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Maths A - Skill sheets answers
 

Maths A - Skill sheets answers

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    Maths A - Skill sheets answers Maths A - Skill sheets answers Document Transcript

    • SkillSHEET 1.1 — Percentages 1 a 6 b 6.5 c $320 d 175 students e 12 f $10.60 g 5.28 h 19.5 articles 2 133 passed 3 Approx. 571 enrolments 4 a i 1.10 ii 1.20 iii 1.25 iv 1.07 v 1.125 b i $286 ii $312 iii $325 iv $278.20 v $292.50 5 a i 0.90 ii 0.80 iii 0.75 iv 0.93 v 0.875 b i $324 ii $288 iii $270 iv $334.80 v $315 SkillSHEET 1.2 — Expressing one number as a percentage of another 1 79.25% 2 17.33% 3 22.67% 4 49.47% 5 14.29% 6 34.29% 7 38.33% 8 32.82% 9 10.77% 10 12.20% 11 42.86% 12 60.66% 13 46.71% 14 44% 15 62.5% SkillSHEET 1.3 — Ratio 1 a 192 b 150 c 22.5 2 a 1600 b 0.25 c 18.75 3 11.36 km/L, 52.8 L 4 8.33 km/L, 60 L 5 1200 mL 6 Patsy $252.63, Crystal $147.37 7 $178.29 8 $19 9 a 80 000 m/h b 1333.3 m/min c 22.2 m/s d 1.25 hours 10 30 km/h 11 a 1224 km/h b 0.50 s, faster SkillSHEET 2.1 — Finding a percentage of a quantity 1 a $8.00 b $230 c $63 d $56 e $41.60 f $18.72 g $180 h $240 i $50 j $3.20 k $4.39 l $47.41 2 $12.60 3 $1260 4 $4800 5 $587.50 6 $53.76 billion SkillSHEET 2.2 — Increase or decrease by a percentage 1 a $399 b $952 c $140.25 d $768.75 2 a $142.50 b $231.60 c $125 d $74.25 3 $146.88 4 $134.40 5 $322.50 6 $91.11 SkillSHEET 2.3 — Ratio 1 a 192 b 150 c 22.5 2 a 1600 b 0.25 c 18.75 3 11.36 km/L, 52.8 L 4 8.33 km/L, 60 L 5 1200 mL 6 Patsy $252.63, Crystal $147.37 7 $178.29 8 $19 9 a 80 000 m/h b 1333.3 m/min c 22.2 m/s d 1.25 hours 10 30 km/h 11 a 1224 km/h b 0.50 s, faster SkillSHEET 3.1 — Finding a percentage of a quantity 1 a $8.00 b $230 c $63 d $56 e $41.60 f $18.72 g $180 h $240 i $50 j $3.20 k $4.39 l $47.41 2 $12.60 3 $1260 4 $4800 5 $587.50 6 $53.76 billion SkillSHEET 3.2 — Increase or decrease by a percentage 1 a $399 b $952 c $140.25 d $768.75 2 a $142.50 b $231.60 c $125 d $74.25 3 $146.88 4 $134.40 5 $322.50 6 $91.11 SkillSHEET 3.3 — Ratio 1 a 192 b 150 c 22.5 2 a 1600 b 0.25 c 18.75 3 11.36 km/L, 52.8 L 4 8.33 km/L, 60 L 5 1200 mL 6 Patsy $252.63, Crystal $147.37 7 $178.29 8 $19 9 a 80 000 m/h b 1333.3 m/min c 22.2 m/s d 1.25 hours 10 30 km/h 11 a 1224 km/h b 0.50 s, faster SkillSHEET 4.1 — Rounding decimal numbers to 2 decimal places 1 0.32 2 0.26 3 1.72 4 2.56 5 4.31 6 12.20 7 8.47 8 25.03 9 18.33 10 0.17 SkillSHEET 4.2 — Multiplying decimal numbers by powers of 10 1 25.6 2 76 3 9.8 4 349 5 260 6 7010 7 20 8 5321 9 10 200 10 758 11 25 000 12 35 760 13 3 14 6 15 8 16 400 SkillSHEET 4.3 — Multiplying decimal numbers by 100 1 56 2 76 3 98 4 49 5 260 6 110 7 20 8 532.1 9 1020 10 75.8 11 50 12 0.06 SkillSHEET 4.4 — Dividing whole numbers and decimals by 100 1 a 0.28 b 0.6 c 0.34 d 0.02 e 0.15 f 0.07 g 5.6 h 7.21 i 0.03 j 0.75 k 6 l 2.5 2 a 0.092 b 0.523 c 0.005 d 0.0819 e 0.049 f 1.234 g 0.003 h 0.711 i 1.556 j 0.0425 k 0.753 l 1.005 SkillSHEET Answers
