x+y x 2 y (i) 3+a a 2

18 2. (a) 3p+5 p(p+5) 3 x x(x+1) 8 a a(a+4) (d) 2p+14 (p+1)(p+5) (e) 6x (x 1)(x+2) (f) 5a 8 (a 3)(a+4) (g) p 2 +p 1 p(p 1) (h) 2 6x 4x 2 (x+2)(x+1) (i) 2a 2 +3a 10 (a+2)(a+4) (j) 5p+15 6 (k) x 3 (l) a O3 1. (a) 5p 4 3s 2 4x 4 y 2 3 (d) 4pr 5 5 (e) 2. y2 km/h 3. 10xt 3 4x 3 5. Proof (a) (2x y)(2x + y) 9. 7m+3 m(m+1) 7 (f) p 3 3s 3 t p+5 p(p+5) 2x y 3 metres 4. Proof 8. x = Proof 11. m = 1 a+t 12. (a) (x 4)(x + 4) 13. (a) x x+3 hours 60 km/h 14. (a) (p 2q)(p + 2q) Cumulative Revision Exercise #10 1. p 2q x 1 x(3x 1)

19 2. (a) 84 kg 23 kg The average weight has reduced from a mean of 84kg to 68kg. The range has also reduced from 23kg to 21kg which shows the weights have become slightly more consistent (a) Pie chart drawn (a) Book 18 Change The Subject O1 1. (a) x = y 8 4 s = p t a (d) b = a+2 3 w = v+pq p 2. (a) y = 2x + 6 y = 1 x + 4 y = 2x + 7 (d) y = 2 3 x (e) y = 4x 3 (f) y = 2 3 x (g) y = 5x 3 5 (h) y = 6x (i) y = 2x 6 (j) y = 3x 8 (k) y = 2x + 8 (l) y = 1 5 x + 2 (m) y = 3 4 x + 2 (n) y = 3 2 x (o) y = 3x

20 O2 1. (a) x = y 3 2 s = p t r 2 m = k+3n n (d) x = (y sr2 ) 2 9 (e) g = 7t h (f) t = (5 3p)2 25 (g) y = x2 t 2r (h) c = 2ab 3 (i) k = gh 2 (j) x = 2(y + 3) seconds O3 1. (a) t = 8 p x = a+1 d (e) (g) a = y = 5 x 3b m = 5a+3b 2k y p q (d) x = (f) m h k c = 3a 5b p (h) z = x y m O4 1. (a) t = h 2L x = c b a r = 1 t d (d) p = 1 y 2 (t + 2) (e) n = 1 a 2 (f) r = d ks 2. 5 m/s O5 1. (a) L = t 2 r = t 1 d t = w r 2 +1 (d) t = 1 y 2 1 (e) n = 1 a 2 +1 (f) d = x 3 y

21 2. (a) x = a m = 2E 2gh+v 2 x = 4+3y y 3 (d) r = πt+3 1+2π Cumulative Revision Exercise #11 1. (a) x y y x (a) y = 4 x = 2 3. (a) x = 4 a = 5 b = 6 (d) s = 4

22 4. (a) x = 2 x = 4 x = 4 (d) x = 1 5. (a) x = 1 x = 5 x = 1 (d) x = (a) d = 8 8. W = 6 9. (a) m Straight line O1 1. m = 2 2. m = m = 3 4. m = 3 5. m = m = 3 O2 ICT activity, all questions in this section attempted on computer. Check with teacher. O3 1. (a) m = 2, c = 1 m = 3, c = 5 m = 4, c = 7 (d) m = 3, c = 4 (e) m = 3, c = 5 (f) m = 4, c = 3 (g) m = 5, c = 6 (h) m = 2, c = 3 (i) m = 1 3, c = 2 (j) m = 3 4 1, c = 5 (k) m =, c = 5 (l) m =, c = (m) m = 1 5, c = 2 5 (n) m = 3 1, c = 8 8 (o) m = 3 7, c = 4 7

