Mathematics Higher Level Robert Joinson

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<strong>Higher</strong>11) 0.79 or – 2.12 12) 0.19 or – 2.6913) 1 or 0.75 14) 0.23 or –0.7315) 0.18 or –1.61 16) 3.24 or 0.1217) 0.78 or –0.92 18) 1.92 or 0.4619) 0.37 or – 5.37 20) 0.52 or – 9.5221) 1.44 or – 0.69 22) 2.77 or – 1.2723) 2.30 or –1.30 24) 1.81 or –1.4725) 2.78 or 0.72 26) 10.18 or –1.18Exercise 21) a = 5 k = 25 2) a = 2 k = 43) a = 3 k = 9 4) a = 7 k = 495) = 1.5 k = 2.25 6) a = 2 k = 47) a = 5 k = 25 8) a = 8 k = 649) a = 6 k = 36 10) a = 4 k = 1620. Problems Involving Equations1) a) xb) x= 34°= 30°34° , 68° , 78°90° , 40° , 50°2) a) 538.46 mphx538.46yb) --------------- hours c) ------------------ miles538.46603) a) x = 4.5 cm b) 30.25cm 24) a) x – 1 and x + 1 b) x = 52y3y5) a) i) x + -- ii) -----44b) y = 8x c) 18,000 bottles6) a) 250 – xb) x = 110 c) 1407) a) x – 6 and x – 21 b) 3x – 27 c) x = 4034, 40 and 1921. Simultaneous Equations1) 4,1 2) 5,3 3) 1,–14) 3,1 5) 3,–2 6) 3,57) 4,1 8) 2,3 9) 5,–310) 5,4 11) 2,–1 12) 3,–213) 5,6 14) 9,–1 15) 2.5,116) 4,–217) a) 2x + 2y=14 x + 4y=13.60 b) x = 4.80c) Adults £4.80 Children £2.2018) a) x + y = 39 x – y = 9 b) 24,1519) 25.8 by 2.7 20) 90g and 120g21) £1.72 and £1.02 22) 17 and 623) 5, 3 24) £22, £1225) 11, 7 26) 28p and 22p22. Problems Involving Quadratic Equations1) a) x = 7b) x = 6.5 cm2) a) x = 10b) 105cm 220 103) a) ----- +x=x – 5x = 2.5 or 10b) 10 kph and 5 kph4) a) x 2 and 8x b) x 2 + 8x = 105so x 2 + 8x – 105=0 c) 64 cm5) a) 2x + 4 and x + 4 d) x = 4 m 8m by 4m.6) a) ( x + 4) ( x – 1) and 3x( x–2)b) x = 4 c) 8 km/hour23. Straight Line GraphsExercise 11) 1 2) 3 3) – 5 4) – 4Page 985) 2 6) 2 7) –--38)9) 2 10) 2 11) – 1 12) – 14113) – 1 14) – 1 15) -- 16) --33Exercise 21) y = x – 3 2) y = 2x – 10 3) y = 3x4) y = – x + 2 5) y = – 3x + 4 6) y = 4x – 14Exercise 31) b) m = 2 , c = – 6 c) 124 d) 1202) b) m = 5 , c = 20 c) 95 d) 173) a) C = 10H + 40 b) £90 c) £105 d) 6 hours24. InequalitiesExercise 11) x > 6 2) x > 2 3) x > 8 4) x > – 35) x > – 3 6) x > 2 7) x > 6 8) x > 49) x > 5 10) x < 1 11) x ≤ 3 12) x ≤ 513) x ≥ 8 14) x < 3 15) x < 5 16) x > 2 2 5 --17) x ≤ 11 18) x ≤ – 7 2 3 -- 19) x ≤ – 1 20) x ≥ – 2621) x ≤ – 2Exercise 21) x x x–4 –3 –2 –1 0 1 2 3 42) x x x x x0 1 2 3 4 5 6 7 83)4)x x–8 –7 –6 –5 –4 –3 –2 –1 05)–3 1 2 --–4 –3 –2 –1 0 1 2 3 43 1 3 --–1 0 1 2 3 4 5 6 76) 27) 18) a) 20x < 10x + 70b) x < 7 Company A is cheaper when the numberof hours is less than 7Company A and B offer the same price when thenumber of hours is 7Company B is cheaper when the number ofhours is greater than 725. Linear Inequalities1) (4,6) (5,5) (5,6) (6,4) (6,5) (6,6) (6,7)2) (0,6) (1,4) (1,5) (1,6) (2,6)3) (2,4) (3,3)4) (3,4) (3,5)5) (3,4) (3,5) (2,5)6) (2,0) (3,0) (4,0) ( 3,– 1)7) ( 1,– 1) ( 2,– 1)8) (1,2) (1,3) (2,3)9) (0,2) (– 1,3)(0,3) (1,3) (0,4) (0,5)51–--41--2
