Aviation Australia Mathematics Workbook 2025 PDF

MODULE 1 Mathematics Workbook  Workbook Copyright© 2025 Aviation Australia All rights reserved. No part of this document may be reproduced, transferred, sold, or otherwise disposed of, without the written p...

MODULE 1 Mathematics Workbook  Workbook Copyright© 2025 Aviation Australia All rights reserved. No part of this document may be reproduced, transferred, sold, or otherwise disposed of, without the written permission of Aviation Australia. CONTROLLED DOCUMENT 2025-01-22 Module 1 - Mathematics Page 2 of 28 Training Material Only  Workbook Table of Contents Exercise 1................................................................................................................................... 6 Exercise 2................................................................................................................................... 6 Exercise 3................................................................................................................................... 6 Exercise 4................................................................................................................................... 6 Exercise 5................................................................................................................................... 6 Exercise 6................................................................................................................................... 7 Exercise 7................................................................................................................................... 7 Exercise 8................................................................................................................................... 7 Exercise 9................................................................................................................................... 7 Exercise 10................................................................................................................................. 7 Exercise 11................................................................................................................................. 8 Exercise 12................................................................................................................................. 8 Exercise 13................................................................................................................................. 8 Exercise 14................................................................................................................................. 8 Exercise 15................................................................................................................................. 9 Exercise 16................................................................................................................................. 9 Exercise 17................................................................................................................................. 9 Exercise 18................................................................................................................................. 9 Exercise 19................................................................................................................................. 9 Exercise 20............................................................................................................................... 10 Exercise 21............................................................................................................................... 10 Exercise 22............................................................................................................................... 10 Exercise 23............................................................................................................................... 11 Exercise 24............................................................................................................................... 11 Exercise 25............................................................................................................................... 11 Exercise 26............................................................................................................................... 11 Exercise 27............................................................................................................................... 11 Exercise 28............................................................................................................................... 11 Exercise 29............................................................................................................................... 