Extra Practice 1

Transcription

Extra Practice 1

Name
Master 1.18
Date
Extra Practice 1
Lesson 1.1: Numbers in the Media
1. Use mental math to evaluate.
a) 64 + 78
b) 2978 – 1988
c) 274 + 196
d) 296 – 82
e) 5 × 7 × 20
f) 4 × 25 ÷ 10
2. Evaluate. Describe the strategies you used.
a) 129 + 71
b) 18 × 23
c) 324 – 169
d) 666 + 444
e) 6943 ÷ 100
f) 75% of 400
3. In 2004, 6634 fires destroyed 3 277 181 ha of Canada’s forests.
Estimate the mean area destroyed by each fire.
4. In 2004, different regions of British Columbia reported that forest fires destroyed
these areas: 2437 ha, 89 272 ha, 75 573 ha, 16 176 ha, 778 ha, and 36 274 ha
Approximately how many hectares were destroyed in British Columbia?
5. This table shows the number of people the chairlift can transport per hour at
various ski resorts.
Resort
Number of People per Hour
Blue Ridge
19 000
Mount Ellen
59 000
New Ridge
23 000
Big Tree
5 500
Bear Mountain
12 000
Mount Biggar
6 500
a) What is the total number of people who can be transported in 1 h?
b) How many people can be transported in 3 h at Big Tree Resort?
c) Which resort has about double the capacity of Bear Mountain Resort?
d) Which resort has about one-third the capacity of Blue Ridge Resort?
6. This table gives the highest elevations in different regions of Canada.
Location
Mount Logan, Yukon
Highest Elevation (m)
5959
Barbeau Peak, Nunavut
2616
Fairweather Mountain, BC
4663
Ishpatina Ridge, Ontario
693
a) How much higher is Mount Logan than Fairweather Mountain?
b) What is the approximate ratio of the height of Mount Logan to the height of Barbeau Peak?
c) About how many times as high as Ishpatina Ridge is Fairweather Mountain?
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Name
Master 1.19
Date
Extra Practice 2
Lesson 1.2: Prime Factors
1.
2.
3.
4.
Write each product as a number in standard form.
a) 32  53
b) 23  5  73
c) 24  72  11
d)
33  52  7
List the prime factors of each number.
a) 45
b) 84
c)
d)
63
Write each number as a product of prime factors.
Use exponents where possible.
a) 96
b) 220
c) 144
d)
126
Find all the common factors of each pair of numbers.
a) 16, 24
b) 36, 60
c) 45, 75
d)
36, 54
90
5.
Find the first 4 common multiples of the numbers in each pair of numbers in question 4.
6.
a) Write 180 as a product of prime factors.
b) List all the factors of 180.
7.
Write three other numbers that have the same prime factors as 28.
8.
a) Find the least number with factors 15, 33, and 45.
b) Write the prime factorization of this number.
9.
a) Write a 5-digit number that is divisible by 11 and 13.
b) Write the prime factorization of this number.
10. a)
Find the least 3-digit number that has 2, 3, and 7 as factors.
Write the prime factorization of the number.
b) Find the greatest 3-digit number that has 2, 3, and 7 as factors.
Write the prime factorization of the number.
Is 32  62 a prime factorization of 324?
If yes, explain how you know.
If no, write the prime factorization of 324.
b) Use the prime factors to list all the factors of 324.
11. a)
Name
Master 1.20
Date
Extra Practice 3
Lesson 1.3: Expanded Form and Scientific Notation
1.
2.
Write each number in expanded form using powers of 10.
a) 37 298
b) 1073
c) 52 611
d)
100 327
Write each number in scientific notation.
a) 17
b) 3 457 000
c)
d)
5 003 200
27 003
3.
Add 4 364 300, 1 295 600, 847 900, and 984 200.