    • SkillSHEET 4.5 — Finding the size of a sector in degrees, given its size as a fraction of a circle 1 144° 2 120° 3 108° 4 270° 5 150° 6 80° 7 315° 8 96° 9 288° 10 60° 11 230° 12 174° SkillSHEET 6.1 — Trigonometry review 1 1 a Opposite b Adjacent c Adjacent d Opposite e Opposite f Adjacent g x = adjacent, y = hypotenuse h x = opposite, y = hypotenuse i x = opposite, y = hypotenuse 2 a Sine b Tangent c Cosine d Sine or tangent e Sine f Tangent g Tangent h Tangent i Tangent SkillSHEET 6.2 — Trigonometry review 2 1 a 0.2588 b 0.5592 c 0.9816 d 0.3546 e 0.6076 f 0.9931 g 0.9659 h 0.8290 i 0.1908 j 0.9350 k 0.7942 l 0.1170 m 0.2679 n 0.6745 o 5.1446 p 0.3792 q 0.7650 r 8.4913 2 a 1 b 0 c 0 d −0.654 e −0.760 f −4.165 g 0.906 h −0.588 i 0.176 j 0 k −1 l Undefined 3 a 30° b 18°20′ c 52°53′ d 60° e 60° f 71°40′ g 37°07′ h 30° i 26°34′ j 17°28′ k 38°34′ l 40°54′ m 43°32′ n 72°22′ o 60°49′ p 68°43′ SkillSHEET 7.1 — Conversion of units — length 1 200 cm 2 5.3 cm 3 610 000 m 4 30 cm 5 5.6 m 6 113 mm 7 12.304 km 8 0.7 mm 9 6.3 m 10 800 m 11 1100 cm 12 4200 mm 13 9 m 14 0.765 km 15 89 mm 16 0.014 683 km SkillSHEET 7.2 — Reading scales (How much is each interval worth?) 1 1 unit 2 1 unit 3 0.1 of a unit 4 0.1 of a unit 5 2 units 6 20 units 7 0.2 of a unit 8 5 units 9 25 units 10 500 units SkillSHEET 7.3 — Pythagoras’ theorem 1 13.0 2 33.8 3 8.3 4 20.7 5 17.3 6 113.6 7 17.9 8 0.9 SkillSHEET 7.4 — Using trigonometric ratios 1 a Sine b Cosine c Tangent d Cosine e Sine 2 a 4.243 cm b 7.247 cm c 10.990 cm d 3.801 cm e 22.027 cm 3 a 47° b 52° c 56° d 45° e 67° SkillSHEET 7.5 — Identifying sides of a right-angled triangle with respect to the given angle 1 Opposite 2 Adjacent 3 Adjacent 4 Opposite 5 Opposite 6 Adjacent 7 x = adjacent, y = hypotenuse 8 x = opposite, y = hypotenuse 9 x = opposite, y = hypotenuse SkillSHEET 7.6 — Finding trigonometric values and angles 1 a 0.2588 b 0.5592 c 0.9816 d 0.3420 e 0.6018 f 0.9925 g 0.9659 h 0.8290 i 0.1908 j 0.9397 k 0.7986 l 0.1219 m 0.2679 n 0.6745 o 5.1446 p 0.3640 q 0.7536 r 8.1443 2 a 30° b 18.3° c 52.9° d 60° e 60° f 71.7° g 37.1° h 30° i 26.6° j 17.5° k 38.6° l 40.9° m 43.5° n 72.4° o 60.8° p 68.7° SkillSHEET 8.1 — Area and perimeter of composite figures 1 a 240 m2 b 72 m 2 a 240 cm2 b 68 cm 3 a 526.88 cm2 b 164.29 cm 4 a 76.16 m2 b 36.00 m 5 a 138.62 mm2 b 50.27 mm 6 a 120.56 cm2 b 42.71 cm SkillSHEET 8.2 — Volume 1 3952 m3 2 452.39 cm3 3 384 mm3 4 100.53 cm3 5 585 cm3 6 1199.07 m3 7 4222.30 cm3 8 5747.02 cm3 9 4755.35 m3 10 105.47 cm3 11 294 mm3 12 33 997.39 cm3 SkillSHEET 8.3 — Conversion of units — volume 1 0.268 cm3 2 35 000 cm3 3 0.61 mm3 4 0.000 037 569 m3 5 5030 mm3 6 68.005 624 m3 7 3 100 000 000 mm3 8 15 m3 9 0.000 000 086 m3 10 70 400 000 mm3 SkillSHEET 8.4 — Labelling right-angled triangles 1 a 45° Opposite 6 cm Hypotenuse Adjacent
