MRH 9: Chapter 1 Get Ready
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Extra Practice Answers BLM 1 GR
Chapter 1 Get Ready
1. a) –0.375 b) 1.28 c) –0.45 7. a) = b) > c) < d) 0.06 e) 2.46 f) 0.045 d) < e) > f) <
2. a) rational, integer, whole, natural 5 b) rational, integer 8. a) –116 b) –4 c) - 2 c) rational, integer, whole 35 d) rational d) –0.15 e) e) rational 36 f) rational g) rational 9. a) 60 b) 55 c) 21 h) rational, integer, whole, natural d) 26 e) 2 f) 84 i) rational 3. 10. a) 8.1 b) 2.6 c) 11.7 Base Exponent Power Value a) (–10) 4 (–10)4 10 000 11. a) 27.7 cm b) 3.8 m b) 5 3 53 125 c) 7 2 72 49 12. d) (–2) 7 (–2)7 –128 Standard Notation Product Scientific Notat 4. a) 210 b) 45 c) 322 ion a) 7 200\ 7.2 1 000 7.2 103 5. a) 4 b) 3 c) 5 b) 45 000 4.5 10 000 4.5 104 d) any even exponent e) 1 f) 4 c) 85 000 8.5 10 000 8.5 104 g) any odd exponent h) 3 i) 2 d) 110 000 1.1 100 000 1.1 105 j) 5 e) 978 000 000 9.78 100 000 000 9.78 108 f) 20 300 000 2.03 10 000 000 2.03 107 4 2 ж1 ц 1 ж1ц 1 g) 0.000 000 000 34 3.4 0.000 000 000 1 3.4 10–10 6. a) = b) з ч з ч = h) 0.000 028 9 2.89 0.000 01 2.89 10–5 и10ш 10 000 3 9 и ш i) 0.000 000 005 9 5.9 0.000 000 001 5.9 10–9 2 5 ж1ц 1 ж1ц 1 c) d) з ч = з ч = 7 49 2 32 и ш и ш 3 2 ж 1 ц 1 ж3ц 9 e) f) з ч = - з ч = -2 8 2 4 и ш и ш 3 ж4ц 64 g) 54 = 625 h) з ч = 3 27 и ш
Copyright 2006, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher. Extra Practice Answers BLM 1.1 1.1 Real Numbers
1. 4. Answers may vary. 1 1 1 N: 1, , 51 a) , , , and so on. 6 7 21 -4 -8 -13 b) , , , and so on. W: 0, 1, , 51 1 3 4 3 5 7 c) , , , and so on. I: –5, 0, 1, , 51 -16 -16 -16
5. a) 0.09 , 0.18 , 0.27 Q: –5, , , –0.28, b) Answers may vary. The answers are the : 0, 1, , , 51 products of the numerator and 0.09.
6. approximately –0.86C
7. Total sales cost is $250.40 and cost for more milk 1 3 -3 -2 8 2 2. a) < b) < c) = 2 is $120. Total profit will be $130.40. 2 4 5 5 3 3 3 -2 -3 11 5 3 -1 8. The first number, , is a positive value, while the d) > e) > f) < 4 3 4 12 6 -4 8 other three numbers are negative.
1 1 3 3. a) , , 0.59, 9. 18 different numbers in descending order: –2.34, – 2.43, –3.24, –3.42, –4.23, –4.32, –23.4, –24.3, – 3 2 5 32.4, –34.2, –42.3, –43.2, –234, –243, –324, –342, 711 –423, –432. b) 0.71, , 0.71 , 0.7 1000 10. Answers may vary. 0.637, 0.638, 0.639. c) -9.1, -9.01, -8.9, -8.93 d) 0.1 , 0.113, 0.113 , 0.113 4 3 e) - , , 0.375 , 0.37 7 8
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ж1 1ц 2 5 d) Always false. The square of a rational number 1. a) + 4 з + ч 3 = 2 4 is always equal to or greater than 0. 3 и ш 3 b) (0.52 – 0.1) 8 2 = 0.6 e) Always true. Two negative numbers will always multiply to give a positive number c) –2 (18.5 – 6.3) 4 = –6.1 which is greater than any negative number. f) Sometimes true. If at least one of the rational 39 2. a) b) 39 c) 9 numbers is zero, 0 4.2 = 0, then the 2 statement is true. d) 36 e) 36 But 3 1.5 = 4.5, 4.5 ≠ 0. g) Always true. For example, 10 = 10.0, 3. a) 53.64 b) 46.258 c) 12.6 1 d) –6.48 e) 4.5 –3 = –3.0, and = 0.5. 2 1 h) Sometimes true. For example, 3.6 is rational 4. There is 1 pizzas left. but decimals that have non-terminating, non- 8 repeating digits are irrational numbers like 1.786 542 371 69… 39 5. a) 9. 40 117.8 168.2 2.6 53 103.4 b) Gas: $460, Food/hotels: $1104, Tourist 161 31.4 45.8 96.2 110.6 attractions: $230. They have $46 left over. 24.2 37.6 89 140.4 153.8 67.4 81.8 132.2 146.6 17 6. 546 h 74.6 126 175.4 8.8 60.2
7. a) –6.5 C b) –4.5C
8. Answers may vary. a) Sometimes true. If the second number is greater than the first, then the difference will be less than zero. For example, –5 – (–3) = –2. If the second number is less than the first, then the difference will be greater than zero. For example, –5 – (–7) = +2. b) Always true. Natural numbers are greater than zero, so any two added will give a greater number. c) Sometimes true. For example, 5 – 2 = 3, and 3 is an integer, but 2.4 – 0.2 = 2.2, and 2.2 is not an integer.