23 2. (a) m = 2, c = 6 m = 1, c = 4 m = 2, c = 7 (d) (g) m = 2 4, c = 3 3 m = 5, c = (e) m = 4, c = 3 (f) m = 2 3, c = 1 3 (h) m = 6, c = 3 2 (i) m = 2, c = 6 (j) m = 3, c = 8 (k) m = 2, c = 8 (l) m = 1 5, c = 2 (m) m = 3 4, c = 2 (n) m = 3 2, c = 1 2 (o) m = 3, c = 17 O4 1. f = d y = 2x y = 2x 1 4. (a) y = 4x 6 y = x y = 2x One possible example of each shown: (a) y y x x y x

24 O5 1. m = 3 3, c = 2 2. y = x m = 3, c = m = 3, c = P(0, 4) 6. y = 3 2 x y = 1 x y 55 x Cumulative Revision Exercise # m m (a)

25

26 Scattergraphs O1 Shoe Size Mass (kg) Shoe size There is a (strong) positive correlation between shoe size and mass

27 2. Museum Visitors Visitors Hours of Sunshine There is a (strong) negative correlation between hours of sunshine and museum visitors

28 3. 34 Papaya Fruit Weights 32 Seeds Weight (lbs) There is a no correlation between weight and number of seeds

29 Marks Maths Prelim Results Hours of Sleep There is a (very strong) positive correlation between hours of sleep and marks in the prelim but with the occasional anomaly.

30 O2 1. (a) and Bird Statistics Wingspan (cm) Length (cm) Approximately 57 cm (d) Approximately 32 cm

31 2. (a) and Reaction Reaction Time Test Time (tenths of Second) Age (d) Approximately 17 secs Approximately 38 years old

32 3. (a) and Test Marks 100 Test B (%) Test A (%) Approximately 60% (d) No, the teacher has estimated too high, the estimate should be approximately 42% O3 1. y = 1 x (a) C = 15F Calories 2 Right Angled Trigonometry O1 1.(a) 283 cm 33 cm 349 cm (d) 11 cm (e) 27 cm (f) 59 cm

33 m cm 4. 8 cm m O2 1.(a) 625 cm 91 cm 006 cm (d) 27 cm (e) 150 cm (f) 163 cm m m m cm O3 1.(a) (d) 43 (e) 369 (f) O cm m Yes, support with working

34 Book 19 Circle Geometry O1 1. (a) 31 4 cm 19 9 cm 84 4 cm 2 (d) 50 9 cm 2 O2 1. (a) 17 6 m m 2 2. (a) cm 6 5 cm 130 cm 2 3. (a) 25 1 cm 2 21 cm cm cm 2 6. (a) 2 6 m 7 2 m 3 0 m 2 O cm 2 4. (a) cm Cumulative Revision Exercise # hours m km tonnes l Volume O1 1. (a) 24 m cm cm 3 (d) cm 3 (e) 960 cm 3 (f) 84 7 m 3 (g) 130 m 3 (h) cm 3 2. (a) 540 cm cm 3 3. (a) m m 3 4. (a) 1200 cm cm l cm

35 7. (a) cm cm mm mm 3 Cumulative Revision Exercise #15 1. (a) No - Mathematical justification required in form of calculation.

36 Blue 20 Answers Function Notation O1 1. (a) f(3) = 15 f( 3) = 15 f(0) = 6 2. (a) g(2) = 2 g( 1) = 4 g(0) = 0 3. f( 3) = 5 4. f( 1) = 6 5. f( 5) = f( 2) = (a) f(x) = 21 x = 3 f(t) = 14 t = 4 f(2p) = 46 p = 4 8. (a) f( 2) = 15 f(t) = 9 t = g(n) = 3 n = (a) The function will be undefined as x = 1 would make the denominator zero. (i) f(0) = 8 (ii) f( 1) = 4 (iii) f( 1 2 ) = 16 f(x) = 2 x = x (a) y x (-2, -4