12 Exercise 30............................................................................................................................... 12 Exercise 31............................................................................................................................... 12 Exercise 32............................................................................................................................... 12 Exercise 33............................................................................................................................... 13 2025-01-22 Module 1 - Mathematics Page 3 of 28 Training Material Only  Workbook Exercise 34............................................................................................................................... 13 Exercise 35............................................................................................................................... 13 Review Homework................................................................................................................... 14 Exercise 36............................................................................................................................... 14 Exercise 37............................................................................................................................... 15 Exercise 38............................................................................................................................... 15 Exercise 39............................................................................................................................... 15 Exercise 40............................................................................................................................... 15 Exercise 41............................................................................................................................... 15 Exercise 42............................................................................................................................... 16 Exercise 43............................................................................................................................... 16 Exercise 44............................................................................................................................... 16 Exercise 45............................................................................................................................... 16 Exercise 46............................................................................................................................... 17 Exercise 47............................................................................................................................... 17 Exercise 48............................................................................................................................... 17 Exercise 49............................................................................................................................... 17 Exercise 50............................................................................................................................... 18 Exercise 51............................................................................................................................... 18 Exercise 52............................................................................................................................... 18 Exercise 53............................................................................................................................... 18 Exercise 54............................................................................................................................... 18 Exercise 55............................................................................................................................... 19 Exercise 56............................................................................................................................... 19 Exercise 57............................................................................................................................... 19 Exercise 58............................................................................................................................... 19 Exercise 59 (Simplify)............................................................................................................... 20 Exercise 59 (Expand and Simplify)............................................................................................. 20 Exercise 59 (Factorise).............................................................................................................. 