Copyright 2006, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher. Extra Practice Answers BLM 1.3 1.3 Applications of Square Roots
1. a) i) 7 ii) 2.3 iii) 25 iv) 2.6 v) –3 vi) –8.4 vii) –2.1 viii) –80 b) The square root is negative since you are multiplying by –1.
2. = 4, = –4, and has no answer. 16 - 16 -16 There are no two identical numbers that when multiplied together give a negative number.
3. a) 4.4 b) 9.9 c) 2.4 d) 1.7 e) 25.9 f) 10.8
4. a) 12 cm b) 1 cm
5. a) 12.5 m2 b) 12.5 m2 c) 314 yellow tiles and 556 blue tiles d) $1250.63 e) $1883.13
6. 9.8 m
7. As you subtract the odd numbers in ascending order, the differences between pairs of consecutive differences is also an odd number. The consecutive differences are the odd numbers in ascending order. Eventually, you will have enough differences to reach a final difference of zero. a) 17 b) 24 c) 28 d) 33
Copyright 2006, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher. Extra Practice Answers BLM 1.4 1.4 Working With Exponents
1. a) 612 b) 47 c) 218 d) (–8)20 10. a) 4 b) 62 c) 76 13 d) 106 e) 5 13 18 ж3ц e) y f) (1.6) g) з ч 2 и ш 1 1 11. a) 0.001 b) c) - 2. a) 35 b) (–9)4 c) 73 4 27 d) x5 e) 67 f) y–4 1 16 d) e) 144 25 3. a) 210 b) 4–45 c) (–3)–18 d) (–y)48 1 1 12. a) b) c) 25 18 24 35 14 - 4. a) 4 5 b) 2 5 9 1728 c) 32 910 d) 84 1124 13. Answers may vary. For example, consider 5 = 53 5. a) 144 b) 256 c) 6561 5 5 5 d) 16 e) 243 f) 64 53, which can also be written as ҙ ҙ , and 5 ҙ 5 ҙ 5 6. a) Must add exponents, not multiply. which will simply to 1. b) Do not multiply bases. c) The powers must be multiplied to use the rule 14. 32 34 = (3 3)(3 3 3 3) = 36 = 729 and of adding the exponents. (32)4 = (3 3)(3 3)(3 3)(3 3) = 38 = 6561 d) Not the same base, so cannot add exponents. e) Should have multiplied the exponents, not 15. Answers may vary. For example, if you have 35 added them. 2 3 ҙ 3 ҙ 3 ҙ 3 ҙ 3 f) Forgot that the first base has an exponent of 1. divided by 3 then you would have 3 ҙ 3 and two threes from the numerator and 7. a) 216 b) 315 c) 212 denominator cancel each other out, leaving you d) 56 e) 312 with 3 3 3 or 33, and 5 – 2 = 3. 8. a) 212 b) x5 c) 89 d) m e) 42 5 f) 78 64 g) 219 32 h) y20 x17
9. 1022
Copyright 2006, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher. Extra Practice Answers BLM 1.5 1.5 Scientific Notation
1. 6. Scientific Standard Product in Standard Standard Form Object Result Notation Notation Form 0 1.2 10 m 1.2 m b) 68 000 6.8 10 000 6.8 104 9.9 107 m 99 000 000 m h) 1.1 102 m 110 m d) 380 000 3.8 100 000 3.8 105 1.3 10–6 cm 0.000 001 3 cm c) 9 123 000 9.123 1 000 000 9.123 106 1.5 10–2m 0.015 m f) 11 9.75 10 m 975 000 000 000 m e) 710 000 7.1 100 000 7.1 105 2.0 10–4 m 0.000 2 m a) 9 1.39 1013 km 13 900 000 000 000 km g) 5 370 100 000 5.3701 1 000 000 000 5.3701 10 460 000 000 000 4.6 100 000 000 000 4.6 1011 2. a) 3.7 103 b) 1.5 105 c) 7.35 10-2 –7 5 –2 d) 4.2 10 e) 2.38 10 f) 8.81 10 0.000 000 056 5.6 0.000 000 01 5.6 10–8
3. a) 1.127 10–1 b) 5.612 10–14 c) 1.2 1031 0.0075 7.5 0.001 7.5 10–3 d) 9 10–2 e) 7.728 107 f) 3 105 0.000 000 54 5.4 0.000 000 1 5.4 10–7 g) 5 103 0.000 007 45 7.45 0.000 001 7.45 10–6 4. A number in scientific notation must be written in the form a 10n where a is superior or equal to 1 and less than 10, and must be multiplied by a 7. a) The base is not between 1 and 10. Answer 8 power of 10. should be 5.6 10 . b) The base is not between 1 and 10. Answer 5. Answers may vary. Very large or very small should be 7.9 10–5. numbers are easier to read if they are written in c) Must be a power of 10. Answer should be scientific notation. For example, in standard 2.3 106. notation the number 34 000 000 000 000 000 is d) Must be a power of 10. Answer should be more difficult to read than when written in 4.8 10–6. scientific notation, 3.4 1016.