37 Equations and Inequations O1 1. (a) x = 7 a = 5 b = 6 (d) p = 2 (e) r = 3 (f) s = 4 2. (a) x = 4 x = 2 x = 6 (d) x = 2 (e) x = 1 2 (f) x = 1 3. (a) x < 1 t 5 x > 10 (d) m 1 (e) y > 16 (f) p < 3 (g) c 2 (h) a 0 (i) q > 0 O2 1. (a) x = 2 x = 1 x = 4 (d) x = 2 (e) x = 3 (f) x = 10 (g) x = 3 (h) x = 2 2. (a) x = 12 x = 7 x = 6 (d) x = 20 (e) x = 12 (f) x = 3 (g) x = 4 (h) x = 7 3. (a) x > 1 x > 2 x 1 3 (d) x 1 (e) x 3 (f) x < 7 (g) x < 1 (h) x (a) 2(x + 8) 1 x 12 kmph 2 5. x = 1 2 or x = 6 5 Cumulative Revision Exercise #16 1. (a) x = 3 x = 2 y = 5 (d) a = 6 2. (a) x = 4 b = 4 a = 3 (d) a = 4 3. Area = 15 m 2 4. Area = cm 2

38 5. Number of long lengths (a) (l) Number of short lengths (s) s = 3l 3 l = (a) 13 and 15 2n S = 40 kmph 8. T = 4 6 hours = 4 hours 36 minutes 9. D = 145 m 10. Area shaded = 96 cm 2 Simultaneous Equations O1 1. (a) x = 7, y = 1 x = 2, y = 3 x = 2, y = 5 (d) x = 2, y = 1 (e) x = 1, y = 1 (f) x = 1, y = 2 (g) x = 3, y = 4 (h) x = 4, y = 1 2. (a) x = 1, y = 2 x = 4, y = 2 x = 3, y = 1 (d) x = 3, y = 2 (e) x = 3, y = 2 (f) x = 4, y = 3 (g) x = 3, y = 2 (h) x = 3, y = 5 O2 1. (a) 280x + 70y = x + 40y = x = 0 16, y = per minute and 0 11 per text 2. x = 4, y = 5 P(4, 5) 3. (a) 7 = 2m + c 17 = 4m + c m = 5, c = 3 (d) The gradient is 5 and the y intercept is (0, 3). 4. (a) 6x + 2y = 42 5x 2y = 2 x = 4 and y = 9 5. (a) 24x + 6y = 60 20x + 10y = 40 x = 3, y = 2 David scored 25 points.

39 Changing the Subject O1 1. (a) x = y 3 2 s = p t r 2 m = k+n 5 (d) x = ( y sr2 ) 2 (e) g = 7 h (f) t = 5 3p 3 2 (g) y = x2 t 2r (j) x = 2y (a) t = 8 p (d) x = m h k (h) c = 2ab 3 x = a+1 d (e) m = 2k 3n 5 (i) k = h 2 g y = 3 4b (f) b = 3a cp 5 3. (a) t = h 2L x = c b a (d) x = 1+2y2 1 (e) n = 1 y2 a 2 +1 n = t t d (f) d = 2b k b 4. g = V2 2R 5. v = 2E m Cumulative Revision Exercise #17 1. h = 6 9 metres 2. No the ladder is not safe as 72 1 > Yes it would allow a safe turn as 31 8 > h = 29 metres 5. h = 54 8 cm 6. Perimeter = cm

40 7. Mat Phys Jamal is wrong as using the line of best fit he would be estimated 92% for Maths. 8. Sarah is wrong as Bag 2 has a greater chance of picking a yellow since > 3 8 Statistics O1 1. Median = 8, SIR = 1 2. Median = 7, SIR = 1 3. Median = 6 5, SIR = 2 4. (a) Median = 19 5, SIR = 4 5 The second round, on average, scored higher marks. The second round results were more consistent. O2 1. Mean=172 cm, standard deviation= Mean=101 pins, standard deviation= Mean=24 birds, standard deviation=7

41 4. Mean=7 points, standard deviation= (a) Proof 3 6. Mean=7 6 minutes standard deviation=0 44 O3 1. (a) Median = 58 5, IR = 22 On average the December scores are higher. The December scores are more consistent. 2. Mean= 372, standard deviation= (a) Maths standard deviation=14 8 Physics results were more consistent. 4. (a) Mean=41 2 matches, standard deviation=2 3 Yes their claim is true as both the mean and standard deviation fall in the required tolerances. 5. (a) Mean=116 points, standard deviation=16 3 (i) True (ii) False (iii) False (iv)true (v) False