20 Exercise 59 (Solve)................................................................................................................... 20 Exercise 60............................................................................................................................... 21 Exercise 61............................................................................................................................... 21 Exercise 62............................................................................................................................... 21 Exercise 63............................................................................................................................... 21 2025-01-22 Module 1 - Mathematics Page 4 of 28 Training Material Only  Workbook Exercise 64............................................................................................................................... 21 Exercise 65............................................................................................................................... 22 Exercise 66............................................................................................................................... 22 Exercise 67............................................................................................................................... 22 Exercise 68............................................................................................................................... 23 Exercise 69............................................................................................................................... 23 Exercise 70............................................................................................................................... 24 Exercise 71............................................................................................................................... 24 Exercise 72............................................................................................................................... 24 Exercise 73............................................................................................................................... 24 Exercise 74............................................................................................................................... 25 Exercise 75............................................................................................................................... 25 Exercise 76............................................................................................................................... 26 Exercise 77............................................................................................................................... 26 Exercise 78............................................................................................................................... 27 Exercise 79............................................................................................................................... 27 Exercise 80............................................................................................................................... 28 Exercise 81............................................................................................................................... 28 Exercise 82............................................................................................................................... 28 2025-01-22 Module 1 - Mathematics Page 5 of 28 Training Material Only  Workbook Exercise 1 f) 1903 × 274 = ____ (Find the following sums) a) 32 + 45 = ____ Exercise 4 (Find the following quotients. Leave the answers b) 36 + 21 + 42 = ____ as whole numbers, with remainders if necessary) c) 36 + 46 + 531 = ____ a) 740 ÷ 5 = ____ d) 111 + 380 + 2747 = ____ b) 1482 ÷ 6 = ____ e) 463 + 39 + 2975 = ____ c) 1385 ÷ 4 = ____ f) 1192 + 2749 + 14982 = ____ d) 8901 ÷ 23 = ____ g) 6752 + 4097 + 208 = ____ e) 2496 ÷ 62 = ____ f) 74938 ÷ 34 = ____ Exercise 2 (Find the following differences) Exercise 5 a) 96 − 43 = ____ (Find the averages of the following number sets) b) 6145 − 5023 = ____ a) 34, 26, 28, 32 c) 856 − 37 = ____ b) 121, 157, 230, 217, 303, 196 d) 853 − 442 = ____ c) 40, 13, 15, 23, 21, 41, 20, 11 e) 50063 − 3294 = ____ d) 491, 301, 337, 397, 413, 228, 535 f) 47196 − 26787 = ____ Exercise 3 (Find the following products) a) 46 × 6 = ____ b) 142 × 5 = ____ c) 67 × 14 = ____ d) 104 × 25 = ____ e) 2398 × 33 = ____ 2025-01-22 Module 1 - Mathematics Page 6 of 28 Training Material Only  Workbook Exercise 6 Exercise 9 (Use approximation to estimate the following) (Find the following products) a) 296.438 × 61.8 = ____ a) 3 × 0.3 = ____ b) 87.5563981 − 53.864 = ____ b) 18 × 0.04 = ____ c) 120318 × 0.4987 = ____ c) 1.103 × 0.02 = ____ d) 496.3179 ÷ 23.91 = ____ d) 0.8316 × 4.3 = ____ e) 789.48329 ÷ 0.0187 = ____ e) 37.96 × 4.5 = ____ f) 124.03 × 12 = ____ Exercise 7 (Find the following sums) Exercise 10 a) 3.46 + 4.72 = ____ (Find the following quotients. For irrational answers, leave answers to two decimal places) b) 3.801 + 0.76 = ____ a) 6.27 ÷ 2 = ____ c) 24.36 + 13.82 = ____ b) 2406.84 ÷ 6 = ____ d) 19.89 + 1.35 + 20.001 = ____ c) 243 ÷ 0.6 = ____ e) 8.2 + 0.102 + 104.082 = ____ d) 8.94 ÷ 0.9 = ____ f) 18327.001 + 698.477 + 3014.896 = ____ e) 0.747 ÷ 0.06 = ____ f) 24.276 ÷ 5.1 = ____ Exercise 8 g) 0.7252 ÷ 0.37 = ____ (Find the following differences) a) 6.96 − 5.85 = ____ b) 6.39 − 2.17 = ____ c) 303.91 − 18.72 = ____ d) 24.3 − 12.74 = ____ e) 7.03 − 3.924 = ____ f) 1817.001 − 218.9 = ____ 2025-01-22 Module 1 - Mathematics Page 7 of 28 Training Material Only  Workbook Exercise 11 Exercise 13 (Round the following values to the indicated (Express the following improper fractions as number of decimal places) mixed numbers) a) 6.499 (to a whole number) a) 21 = ____ 2 b) 5.737800 (to a whole number) 61 b) 16 = ____ c) 2.96438 (to 2 decimal places) 68 c) 8 = ____ d) 496.3179 (to 3 decimal places) 58 d) = ____ e) 769.48329 (to 1 decimal place) 12 f) 769.48329 (to 4 decimal places) Exercise 14 g) 172.25486 (to 2 decimal places) (Solve the following. Leave the answers in h) 3.1415926536 (to 5 decimal places) simplest form, or as mixed numbers where necessary) 1 1 a) + 4 = ____ Exercise 12 4 7 1 (Reduce the following common fractions to their b) + 2 = ____ 8 simplest form) 1 1 1 18 c) + 4 + 8 = ____ a) 36 = ____ 2 3 5 5 d) 2 4 + 1 8 = ____ b) 30 = ____ 5 4 18 e) − 6 = ____ c) 33 = ____ 6 3 1 9 f) 4 4 − 16 = ____ d) 108 = ____ 1 5 33 g) 2 16 − 32 = ____ e) 121 = ____ 1 3 75 h) 5 2 − 2 4 = ____ f) 175 = ____ 10 g) 360 = ____ 56 h) 80 = ____ 2025-01-22 Module 1 - Mathematics Page 8 of 28 Training Material Only  Workbook Exercise 15 Exercise 17 (Solve the following. Leave the answers in (Convert the following decimals to common simplest form, or as mixed numbers where fractions, or mixed numbers where necessary) necessary) a) 0.79 2 1 a) 3 × 4 = ____ b) 0.925 5 12 b) × 14 = ____ 6 c) 2.875 1 5 c) 1 3 × 2 8 = ____ d) 0.4 d) 4 1 2 7 × 3 2 × 6 = ____ 5 e) 2.9 e) 1 10 7 ÷ 8 = ____ Exercise 18 (Convert the following common fractions to 5 1 f) 1 9 ÷ 2 3 = ____ decimals. Round to 2 decimal places where necessary) 1 2 g) 3 8 ÷ 2 9 = ____ 1 a) 2 = ____ Exercise 16 b) 3 = ____ 10 (Use cancelling techniques to reduce the following fractions to their simplest form) c) 5 = ____ 9 20×2 a) = ____ 4 10×4 d) 7 = ____ 7×3 b) = ____ 14×6 Exercise 19 120×120 c) 600×4 = ____ (Convert the following thousandths of inch [“thou”] values to 16th and 64th [fractional] d) 4.2×6.3 = ____ values) 2.1×2 4×3×6.4 a) 125 𝑡𝑡ℎ𝑜𝑜𝑜𝑜 = ____ e) 2×3 = ____ b) 500 𝑡𝑡ℎ𝑜𝑜𝑜𝑜 = ____ 9.6×7.5 f) 3.2×5 = ____ c) 250 𝑡𝑡ℎ𝑜𝑜𝑜𝑜 = ____ d) 875 𝑡𝑡ℎ𝑜𝑜𝑜𝑜 = ____ 2025-01-22 Module 1 - Mathematics Page 9 of 28 Training Material Only  Workbook Exercise 20 p) 24 ÷ 6 × (2 + 3 × 4) = ____ (Convert the following fractional values to q) 24 ÷ (6 × 2 + 3 × 4) = ____ thousandths of inch [“thou”] values. Round to the nearest thousandth where necessary) r) 4 × 8 − 5 × 3 + 6 × 2 = ____ 1 a) 3 = ____ s) 4 × (8 − 5) × (3 + 6) × 2 = ____ b) 3 = ____ t) 4 × 8 − 5 × (3 + 6 × 2) = ____ 4 8+7 27 u) = ____ c) 32 = ____ 4+21 20 9 v) = ____ d) 64 = ____ 6+9 18−3 w) = ____ Exercise 21 35 (Solve the following using “BODMAS”) Exercise 22 a) 7 − 3 × 2 = ____ (Solve the following “directed” numbers) b) (7 − 3) × 2 =? a) 3 − 5 = ____ c) 6 + 4 × 3 = ____ b) −8 + 5 = ____ d) (6 + 4) × 3 = ____ c) −5 − 4 = ____ e) 8 × 3 − 2 = ____ d) 8 − (−1) = ____ f) 8 × (3 − 2) =? e) −5 − (−2) = ____ g) 4 × 22 = ____ f) 9 + (−3) = ____ h) (4 × 2)2 = ____ g) 4 × −7 = ____ i) 16(2 × 2) = ____ h) −3 × −8 = ____ j) √36 + 64 = ____ i) −40 ÷ 10 = ____ k) √25 + 144 = ____ j) −60 ÷ −4 = ____ k) −12 − 3 × −2 = ____ l) √25 − 9 = ____ l) −12(−3 × −2) =? m) 24 ÷ 6 × 2 + 3 × 4 = ____ n) 24 ÷ (6 × 2) + 3 × 4 = ____ m) 5 − (16 − 3 × 4) =? o) 24 ÷ 6 × (2 + 3) × 4 = ____ n) −2 − 8(8 + 5 × −3) = ____ 2025-01-22 Module 1 - Mathematics Page 10 of 28 Training Material Only  Workbook Exercise 23 Exercise 26 (Complete the following table. Ensure fractions (Calculate the values with the change in are reduced to their simplest form. Percentages percentages as indicated) should be rounded 3 decimal places where necessary) a) 360.00 plus 10% Fraction Decimal Percentage b) 48 plus 5% A 0.65 c) 110 minus 11% B 1.2 C 3/4 d) 55 minus 55% D 7/10 Exercise 27 E 40% (Determine the following ratios and express in F 0.3% their simplest form) a) 0.5km to 300m Exercise 24 (Find the percentages