<strong>Higher</strong>26. Linear Programming1) a) y ≥ 7 y ≤ 2x x + 2y ≤ 20 c) 360kg d) 6,7 and4,82) a) x + y≤ 50 y ≤ 2x x ≤ 2yc) i) 33 1 3 -- tins of red, 3 -- tins of orangeii) 33 1 3 -- tins of yellow, 3 -- tins of oranged) 8.4 litres3) a) i) 2x + y≤ 100 ii) 5x + 8y ≥ 400 iii) y ≤ 2xc) 25 large, 50 small.4) a) i) x + y< 15 ii) x + y> 10 iii) y> x iv) y < 2xc) (4,7) (5,6) (5,7) (5,8) (6,7) (6,8) (5,9)27. Recognising Graphs1) c 2) a 3) c 4) a28. Graphs 11) a)5 0 – 3 – 4 – 3 0 5d) –2.8 and 1.8e) x 2 + x – 5=02) a)– 8.625 – 2d) – 2.55 and 1.6 x 2 + x – 4 = 029. Graphs 21) a)d) 0.6 and 6.4 e) 0.8 and 4.0 f) 1.52) a)– 24 – 14 – 6 0 4 6 6 4 0 –6c) x = – 0.25 and 3.25e) x = – 1 and 4f) y = – 4 . x = – 1.7 or 4.73) a) x = – 3.25 and 1 b) x = – 2.2 and 0.730. Graphs 31) c) c = 1.52) b) a = 3 , b = 50 c) 1973) b) p = 3 , q = 2 c) 14.34) b) a = 1.5 , b = – 0.5 c) 0.565) b) a = 3 , b = 2 c) 6.23 2 1 6 12.625b) x = – 2.25 , 0 and 2.253) a)13 3 – 3 – 5 – 3 3 13c) x = – 0.6 and 2.6d) x = – 1.1 and 3.14) a)–1 0 1 2 3 4 5– 5 – 4 – 3 – 2 – 1 0 15 0 – 3 – 4 – 3 0 517 10 8.3˙ 8 8.2 8.6˙ 10 13.3˙ 15.1Page 9931. Growth and Decay1) a)0 1 2 3 4 5 61 0.667 0.444 0.296 0.198 0.132 0.088c) i) 0.85 ii) 0.242) a)0 1 2 3 4 5 6 710 11 12.1 13.31 14.64 16.11 17.72 19.49c) 16.9 million d) 4 1 years4 --3) a)0 0.5 1 1.5 2 2.5 3 3.5 4100 57.7 33.3 19.3 11.1 6.4 3.7 2.1 1.2c) i) 0.63 days (15 hours 7 minutes)ii) 8.44% iii) 0.26 days32. Distance - Time Diagrams1) a) 3.2 miles per hour b) 1.61c) 1.7 miles per hour d) 2.6 miles per hour2) a) 0.8 b) 2.3ms 13) a) 8.8ms 1 b) Speed is increasing (accelerating)c) Speed is approximately constantd) Speed is decreasing4) a) 30 metres b) 6ms 1 c) 12m d) 37.5m–2.4ms 233. Velocity - Time Diagrams1) a) Area = 363 b) 363 metres c)–2) a) 2880 metres b) 0.5ms – 23) 995 metres4) a)0 0.5 1 1.5 2 2.5 3 3.5 4 4.5 50 3 7 12 18 25 33 42 52 63 75b) 40.75 metres c) 17ms – 234. Angles and Triangles1) 49° , 131° , 49° 2) 79° , 84° , 17°3) 120° , 60° , 30° 4) 42° , 45° , 93°5) 60° , 60° , 60° , 30° 6) 57° , 57° , 33°7) 45° , 27° , 45° 8) 44° , 69° , 67°9) 150° , 150° , 30° 10) 40° , 70° , 30°35. Regular Polygons1) a) 135° b) 67.5° c) 45° 2) 360°3) 360° minus the two interior angles of the shapes4) x = 108° (Interior angle of a regular pentagon)y = 36° ( 180° – 2×72° )5) Regular triangle with side 3x6) a) 128.6° , 77.1° b) ∠HCB= ∠HDA7) 24 sides36. Congruent Triangles1) All 2) a and b 3) a and c 4) b and c5) Two sides and the included angle are equal on bothtriangles.
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Mathematics Higher Level Robert Joinson

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