Answers to selected quizzes

The language of mathematics page 4: Quiz 1, a 10 + 11 = 21 (true), b 2 × 2 = 2 + 2 (true), c 5 − 4 = 2 ÷ 2 (true), d 5 ÷ 2 ≥ 3 (false), e 5 × 4 <3 × 7 (true). Quiz 2, a (1 + 2) + 3 = 6 & 1 + (2 + 3) = 6, b (4 + 6) ÷ 2 = 5 & 4 + (6 ÷ 2) = 7, c (2 × 3) × 4 = 24 & 2 × (3 × 4) = 24, d (20 − 6) × 3 = 42 & 20 − (6 × 3) = 2, e (2 × 3) + (4 × 5) = 26 & 2 × (3 + 4) × 5 = 70. Quiz 3, a Both correct, b 4 + (6 ÷ 2) = 7, c Both correct, d 20 − (6 × 3) = 2, e (2 × 3) + (4 × 5) = 26. Quiz 4, − & ÷

Addition page 11: Quiz 1, a 11, b 13, c 18, d 12, e 21. Quiz 2, a 70, b 7000, c 1100, d 11,000, e 120,000. Quiz 3, a 78, b 99, c 698, d 785, e 9775. Quiz 4, a 41, b 74, c 161, d 471, e 401. Quiz 5, a 59, b 87, c 101, d 93, e 161. Quiz 6, a 83, b 89, c 86, d 97, e 144.

Subtraction page 18: Quiz 1, a 3, b 4, c 7, d 8, e 8. Quiz 2, a 21, b 28, c 430, d 2838, e 2140. Quiz 3, a 54, b 17, c 34, d 19, e 99. Quiz 4, a 37, b 61, c 22, d 49, e 58. Quiz 5, a 38, b 55, c 26, d 38, e 42.

Multiplication page 24: Quiz 1, a 16, b 30, c 54, d 49, e 56. Quiz 2, a 68, b 88, c 93, d 128, e 205. Quiz 3, a 880, b 690, c 480, d 1890, e 3550. Quiz 4, a 714, b 1530, c 2790, d 8733, e 54,864. Quiz 5, a 912, b 2074, c 1653, d 11,096, e 26,292.

Division page 35: Quiz 1, a 3, b 6, c 9, d 8, e 7. Quiz 2, a 2 r 3, b 2 r 4, c 3 r 3, d 9 r 3, e 7 r 3. Quiz 3, a 12, b 22, c 31, d 62, e 1061. Quiz 4, a 432, b 110, c 301, d 4241, e 3012. Quiz 5, a 121, b 142, c 131, d 142, e 124. Quiz 6, a 21, b 18, c 31, d 105, e 61.

Primes, factors and multiples page 44: Quiz 1, a 3 × 5, b 2 × 3 × 3, c 3 × 7, d 2 × 2 × 2 × 3, e 2 × 2 × 2 × 2 × 2. Quiz 2, a True & false, b False & false, c False & false, d True & true, e True & true. Quiz 3, a Divisible by 2, 4, & 8, b Divisible by 2, 3, 6, & 7, c Divisible by 3 & 5, d Divisible by 2, 4, 8, & 11, e Divisible by 2 & 4. Quiz 4, a 2 × 3 × 5, b 2 × 3 × 5 × 7, c 2 × 2 × 3 × 3 × 3, d 3 × 3 × 3 × 7, e 3 × 7 × 7 × 11. Quiz 5, a 3 + 7 or 5 + 5, b 5 + 7, c 3 + 11 or 7 + 7, d 3 + 13 or 5 + 11, e 5 + 13 or 7 + 11.

Negative numbers and the number line p 50: Quiz 2, a 15 & 1, b 6 & 0, c 9 & −3, d −1 & −9, e 1 & −5. Quiz 3, a 1 & 9, b −1 & 5, c −5 & 5, d −6 & −2, e −8 & 2. Quiz 4, a −6 & 6, b −20 & 20, c −21 & 21, d −32 & 32, e −100 & 100. Quiz 5, a 4 & −4, b −3 & 3, c 4 & −4, d −11 & 11, e −3 & 3.

Decimals page 57: Quiz 1, a 5.5, b 13.1, c 15.50, d 10.11, e 0.01111. Quiz 2, a 4.3, b 4.12, c 7.9, d 4.19, e 9.83. Quiz 3, a 0.8, b 0.08, c 3.5, d 0.35, e 0.035. Quiz 4, a 3.91, b 32.24, c 9.86, d 174.76, e 45.188. Quiz 5, a 5.3, b 0.16, c 0.2, d 10.0, e 0.720.