of the following numbers. b) 1kV to 20000V Round to 2 decimal places where necessary) c) 250mL to 2.5L a) 15% 𝑜𝑜𝑜𝑜 25 = ____ d) 1kg to 15g b) 27% 𝑜𝑜𝑜𝑜 500 = ____ e) 2.5m to 60cm c) 75% 𝑜𝑜𝑜𝑜 1.5 = ____ d) 10% 𝑜𝑜𝑜𝑜 12 = ____ Exercise 28 (Solve the following word problems) e) 1% 𝑜𝑜𝑜𝑜 15 = ____ a) 720 kg of a mixture is made from three f) 115% 𝑜𝑜𝑜𝑜 30 = ____ ingredients, a, b and c, in the ratio 2:3:5. How many kgs of each part is required? b) 1080 kg of concrete is made from cement, Exercise 25 sand, and water in the ratio 2:3:4. How many kgs of sand is required? (Express the following as percentages. Round to 1 decimal place where necessary) c) On a flight, three flavours of milk were offered to passengers. For every 8 passengers a) 3 as a percentage of 6 on the aircraft, two would have strawberry milk and one would have plain milk. If there b) 7 as a percentage of 28 were 72 passengers on a flight, how many would have chocolate milk? c) 20 as a percentage of 100 d) 12 as a percentage of 72 2025-01-22 Module 1 - Mathematics Page 11 of 28 Training Material Only  Workbook Exercise 29 (Determine the unknown in the following Exercise 31 equivalent ratios. Some of these problems require (Complete the units from Column 1 to those as algebra to solve. If you are uncomfortable with indicated in columns 2 and 3) this, it may be better to complete this section after studying the sections on algebra which follow) Column 1 Column 2 Column 3 a) 5 ∶ 3 = 5 ∶ 𝑥𝑥 0.02A mA µA 0.42V mV kV b) 8 ∶ 7 = 𝑥𝑥 ∶ 6 25m cm mm 𝑥𝑥 2 c) 4 =5 0.000 25mF F pF 358mH H mH d) An 8 ft long steel beam weighs 2200 lb. What would be the weight of a similar 13.5kV V mV beam which is 10 ft long? e) If 144 resistors cost $2.60, how much do 36 resistors cost? Exercise 32 (Convert the following quantities to those with f) An aeroplane can travel 2040 nautical the units indicated. Leave answers to 2 decimal miles in 6 hours. At the same speed, how places where necessary) long would it take the plane to travel 1530 nautical miles? a) 440𝑘𝑘𝑘𝑘 𝑡𝑡𝑡𝑡 𝑙𝑙𝑙𝑙𝑙𝑙 Exercise 30 b) 67.5𝑙𝑙𝑙𝑙𝑙𝑙 𝑡𝑡𝑡𝑡 𝑘𝑘𝑘𝑘 (Solve the following ratio word problems) c) 55𝑘𝑘𝑘𝑘𝑘𝑘 𝑡𝑡𝑡𝑡 𝑘𝑘𝑘𝑘/ℎ a) Pressure is inversely proportional to volume, d) 611𝑘𝑘𝑘𝑘/ℎ 𝑡𝑡𝑡𝑡 𝑘𝑘𝑘𝑘𝑘𝑘 what would happen to pressure in volume is halved? e) 567.9𝑙𝑙 𝑡𝑡𝑡𝑡 𝑈𝑈𝑈𝑈𝑈𝑈 b) An army camp has supplies for 240 men for f) 34𝐼𝐼𝐼𝐼𝐼𝐼𝐼𝐼 𝑡𝑡𝑡𝑡 𝑙𝑙 28 days. How long will the supplies last if only 112 men are sent to the camp? g) 340𝑘𝑘𝑘𝑘 𝑡𝑡𝑡𝑡 ℎ𝑝𝑝 c) A contractor hired 150 workers to pave a road in 30 days. How many workers would h) 660𝑓𝑓𝑓𝑓 𝑡𝑡𝑡𝑡 𝑚𝑚 he need to hire to do the same amount of work in 20 days? d) An aircraft fuel tank can be emptied in 16 minutes if 1 drain valve is fully opened. How long will it take to empty the tank if 2 drain valves are fully opened? 2025-01-22 Module 1 - Mathematics Page 12 of 28 Training Material Only  Workbook Exercise 33 Exercise 35 (Calculate the areas of the following simple (Calculate the volumes of the following objects) shapes) Exercise 34 (Calculate the areas of the following complex shapes) 2025-01-22 Module 1 - Mathematics Page 13 of 28 Training Material Only  Workbook Review Homework Exercise 36 (Solve the following revision problems. Round (Simplify the following algebraic expressions) answers to 3 decimal places where necessary and reduce all fractions to their simplest form or a) 5 × 2 + 4 × 𝑎𝑎 =? mixed numbers) b) 7𝑖𝑖 + 6𝑖𝑖 − 8𝑖𝑖 = ____ a) 4236 + 507 + 98 = ____ c) 2𝑎𝑎 + 3𝑏𝑏 − 𝑎𝑎 − 𝑏𝑏 = ____ b) 5908 − 2471 = ____ d) 8𝑖𝑖 − 2𝑚𝑚 − 6𝑖𝑖 + 7𝑚𝑚 = ____ c) 125 × 306 = ____ e) 5 − 𝑎𝑎 − 7 + 2𝑎𝑎 = ____ d) 5892 ÷ 14 = ____ f) 𝑥𝑥 2 + 3𝑥𝑥 + 5𝑥𝑥 2 − 6𝑥𝑥 = ____ e) 3.68 + 207.9 + 0.0371 = ____ g) 6𝑒𝑒 2 𝑓𝑓 − 11𝑒𝑒𝑓𝑓 2 + 𝑒𝑒 2 𝑓𝑓 − 𝑒𝑒𝑓𝑓 2 = ____ f) 51.7 × 3.6 = ____ h) 4(𝑥𝑥 + 𝑦𝑦 − 𝑧𝑧) = ____ g) 104.65 ÷ 2.5 = ____ i) 𝑎𝑎(𝑏𝑏 + 3) = ____ 36 h) 256 = ____ j) 2𝑒𝑒(𝑎𝑎 − 𝑏𝑏) = ____ i) 𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶𝐶 1.925 𝑡𝑡𝑡𝑡 𝑎𝑎 𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚 𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛𝑛 k) 𝑎𝑎2 (𝑏𝑏 + 𝑐𝑐) = ____ 5 j) = ____ 8 l) 4𝑎𝑎 + 2(𝑎𝑎 − 𝑏𝑏) = ____ 3 1 5 k) 1 4 + 2 2 + 8 = ____ m) 3(𝑥𝑥 + 𝑦𝑦) − 𝑥𝑥 + 𝑦𝑦 = ____ l) 1 2 2 − 1 4 = ____ 3 n) 4(𝑝𝑝 − 𝑞𝑞) + 4(𝑝𝑝 + 𝑞𝑞) = ____ 5 1 o) 5(𝑢𝑢 + 𝑣𝑣) + 10(𝑢𝑢 − 𝑣𝑣) = ____ m) 1 9 × 2 7 = ____ p) 2(𝑥𝑥 − 𝑥𝑥 2 ) + 2(𝑥𝑥 2 − 𝑥𝑥) = ____ n) 5 × (12 − 2 × 7) = ____ o) 4 − 3 × −6 = ____ p) −(3)2 = ____ 8 1 q) 1 9 ÷ 3 = ____ 3 1 r) 15 5 ÷ 3 = ____ 3 1 1 s) 5 ÷ 3 + 5 = ____ 2025-01-22 Module 1 - Mathematics Page 14 of 28 Training Material Only  Workbook Exercise 37 Exercise 40 (Expand and simplify the following) (Transpose the following formulas as indicated) a) (𝑉𝑉 + 3)(𝑉𝑉 + 4) = ____ a) 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 𝑽𝑽 = 𝑰𝑰𝑰𝑰 b) (𝑃𝑃 + 2)(2𝑃𝑃 + 3) = ____ 