Write the answer in scientific notation.
4.
Order the numbers in each set from greatest to least.
a) 1.81 × 103, 8.1 × 102, 1809
b) 7.1 × 103, 7.11 × 103, 7.01 × 103
c) 4.267 × 106, 4 267 100, 4.268 × 106
5.
For each power of 10, write the exponent that makes each statement true.
a) 3 875 000 = 3.875 × 10?
b) 6927 = 6.927 × 10?
c) 7007 = 7.007 × 10?
d) 39 436 = 3.9436 × 10?
6.
a) 32.7 × 102
b) 576 × 103
c) 628.4 × 101
d) 1876 × 104
7.
These facts from Guinness World Records 2005 involve large numbers.
a) The largest keychain collection consists of 24 810 different keychains.
b) The largest collection of cat memorabilia consists of 11 717 cat-related items.
c) The longest paper chain was 83.36 km long and consisted of 584 000 links.
Name
Master 1.21
Date
Extra Practice 4
Lesson 1.4: Order of Operations
1.
2.
Evaluate.
a) 5 × 7 – 13
c) 48 ÷ 6 × 2
e) 38 – (18 + 7)
b) 3 × 5 + 6 × 4
d) 8 + 5(3 + 4)
f) 96 ÷ (4 × 12)
Evaluate.
a) 5.4 – 3.2 + 1.52
c) 13.8 – (6.3 – 2.7)2
e) 39.2 ÷ 2.82
b) 2.7 × 5.8 ÷ 8.7
d) (6.5 + 3.5)2 – (6.5 – 3.5)2
f) 30.8 ÷ 2.8 × 2.2
3.
Insert brackets to make each statement true.
a) 40 ÷ 2 + 3 × 22 – 3 = 29
b) 40 ÷ 2 + 3 × 22 – 3 = 23
c) 40 ÷ 2 + 3 × 22 – 3 = 53
d) 40 ÷ 2 + 3 × 22 – 3 = 89
4.
A model rocket is launched from ground level.
The approximate height reached by the rocket depends on the time since it was launched.
When the time is t seconds, the rocket’s height above the ground, in metres, is expressed as
25t – 5t2.
Find the height of the rocket after each time.
a) 1.5 s
b) 2.5 s
c) 4.5 s
5.
Use the numbers 3, 5, 7, and 9 and any operations or brackets to make each whole number
from 1 to 10.
6.
At a book sale, magazines sell for $1.25 each, paperbacks sell for $2.75 each, and hardcover
books sell for $4.25 each. Carla bought 4 magazines, 4 paperbacks, and 2 hardcover books.
a) Write an expression to show how much Carla spent.
b) Evaluate the expression. How much did Carla spend?
7.
The cost in dollars for a medium pizza can be expressed as 8.49 + 1.59n; where $8.49 is the
cost of the basic pizza, $1.59 is the cost of each additional topping, and n is the number of
additional toppings.
How much will it cost for a medium pizza with:
a) 3 additional toppings?
b) 5 additional toppings?
c) 6 additional toppings?
Name
Master 1.22
Date
Extra Practice 5
Lesson 1.5: Using a Model to Solve Equations
1.
2.
3.
Find the value of the unknown mass on each two-pan balance.
a)
b)
c)
d)
Solve each equation.
a) x – 6 = 11
d) x – 8 = 13
b) x + 6 = 11
e) x – 17 = 23
Solve each equation. Verify the solution.
a) x + 11 = 8 + 5
c) 9 – 5 = x – 7
4.
Seven more than a number is 19.
Let x represent the number.
Then an equation is 7 + x = 19.
Solve the equation. What is the number?
5.
Two less than a number is 14.
Then an equation is x – 2 = 14.
c) x + 8 = 13
f) x + 17 = 23
b) x – 5 = 4 + 3
d) 11 – 4 = 6 + x
Name
Master 1.23
Date
Extra Practice 6
Lesson 1.6: Using Algebra Tiles to Solve Equations
1.
Use algebra tiles to solve each equation.
a) x + 3 = 7
b) x – 4 = 5
c) 9 = x + 4
d) 5 = x – 2
2.
Use algebra tiles to solve each equation.
a) 2x + 5 = 11
b) 3x – 4 = 5
c) 7 = 4x – 1
d) 11 = 2 + 3x
3.
Solve each equation algebraically.
Verify the solution.
a) x + 4 = 9
b) x – 12 = 7
c) 13 = x – 7
d) 9 = x – 11
4.
Solve each equation algebraically.
Verify the solution.
a) 3x + 2 = 14
b) 2x – 7 = 13
c) 7 = 4x – 5