Fractions page 66: Quiz 1, , , , , . Quiz 2, , , , , . Quiz 3, , , , , . Quiz 4, , , , d . Quiz 5, a 0.8, , c 0.1875, d 0.285714, . Quiz 6, All numbers except multiples of 2 & 5.

Arithmetic with fractions p73: Quiz 1, or , , , , . Quiz 2, , , , , . Quiz 3, , , , , . Quiz 4, , , , , . Quiz 5, , , , , .

Powers page 80: Quiz 1, a 27, b 36, c 125, d 81, e 216. Quiz 2, a 3125, b 46,656, c 20,736, d 15,625, e 5,584,059,449. Quiz 4, , , , , . Quiz 5, a 2²², b 2¹⁵, c 15⁵, d 13²⁶, e 100¹⁹.

The power of 10 p 86: Quiz 1, a 7,000,000, b 8,000,000,000, c 9,000,000,000,000, d 10,000,000,000,000,000, e 11,000,000,000,000,000,000. Quiz 2, a 18 kilometers, b 37 megapixels, c 3 nanograms, d 900 kilonewtons or 0.9 meganewtons, e 8 gigabytes. Quiz 3, a one thousandth, b one hundredth, c one hundred thousandth, d one ten millionth, e one trillionth. Quiz 4, a 600,000, b 21000, c 0.00000879, d 0.001332, e 67,100,000,000. Quiz 5, a 8 × 10⁵, b 5.6 × 10⁴, c 6.2 × 10⁻⁴, d 9.87 × 10⁸, e 1.11 × 10⁻⁹.

Roots and logs p 95: Quiz 1, a 2, b 10, c 8, d 7, e 12. Quiz 2, a 3.16, b 2.15, c 1.78, d 2.24, e 1.16. Quiz 3, a 11, b 2, c 8, d 125, e 81. Quiz 4, a 2, b 4, c 3, d 7, e 3. Quiz 5, a log₄48, b log₃26, c log₁₀72, d log₅42, e log₆110.

Percentages and proportions p 102: Quiz 1, a 3, b 308, c 392, d 118,404, e 86.4 billion. Quiz 2, a 32%, b 16%, c 43%, d 16%, e 6%. Quiz 3, , b 1 & 1, , , e 0.04 Quiz 4, a 5% increase, b 23% increase, c 32% increase, d 18% decrease, e 142% increase. Quiz 5, flour water, b Jog 2 miles & Walk 1 mile, c 50g eggs & 150g butter & 300g flour, d 40ml cordial & 320ml water, e 200g eggs & 80g onions & 160g potatoes. Quiz 6, a $231.85, b $90.05, c $18.58, d $2806.79.

Algebra page 110: Quiz 1, a a = 2s, , , d p = 4d + w, . Quiz 2, a 8, b 2, , d 14, e 72. Quiz 3, a 4a, b 3b + 1, c 3x + 2y, d 6x − 3a, e x + 5z + 2y + 2. Quiz 4, a 4x + 4z, b 2x + 8, c x² −x, d x² −2xy, e 2x² −4xy.

Equations page 117: Quiz 1, a 6, b 7, c 6, d 8, e 28. Quiz 3, a x = 3, b x = 12, c x = 3, d x = 2, e x = 7. Quiz 4, a x = 2, b x = 5, c x = 8, d x = 0, e x = 3. Quiz 5, a x < 3, b x < 12, c x < 3, d x < 2, e x < 7.

Angles page 124: Quiz 1, b 1, , , . Quiz 2, a Acute, b Acute, c Acute, d Obtuse, e Reflex. Quiz 3, a 285°, b 210°, c 120°, d 37°, e 34°. Quiz 4, a 90°, 90° & 90°, b 135°, 45° & 135°, c 159°, 21° & 159°, d 58°, 122° & 58°, e 4°, 176° & 4°.

Triangles page 132: Quiz 3, a 60°, b 15°, c 40° at A & 70° at C, d 55° at A & 55° at C. Quiz 4, a 1cm², b 2cm², c 6cm², d 2.5cm², e 9cm².