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑰𝑰 𝑡𝑡ℎ𝑒𝑒 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑜𝑜𝑜𝑜 𝑡𝑡ℎ𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 c) (𝑒𝑒 + 4)(𝑒𝑒 − 5) = ____ b) 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 d) (𝑅𝑅 + 6)(𝑅𝑅 − 6) = ____ 𝑽𝑽 = 𝑰𝑰𝑰𝑰 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑹𝑹 𝑡𝑡ℎ𝑒𝑒 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑜𝑜𝑜𝑜 𝑡𝑡ℎ𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 Exercise 38 (Reduce the following algebraic fractions to their c) 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 simplest form) 𝑷𝑷 = 𝑽𝑽𝑽𝑽 2𝐿𝐿3 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝑰𝑰 𝑡𝑡ℎ𝑒𝑒 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑜𝑜𝑜𝑜 𝑡𝑡ℎ𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 a) 3𝐿𝐿2 = ____ 𝐼𝐼 2 𝑅𝑅 Exercise 41 b) 𝐼𝐼𝐼𝐼 = ____ (Transpose the following formulas as indicated) 2𝐼𝐼 2 c) = ____ 1 3𝐼𝐼 a) 𝑝𝑝 = 2 𝑤𝑤 + 2 (Express in terms of w) 2𝑑𝑑𝑑𝑑𝑑𝑑 d) 𝑒𝑒𝑓𝑓 2 = ____ b) 𝑦𝑦 = 3𝑥𝑥 + 8 (Express in terms of x) 𝐼𝐼(𝑅𝑅1 +𝑅𝑅2 ) 𝑦𝑦 e) = ____ c) 𝑥𝑥 = 10 (Express in terms of x) (𝐼𝐼−2)(𝑅𝑅1 +𝑅𝑅2 ) 22𝑢𝑢 d) 𝑣𝑣 = (Express in terms of u) Exercise 39 25 𝑠𝑠 (Solve for the unknown variable in the following e) 𝑢𝑢 = 𝑡𝑡 (Express in terms of s) equations) f) 𝑉𝑉 = 𝑉𝑉0 + 𝑎𝑎𝑎𝑎 (Express in terms of a) a) 7𝑃𝑃 − 1 = 13 𝑞𝑞 1 g) =3 (Express in terms of p) b) 24 + 13𝑡𝑡 = 21𝑡𝑡 𝑝𝑝 c) 20 = 13 − 𝐿𝐿 h) 𝑤𝑤 = 6(𝑝𝑝 − 7) (Express in terms of p) d) 𝑉𝑉 −3= 4+5 𝑉𝑉 𝑉𝑉 i) 𝑎𝑎𝑎𝑎 = 𝑏𝑏𝑏𝑏 − 𝑐𝑐 (Express in terms of y) 2 4𝜋𝜋𝑟𝑟 3 e) 2(𝐿𝐿 + 1) + 𝐿𝐿 = 8 j) 𝑉𝑉 = (Express in terms of r) 3 f) 5(2 − 𝐸𝐸) − (𝐸𝐸 + 4) = 24 − 3(3 + 𝐸𝐸) 2(𝑊𝑊−4) 1 g) 3𝑊𝑊 − =3 3 2025-01-22 Module 1 - Mathematics Page 15 of 28 Training Material Only  Workbook Exercise 42 k) −21𝑎𝑎 − 7𝑎𝑎2 = ____ (Substitute the values provided for their variables to evaluate the following expressions) Exercise 44 𝑎𝑎 = 5 𝑡𝑡 = −4 𝑢𝑢 = −6 (Express the following in index notation) 𝑃𝑃 = 2 𝑊𝑊 = −3 𝐼𝐼 = 16 𝐸𝐸 = 9 a) 3 × 3 × 3 = ____ a) 𝑎𝑎 + 𝑡𝑡 + 𝑢𝑢 = ____ b) −𝐴𝐴 × −𝐴𝐴 × −𝐴𝐴 = ____ b) 𝑎𝑎 + 𝑢𝑢𝑢𝑢 = ____ 1 1 1 c) 2 × 2 × 2 = ____ c) 𝐼𝐼 ÷ (𝑡𝑡 × 𝑢𝑢) = ____ d) 0.6 × 0.6 = ____ d) 𝑃𝑃𝑃𝑃 = ____ e) 𝑥𝑥 × 𝑥𝑥 × 𝑥𝑥 × 𝑥𝑥 = ____ 1 e) 𝐸𝐸 = ____ 𝑃𝑃 f) −8 × −8 × −8 = ____ f) 𝑎𝑎𝑎𝑎 − 𝑢𝑢𝑢𝑢 = ____ g) √𝐼𝐼 + 𝐸𝐸 = ____ Exercise 45 h) 𝑡𝑡 2 − 𝑊𝑊 3 = ____ (Evaluate the following and leave without an exponent) Exercise 43 a) 25 = ____ (Factorise the following expressions as far as b) 104 = ____ possible) c) (−7)2 = ____ a) 3𝑥𝑥 + 6 = ____ 1 2 b) 5𝑝𝑝 − 5𝑞𝑞 = ____ d) 4 = ____ c) 3𝑥𝑥 2 − 6𝑥𝑥 = ____ 1 3 e) − 2 = ____ d) 2𝑥𝑥 3 − 4𝑥𝑥 2 = ____ f) (−4)3 = ____ e) 𝑥𝑥 2 − 𝑥𝑥 3 = ____ g) (−2)3 = ____ f) 𝑎𝑎𝑏𝑏 2 − 𝑎𝑎2 𝑏𝑏 = ____ g) 15 + 5𝑟𝑟 = ____ h) 𝑚𝑚 − 𝑚𝑚𝑚𝑚 = ____ i) 3𝑟𝑟 2 𝑡𝑡 + 6𝑟𝑟𝑟𝑟 = ____ j) 20𝑥𝑥 3 + 15𝑥𝑥 2 + 25 = ____ 2025-01-22 Module 1 - Mathematics Page 16 of 28 Training Material Only  Workbook Exercise 46 Exercise 48 (Simplify the following and leave in index (Evaluate the following and leave without an notation) exponent) a) 𝑎𝑎3 × 𝑎𝑎2 = ____ a) (23 )3 = ____ b) 34 × 3−8 = ____ b) (𝑎𝑎−6 )3 = ____ c) 57 × 5−1 = ____ c) (10−3 )−2 = ____ d) 𝑥𝑥 6 × 𝑥𝑥 4 × 𝑥𝑥 −2 = ____ 1 10 d) 32 = ____ e) 2−3 × 23 × 21 = ____ 1 3 1 4 Exercise 49 f) 2 × 2 = ____ (Evaluate the following zero exponent expressions) g) 84 × 8−4 = ____ 1 1 a) 20 = ____ h) 𝑒𝑒 × 𝑒𝑒 = ____ 2 4 b) 5 × 100 = ____ c) 100 = ____ Exercise 47 (Simplify the following and leave in index d) (12𝑚𝑚)0 = ____ notation, where appropriate) e) 16𝑚𝑚𝑚𝑚0 = ____ a) 23 ÷ 22 = ____ f) 25 + 100 = ____ b) 35 ÷ 33 = ____ c) 𝑥𝑥 −3 ÷ 𝑥𝑥 3 = ____ d) 𝑎𝑎4 ÷ 𝑎𝑎 = ____ e) 4−4 ÷ 4−2 = ____ 2025-01-22 Module 1 - Mathematics Page 17 of 28 Training Material Only  Workbook Exercise 50 f) 6.3 × 10−9 = ____ (Simplify the following and leave all answers with positive indices where necessary) Exercise 53 (Express the following in scientific notation) a) 3−2 = ____ a) 636.7 = ____ b) 𝑥𝑥 −6 = ____ 1 b) 5400 = ____ c) 3−2 = ____ c) 273 = ____ 2 d) 5−2 = ____ d) 700 000 = ____ 1 e) (𝑥𝑥10 ) = ____ 2 e) 0.0029 = ____ 3 f) 92 = ____ f) 0.08 = ____ g) 0.000 000 56 = ____ Exercise 51 (Simplify the following and leave only positive h) 0.000 000 006 = ____ indices where necessary) 1 Exercise 54 a) 2 𝑎𝑎2 𝑏𝑏 × 6𝑎𝑎𝑏𝑏 2 = ____ (Simplify the following and leave in scientific notation) b) 𝑥𝑥𝑥𝑥 × 7𝑥𝑥 3 𝑦𝑦 4 = ____ a) 2.6 × 108 × 3 × 10−5 = ____ c) 3𝑚𝑚2 𝑛𝑛𝑛𝑛 × 5𝑚𝑚𝑛𝑛3 𝑙𝑙 2 × 2𝑚𝑚𝑚𝑚𝑙𝑙 3 = ____ 4𝑦𝑦 6 ×5𝑥𝑥 −2 b) 7.4 × 10−6 × 2.1 × 108 = ____ d) = ____ 2𝑥𝑥 6 ×10𝑦𝑦 2 c) 5.6 × 10−2 × 3.2 × 10−3 = ____ 3𝑚𝑚2 𝑛𝑛×4𝑚𝑚3 𝑛𝑛4 e) = ____ 2𝑚𝑚𝑛𝑛2 6×106 ×8×10−8 d) = ____ 3×10−5 ×2×10−2 Exercise 52 1.5×10−4 ×8.2×108 e) = ____ 2×105 ×5×10−9 (Express the following in expanded form) a) 5.4 × 103 = ____ b) 6 × 105 = ____ c) 8.1 × 1010 = ____ d) 3.9 × 10−2 = ____ e) 4.8 × 10−5 = ____ 2025-01-22 Module 1 - Mathematics Page 18 of 28 Training