d) 18 = 9 + 3x
5.
Four more than three times a number is 13.
Then, an equation is 13 = 3x + 4.
6.
The perimeter of an isosceles triangle is 11 cm.
Exactly one side has length 3 cm.
Let x represent the length of each of the two equal sides, in centimetres.
Then, an equation to represent the perimeter is 3 + 2x = 11.
Solve the equation. What is the length of each of the two equal sides?
7.
Five less than three times a number is 1.
Then, an equation is 3x – 5 = 1.
8.
Two more than four times a number is 11.
Then, an equation is 4x + 2 = 18.
Name
Master 1.24
Sample Answers
Extra Practice 1 – Master 1.18
Lesson 1.1
1. a)
d)
2. a)
b)
c)
d)
e)
f)
3.
4.
5.
6.
Date
b) 990
c) 470
142
e) 700
f) 10
214
200; 129 + 71 = 130 + 70 = 200
414; I used pencil and paper.
155; I used pencil and paper.
1110; 666 + 444 = 700 + 410 = 1110
69.43; I used mental math.
300; I used mental math:
400  4 = 100, and 100  3 = 300
About 500 ha; 3 000 000  6000 = 500
About 220 000 ha; I rounded each area to the nearest
thousand.
a) 125 000 people
b) 16 500 people
c) New Ridge Resort d) Mount Biggar Resort
a) 1296 m b) About 2:1 c) About 7 times
Lesson 1.2
1. a) 1125
b) 13 720 c) 8624
d) 4725
2. a) 3, 5
b) 2, 3, 7
c) 2, 3, 5 d) 3, 7
3. a) 25  3
b) 22  5  11
4
2
c) 2  3
d) 2  32  7
4. a) 2, 4, 8
b) 2, 3, 4, 6, 12
c) 3, 5, 15 d) 2, 3, 6, 9, 18
5. a) 48, 96, 144, 192
b) 180, 360, 540, 720
c) 225, 450, 675, 900 d) 108, 216, 324, 432
6. a) 22  32  5
b) 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45,
60, 90, 180
7. Any number that is a multiple of 14, for example:
14, 56, 196
8. a) 495
b) 495 = 32  5  11
9. a) For example, 21 450
b) 21 450 = 2  3  52  11  13
10. a) 126; 126 = 2  32  7
b) 966; 966 = 2  3  7  23
11. a) No, 6 is not a prime factor. 324 = 22  34
b) 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, 81, 108,
162, 324
Lesson 1.3
1. a) 3  104 + 7  103 + 2  102 + 9  101 + 8
b) 1  103 + 7  101 + 3
c) 5  104 + 2  103 + 6  102 + 1  101 + 1
d) 1  105 + 3  102 + 2  101 + 7
2. a) 1.7 × 101
b) 3.457 × 106
4
c) 2.7003 × 10
d) 5.0032 × 106
6
3. 7.492  10
4. a)
b)
c)
5. a)
6. a)
c)
7. a)
c)
1.81  103, 1809, 8.1  102
7.11  103, 7.1  103, 7.01  103
4.268  106, 4 267 100, 4.267  106
b) 3
c) 3
d) 4
6
b) 5.76  105
3.27  103
d) 1.876  107
6.284  103
4
b) 1.1717  104
2.481  10
1
8.336  10 ; 5.84  105
Lesson 1.4
1. a) 22
b) 39
c) 16
d) 43
e) 13
f) 2
2. a) 4.45
b) 1.8
c) 0.84
d) 91
e) 5
f) 24.2
3. a) 40  (2 + 3)  22 – 3 = 29
b) 40  2 + 3  (22 – 3) = 23
c) 40  2 + (3  2)2 – 3 = 53
d) (40  2 + 3)  22 – 3 = 89
4. a) 26.25 m b) 31.25 m
c) 11.25 m
5. For example: 9 + 7 – (3  5) = 1;
(9 + 7)  (3 + 5) = 2;
(9 – 3)  (7 – 5) = 3; 9 + 5 – 3 – 7 = 4;
7  (5 – 3) – 9 = 5; 3 + 5 + 7 – 9 = 6;
(5 + 7 + 9)  3 = 7; 9 + 7 – 5 – 3 = 8;
9  (5 + 3 – 7) = 9; 9 + 5 + 3 – 7 = 10
6. a) 4(1.25) + 4(2.75) + 2(4.25)
b) $24.50
7. a) $13.26 b) $16.44 c) $18.03
Lesson 1.5
1. a) A = 17 b) B = 12
2. a) x = 17
b) x = 5
d) x = 21
e) x = 40
3. a) x = 2
b) x = 12
4. x = 12; the number is 12.
c)
c)
f)
c)
C=3
x=5
x=6
x = 11
d) D = 10
d) x = 1
Lesson 1.6
1.
2.
3.
4.
5.
6.
a) x = 4
b) x = 9
c) x = 5
d) x = 7
a) x = 3
b) x = 3
c) x = 2
d) x = 3
a) x = 5
b) x = 19 c) x = 20 d) x = 20
a) x = 4
b) x = 10 c) x = 3
d) x = 3
x = 3; the number is 3.
x = 4; the length of each of the two equal sides
is 4 cm.

Extra Practice 1

Transcription

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