Circles page 140: Quiz 1 Exact answers (to 1 decimal place), a 12.6cm, b 6.3cm, c 25.1cm, d 12.6cm, e 6.3cm. Quiz 2, a 15.71cm, b 31.42cm, c 3.50 miles, d 15.92km, e 0.70mm. Quiz 3, a 78.54cm², b 19.63cm², c 14.25mm², d 3.56mm², e 0.36mm². Quiz 4 Each to 1 decimal place: a 1.3 miles, b 4.1mm, c 8.2km, d 10.2cm², e 7.5m. Quiz 5 Each to 1 decimal place: a 28.3cm² & 50.3cm², b 22.0cm², c 25cm² & 19.6cm², d 5.4cm², e 77.1 cm².

Area and volume p 148: Quiz 1, a 28m², b 5000m², c 600cm², d 16cm², e 144.Quiz 2, a 125,000cm³, b 12,000m³, c 268.1cm³ (to 1 d.p.), d 31,415.93cm³ or 0.03m³ (to 2 d.p.), e 3141.6cm³ (to 1 d.p.). Quiz 3, a 15,000cm² (including the top face), b 3400m² (including the bottom face), c 201.1cm² (to 1.d.p.), d 6911.50cm² or 0.69m², e 993.5cm² (Curved surface only).

Polygons and solids p 156: Quiz 3 (To nearest degree), a 120°, b 129°, c 135°, d 144°, e 179°. Quiz 4, Tetrahedron: 4 corners, 6 edges, 4 faces, Cube: 8 corners, 12 edges, 6 faces, Octahdron: 6 corners, 12 edges, 8 faces, docecahedron: 20 corners, 30 edges, 12 faces, Icosahedron: 12 corners, 30 edges, 20 faces.

Pythagoras’ theorem p 166: Quiz 1 (Each to 1 decimal place), a 5 miles, b 1.4cm, c 3.6m, d 7.8mm, e 17km. Quiz 2 (Each to 1 decimal place), a 2.8mm, b 3.5 miles, c 9.1cm, d 8.5km, e 60 inches. Quiz 3 (Each to 2 decimal places), a 5 meters, b 67.68cm, c 10.05km, d 147.41m, e 500m. Quiz 4 b 6cm², 49cm², 9cm², 16cm², 25cm², c 2.5cm, 6cm, 6.5cm, d 8cm, 15cm, 17cm Quiz 5, a 25, b 17, c 41, d 60, e 12.

Trigonometry p 174: Quiz 1 (Each to 2 decimal places), a 0.31, b 0.48, c 0.98, d 0.52, e 0.88. Quiz 2 (Each to 2 decimal places), a 3.53 miles, b 2.93cm, c 0.67 meters, d 8.49 nm, e 37.31mm. Quiz 3, a 3.5 miles, b 2.0cm, c 0.9km, d 88.8mm, e 4.7µm. Quiz 4 (Each to the nearest degree), a 53°, b 10°, c 54°, d 59°, e 26°.

Coordinates p 182: Quiz 1, a (1, 3), b (−2, 3), c (−3, 2), d (−2, −3), e (4, −3). Quiz 3, a 5, b 13, c 2.83 (to 2.d.p.), d 3, e 12.81 (to 2.d.p.). Quiz 5 (Each to 2.d.p.), a 1.73, b 1.41, c 3.16, d 4.12, e 5.48.

Graphs page 188: Quiz 1, a y = x + 2, b y = 2x, c y = −x, d y = 4x, e y = 2x + 1.Quiz 3, a m = 3 & c = 0, b m = 3 & c = −1, c m = −1 & c = 0, d m = −1 & c = 1, . Quiz 4, a y = 5x + 4, b y = −x−1, , .

Statistics p 197: Quiz 1, a 41kg, b 1.0m, c 45.75, d 33db, e 1.46. Quiz 2, a 42kg, b 0.9m, c 20, d 31db, e 1. Quiz 3, The mode is 1 & the median is 2. Quiz 4, The first quartile is 1, the third quartile is 3. The interquartile range is 2. The 99^th percentile is 5.

Probability p 205: Quiz 2, , , , , . Quiz 3, a Yes, b Yes, c Yes, d No, e Yes. Quiz 4, , , , . Quiz 5, a Yes, , b Yes, , c No, , .

Charts p 212: Quiz 1, a 90°, 180° & 90°, b 240°, 60° & 60°, c 72°, 216°, 36° & 36°, d 225°, 45°, 45° & 45°, e 252°, 72° & 36°. Quiz 3 (Each to the nearest degree), a 164° & 196°, b 15°, 15°, & 330°, c 96°, 180°, 24° & 60°, d 248°, 34°, 72° & 6°, e 168°, 123°, 40° & 29°.