Material Only  Workbook Exercise 55 g) 𝑎𝑎2 + 6𝑎𝑎 = −9 (Solve the following simultaneous linear equations. You may use either the substitution or h) 𝑝𝑝2 + 5𝑝𝑝 = 24 elimination method) a) (1) 𝑥𝑥 + 𝑦𝑦 = 5 Exercise 57 (2) 𝑥𝑥 − 𝑦𝑦 = 1 (Solve for the variable in the following quadratics using either factorisation or the quadratic b) (1) 𝑦𝑦 − 3𝑥𝑥 = 0 formula) (2) 𝑥𝑥 + 𝑦𝑦 = 8 a) 3𝑛𝑛2 + 2𝑛𝑛 − 21 = 0 c) (1) 𝑥𝑥 + 𝑦𝑦 = 3 (2) 2𝑥𝑥 + 3𝑦𝑦 = 8 b) 𝑚𝑚 − 5𝑚𝑚 − 24 = 0 d) (1) 3𝑥𝑥 + 𝑦𝑦 = 13 c) 𝑥𝑥 2 + 6𝑥𝑥 = −2 (2) 𝑥𝑥 + 2𝑦𝑦 = 1 d) 𝑥𝑥 2 + 5𝑥𝑥 = 14 e) One piece of fish and two serves of chips cost $2.80, while one piece of fish and four serves of chips costs $2.60. How much is one piece of fish and one serve Exercise 58 of chips? (Evaluate the following logarithms) f) A jar has a total of 25 coins with a total value of $2.15. The jar contains only 20 cent and 5 a) log 2 16 = ____ cent pieces. What is the total number of each coin value? b) log 4 16 = ____ g) Apples are half the cost of bananas. The c) log 81 81 = ____ cost of eight apples and five bananas is $2.88. What is the cost of a single d) log10 1000 = ____ banana? e) log 10 000 = ____ Exercise 56 f) log 0.001 = ____ (Solve for the variable in the following quadratics using factorisation) g) An amplifier has power input of 1.6 mW and a power output of 3.2 W. a) 𝑥𝑥 2 + 7𝑥𝑥 + 12 = 0 Given that (log10 2000 = 3.3), find the amplifier gain in decibels (dB). b) 𝑦𝑦 2 + 5𝑦𝑦 + 6 = 0 h) An amplifier has power input of 0.0014 W and c) 2 𝑔𝑔 + 9𝑔𝑔 + 20 = 0 a power output of 5.6 W. Given that (log10 4000 = 3.6), find the amplifier gain in decibels (dB). d) 𝑥𝑥 2 − 8𝑥𝑥 + 7 = 0 e) 𝑚𝑚2 − 6𝑚𝑚 + 8 = 0 f) 𝑏𝑏 2 + 𝑏𝑏 − 6 = 0 2025-01-22 Module 1 - Mathematics Page 19 of 28 Training Material Only  Workbook Exercise 59 (Simplify) Exercise 59 (Solve) (Simplify the following expressions) (Solve the following as indicated) a) 3 × 𝑒𝑒 + 5 × 3 = ____ a) 4𝑢𝑢 + 3 = 20 (solve for u) b) 16 − 2𝑛𝑛 − 𝑛𝑛 − 7 = ____ b) 4𝑠𝑠 − 7 = 𝑠𝑠 − 28(solve for s) c) 𝑓𝑓 2 − 4𝑐𝑐 − 3𝑓𝑓 2 + 9𝑐𝑐 = ____ c) 2(𝐿𝐿 + 1) + 𝐿𝐿 = 8 (solve for L) d) 4(𝑃𝑃 − 2) = ____ d) 5(2 − 𝐸𝐸) − (𝐸𝐸 + 4) = 24 − 3(3 + 𝐸𝐸) (solve for E) e) 7 − (𝐼𝐼 − 3) = ____ e) Given the following values f) 4(𝑃𝑃 + 𝑊𝑊) − 2(𝑃𝑃 − 𝑊𝑊) = ____ 𝐸𝐸 = 4 𝐼𝐼 = −3 𝑅𝑅 = 5 Evaluate the following expression Exercise 59 (Expand and Simplify) 𝐸𝐸 2 + 𝐼𝐼𝐼𝐼 = ____ (Expand and simplify the following expressions) 2𝑅𝑅 − 𝐼𝐼 2 a) (𝑎𝑎 + 2)(𝑎𝑎 + 9) = ____ f) Given the following values 𝐿𝐿 = 5 ℎ=3 b) (𝑐𝑐 − 3)(𝑐𝑐 + 8) = ____ Solve for L in the following equation 𝐿𝐿2 = (2𝑅𝑅 − ℎ) Exercise 59 (Factorise) g) 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 (Factorise the following expressions) 𝒗𝒗𝟐𝟐 = 𝒖𝒖𝟐𝟐 + 𝟐𝟐𝟐𝟐𝟐𝟐 a) 12𝑓𝑓𝑓𝑓 − 16𝑐𝑐 2 = ____ 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝒔𝒔 𝑡𝑡ℎ𝑒𝑒 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑜𝑜𝑜𝑜 𝑡𝑡ℎ𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 b) 𝐸𝐸𝐸𝐸 + 𝐸𝐸 2 = ____ h) 𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺𝐺 𝒗𝒗𝟐𝟐 = 𝒖𝒖𝟐𝟐 + 𝟐𝟐𝟐𝟐𝟐𝟐 c) 9𝐿𝐿2 − 27𝑃𝑃2 = ____ 𝑀𝑀𝑀𝑀𝑀𝑀𝑀𝑀 𝒖𝒖 𝑡𝑡ℎ𝑒𝑒 𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠 𝑜𝑜𝑜𝑜 𝑡𝑡ℎ𝑒𝑒 𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓𝑓 d) 𝐸𝐸 2 − 𝐸𝐸𝐸𝐸 = ____ 2025-01-22 Module 1 - Mathematics Page 20 of 28 Training Material Only  Workbook Exercise 60 Exercise 63 (State whether the following angles are acute, (Label the parts of the following circles as right, reflex or obtuse) indicated) a) 234° b) 2° c) 162° d) 71°47′ e) 90°11′ Exercise 61 (Determine the complimentary angles of the following) a) 11° b) 49° c) 17°44′ d) 71°47′ Exercise 64 Exercise 62 (Determine the following from the graphics) (Determine the supplementary angles of the following) a) 169° b) 134° c) 104°14′ a) How many degrees into the cycle is point d) 5°51′ 𝑃𝑃? b) How many degrees into the cycle is point 𝑄𝑄? 2025-01-22 Module 1 - Mathematics Page 21 of 28 Training Material Only  Workbook Exercise 65 Exercise 66 (Determine the types of triangles shown) (Given the standard a, b, c layout of a Pythagorean triangle as shown, solve for the unknown sides in the table below) a) a b c 3 4 b) 6 10 5 12 24 26 Exercise 67 (Determine the unknown sides in the following c) triangles. Round answers to one decimal place where necessary) d) a) b) e) c) f) 2025-01-22 Module 1 - Mathematics Page 22 of 28 Training Material Only  Workbook f) How long must a ladder be to reach 6 meters up a wall if it is at an angle of 27o to the wall? Exercise 69 (Use the trigonometry table provided in the d) student resource to solve the unknown angles in these triangles) Exercise 68 (Use the trigonometry table provided in the student resource to solve the unknown sides in these triangles) a) b) a) b) c) c) d) d) e) e) 2025-01-22 Module 1 - Mathematics Page 23 of 28 Training Material Only  