    • b c d e f g h i j 2 a Opposite, Hypotenuse b Adjacent, Hypotenuse c Opposite, Hypotenuse d Opposite, Hypotenuse e Adjacent, Hypotenuse f Opposite, Hypotenuse g Opposite, Hypotenuse h Opposite, Adjacent i Adjacent, Hypotenuse j Opposite, Adjacent SkillSHEET 8.5 — Using trigonometric ratios 1 a Sine b Cosine c Tangent d Cosine e Sine 2 a 4.243 cm b 7.247 cm c 10.990 cm d 3.801 cm e 22.027 cm 3 a 47° b 52° c 56° d 45° e 67° SkillSHEET 9.1 — Finding the size of a sector in degrees, given its size as a fraction of a circle 1 144° 2 120° 3 108° 4 270° 5 150° 6 80° 7 315° 8 96° 9 288° 10 60° 11 230° 12 174° SkillSHEET 10.1 — Finding a mean 1 4 2 5.5 or 5 3 4 4 6 5 7.75 or 7 6 7 8 9 10 SkillSHEET 10.2 — Finding the median 1 5 2 22 3 45 4 53 5 6 6 32.5 7 9.5 8 20 SkillSHEET 11.1 — Measuring the rise and the run 1 Run = 1, rise = 2 2 Run = 4, rise = 1 3 Run = 3, rise = 5 4 Run = 1, rise = −1 5 Run = 2, rise = −1 6 Run = 1, rise = 2 7 Run = 1, rise = 1 8 Run = 2, rise = 3 9 Run = 1, rise = −3 10 Run = 4, rise = −3 Opposite 22 cm 15 cm Hypotenuse Adjacent θ 47° Opposite18 cm Hypotenuse Adjacent x Opposite 10 cm 12 cm Hypotenuse Adjacent θ 73° x Opposite 13 cm Hypotenuse Adjacent Hypotenuse Adjacent 27° 10 cm x Opposite 8.3 cm Opposite Hypotenuse Adjacent 5.9 cm θ 24 mm 37 mm θ Opposite Hypotenuse Adjacent x 7 cm Opposite Hypotenuse 15° Adjacent Hypotenuse Adjacent 20° x Opposite 4 cm 1 2 --- 2 3 --- 2 3 --- 3 4 --- 7 x+ 2 ------------ 19 x+ 2 --------------- 17 x+ 3 --------------- 6 x+ 3 ------------ 42 x+ 3 ---------------
    • SkillSHEET 11.2 — Substitution into a rule 1 a 14 b 2 c 17 d 20 e 20 f 35 g 11 h 16 i 10 j 41 2 a 12 b 0 c 15 d 22 e 12 f 21 g 5 h 12 i 16 j 29 SkillSHEET 11.3 — Averate rate of change 1 a −81, −167 b 4, 13 c −3, −37 2 a −43 units/s b 3 m/s c −17 3 55 cm/s 4 10.5 m3 /min 5 29 SkillSHEET 11.4 — Using the regression equation to make predictions 1 a y = 21 b y = 57 c x = 41 d x = 101.5 2 a y = 42 b y = 658 c x = 7 d x = 11.55 3 a y = 59.5 b y = 102.7 c x = 70.42 d x = 24.58 4 a y = 12.25 b y = 28 c x = 96.19 d x = 89.52 5 a y = 115.5 b y = 197.75 c x = 14.89 d x = 185.11 SkillSHEET 12.1 — Understanding a deck of playing cards 1 26 2 4 3 12 4 1 5 4 6 13 7 39 8 26 9 4 10 2 11 2 12 2 13 16 14 6 SkillSHEET 12.2 — Converting fractions to percentages 1 75% 2 80% 3 37 % 4 40% 5 87 % 6 33 % 7 83 % 8 42 % 9 55 % 10 58 % SkillSHEET 12.3 — Converting a fraction to a decimal number 1 0.375 2 0.3125 3 0.875 4 0.3125 5 0.41 6 0.15 7 0.710 937 5 8 0.234 375 9 0.69 10 0.993 75 1 2 --- 1 2 --- 1 3 --- 1 3 --- 6 7 --- 5 9 --- 1 3 ---