Copyright 2006, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher. Extra Practice Answers BLM 1.5 1.6 Matrices
1. a) A: 2 2, B: 2 2, C: 4 2, й15 40 10 10щ й45 120 30 30щ D: 4 2, E: 1 4 and F: 3 1 к ъ к ъ b) A(2, 1); B(2, 2); C(4, 1); 2. a) к25 15 10 15ъ b) к75 45 30 45ъ D(3, 2); E(1, 4); F(3, 1) к35 5 25 30ъ к105 15 75 90ъ л ы л ы й-1 0щ c) A + B к ъ 5 3 лк ыъ й12 20 15щ й15 25 21щ к ъ к ъ й5 -2щ 3. a) May к22 10 36ъ June к32 13 10ъ d) A – B = к ъ 1 -3 к18 28 35ъ к6 20 23ъ лк ыъ л ы л ы й4 4 щ й27 45 36щ к ъ 3 -1 к ъ e) C + D = к ъ b) total TV sales к54 23 46ъ к-3 -3ъ к ъ к24 48 58ъ 8 16 л ы лк ыъ й0 -10щ c) Bulk Electronics sold 140 altogether. к ъ -7 1 d) EZTVs sold 130 TV’s among the three stores. f) D – C = к ъ к 5 9 ъ к ъ й120 000 90 000 щ к 2 0 ъ к ъ л ы 4. a) Electronic World 130 000 100 000 g) Answers may vary. Matrix must have к ъ к145 000 110 000ъ dimensions of 1 4. л ы й8 -4щ й90 000 100 000щ h) 4A = к ъ 12 0 к ъ лк ыъ Home of the TV к112 000 107 000ъ й-20щ к138 000 125 000ъ к ъ л ы i) –2F = к-14ъ й30 000щ к -6 ъ к ъ л ы b) Electronic World к30 000ъ й-2 3 щ к35 000ъ к ъ л ы 2 0 j) –D = к ъ й-10 000щ к-1 -3ъ к ъ к ъ Home of the TV к 5 000 ъ -5 -8 лк ыъ к 13 000 ъ k) Answers may vary. For example: л ы c) Home of the TV made only $8000 while й1 4 7 10 13щ Electronic World made $95 000. к ъ к2 5 8 11 14ъ к3 6 9 12 15ъ л ы l) Answers may vary. For example: the high and low temperatures for two days
Copyright 2006, McGraw-Hill Ryerson Limited, a subsidiary of the McGraw-Hill Companies. This page may be reproduced for classroom use by the purchaser of this book without the written permission of the publisher. Extra Practice Answers BLM 1R Chapter 1 Review
1. I –4, 0, 10 7. a) 30 b) 88 Q 3.14…, 6 8. a) 52 b) 2–9 W 0, 10 c) 2 32 d) 38 54 N 10 Q 2 9. a) 1.7 108 b) 1.116 1022 –4, 0, –0.75, 10, 1 , 0.36 3 c) 1.5 1018 d) 6.3 102 e) 5.59 105
- 51 55 5 6 2. a) –0.51, , , 0.5 10. a) 2.016 10 b) 1.4742 10 100 100 c) Explanations may vary. No, some people are unlisted or have more than one phone number, - 2 3 b) , –0.35; –0.33; and some numbers belong to businesses. 3 9 c) –4.379, –4.37, –4.351,–4.35 й104 99 щ к ъ 11. a) к90 108ъ; 3 2 1 3. a) –116 b) –4 c) –2 к75 120ъ 2 л ы 35 й203щ d) –0.15 e) к ъ b) 189 36 к ъ к195ъ 4. 6.3 m л ы 5. 50 m й91.35щ к ъ c) к89.10ъ; Store 1 is most profitable. 6. a) correct к87.75ъ b) Incorrect; can't add powers and use exponents л ы laws. c) Incorrect; different bases, can’t use exponent law or multiply bases. d) correct e) Incorrect; forgot the exponent 1 on the middle term. f) Incorrect; forgot the negative sign.
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1. d)
2. a)
3. c)
4. b)
5. d)
6. a)
7. a) and iii); b) and iv); c) and ii); d) and i)
13 8. 1.30 6 10 red blood cells
9. a) 27; natural, whole, integer, rational b) –2; integer, rational 216 c) - ; rational 100 d) 49.446; rational
10. x = 8.49 m ; y = 7.62 m
11. a) 52.62 m2 b) He will need 1 can of white paint and 3 cans of blue paint. c) $151.75
й5500 4600 8900щ к ъ 12. a) к1400 2300 1800ъ к2300 2000 1200ъ л ы й38 000щ к ъ b) к11 000ъ к11 000ъ л ы c) $5 790 000
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