Workbook Exercise 70 e) How many degrees (of arc) represent hospitals? (Use the pictograph shown to answer the questions which follow) Exercise 72 (Use the pie chart shown to answer the questions which follow) a) How many visitors attended in April? b) Which month had the least visitors? a) If the pizza is 900g, how many grams of sausage are used? c) How many visitors attended per month on average from January through May? b) How many degrees (of arc) represent sausage? Exercise 71 c) Which ingredient accounts for one quarter of the total mass? (Use the pie chart shown to answer the questions which follow) Exercise 73 (Use the bar graph shown to answer the questions which follow) The chart shows healthcare costs, totalling $68 Billion. a) What percentage is accounted for by hospitals? b) What is the combined cost (in $) for physicians and dentists? c) What is the total cost (in $) for a) Which destination has the least daily hospitals? flights? d) How many degrees (of arc) represent b) Which destination has the second most “other” costs? daily flights? 2025-01-22 Module 1 - Mathematics Page 24 of 28 Training Material Only  Workbook c) Which destinations have at least ten daily Exercise 75 flights? (Use the histogram shown to answer the d) How many flights (combined) depart to questions which follow) the three most popular destinations? Exercise 74 (Use the bar graph and legend shown to answer the questions which follow) The histogram shows case numbers of patients who suffer with mononucleosis. a) What type of graph has bars which are not separated? b) At what age is mononucleosis most common? c) Which of the following age groups has the most cases? (i) 12 - 18 (ii) 17 - 23 (iii) 21 - 26 (iv) 25 - 30 d) Which of the following age sectors has the least cases? (i) Under 6 (ii) Under 20 (iii) Over 25 (iv) Over 31 a) Which aircraft has the highest fuel consumption? b) Which aircraft has a payload index of 65? c) Which aircraft can carry the highest payload per kilometre travelled? d) Which aircraft carries the lowest payload per unit of fuel consumed? 2025-01-22 Module 1 - Mathematics Page 25 of 28 Training Material Only  Workbook Exercise 76 Exercise 77 (Use the graph shown to answer the questions (Use the graph shown to answer the questions which follow) which follow) a) Determine the temperature at 09:30. b) Estimate what the temperature will be at 14:00. a) If the aircraft is using 140HP, what is the speed? b) If the aircraft is using minimum power, what is the speed? c) Determine the maximum cruise speed of the aircraft. 2025-01-22 Module 1 - Mathematics Page 26 of 28 Training Material Only  Workbook Exercise 78 Exercise 79 (Use the graph shown to answer the questions (Use the graph shown to answer the questions which follow) which follow) “CD” refers to Coefficient of Drag and 𝛼𝛼 represents the Angle of Attack. a) What is the effect of adding a nacelle and air intakes to the G97 fuselage? b) For the fuselage without a nacelle or air intake, at which angle(s) of attack is the coefficient of drag 0.01? c) What is the coefficient of drag for the fuselage with a nacelle and air intake a) If a 2800CID engine is developing 1750HP when the angle of attack is 3o? at 2400RPM, what is the BMEP? b) If a 1830CID engine is developing 1000HP at 1800RPM, what is the BMEP? c) If a 2800CID engine is developing 900HP with 208BMEP, what is the RPM? 2025-01-22 Module 1 - Mathematics Page 27 of 28 Training Material Only  Workbook Exercise 80 Exercise 81 (Define the points shown using the rectangular (Consider the following straight-line graphs) coordinate system) a) Given that 𝑦𝑦 = 3𝑥𝑥 − 7, determine the gradient and 𝑦𝑦-intercept b) Given that 𝑦𝑦 = 5 − 2𝑥𝑥, determine the gradient and 𝑦𝑦-intercept c) Given that 2𝑦𝑦 = 6𝑥𝑥 + 1, determine the gradient and 𝑦𝑦-intercept d) The oil required for an aircraft fleet is given by the equation 𝑄𝑄 = 10𝑛𝑛 + 70, where 𝑄𝑄 is the total quantity of oil consumed (in litres) and 𝑛𝑛 is the number of aircraft. How much oil is used by each aircraft? e) Using the same information from (d) above, if the fleet size was increased to a) Point 𝐴𝐴 35, how much oil would be consumed? b) Point 𝐵𝐵 Exercise 82 c) Point 𝐶𝐶 (Solve the following problems using the polar coordinate system) d) Point 𝐷𝐷 a) A body undergoes a displacement 12m due e) Point 𝐸𝐸 north, followed by a displacement 5m due east. What is the resultant displacement? f) Point 𝐹𝐹 b) An aircraft departs a point and tracks bearing 1350 for 20 nautical miles. How far East of its starting point has it travelled? c) An aircraft departs a point and tracks bearing 0370 for 300 nautical miles. How far North of its starting point has it travelled? 2025-01-22 Module 1 - Mathematics Page 28 of 28 Training Material Only