Chapter Review on Algebra
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8 Math AW
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Chapter 1
Section
Chapter Review on Algebra
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Solutions 46 Videos

Here are some data about voluntary organizations in 2003:

Canadians took out 139 000 000 memberships in these organizations.

Nineteen million Canadians contributed more than 2 000 000 000 h of voluntary time.

These organizations had $112 000 000 000 in revenues.

Write a problem with these data. Solve your problem. Justify the strategy you used.

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Q1

Write each number as a product of prime factors.

64

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Q2a

Write each number as a product of prime factors.

42

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Q2b

Write each number as a product of prime factors.

60

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Q2c

Write each product in standard form.

\displaystyle2^{4} x 3

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Q3a

Write each product in standard form.

\displaystyle5^{2} x 2^{2}

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Q3b

A number has 11 and 23 as factors.

a) Which is the least number this could be?

b) Which is the greatest number with these factors that can be displayed on your calculator?

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Q4

Which expression shows the prime factorization of 600? Explain.

a) \displaystyle1 x 2^{3}x 3 x 5^{2}

b) \displaystyle2^{2}x 3 x 5^{2}

c) \displaystyle2^{3}x 5^{2} x 3

d) \displaystyle2x 2 x 2 x 75

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Q5

For each pair of numbers below:

i) Find all the common factors.

ii) Find the first 3 common multiples.

15, 35

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Q6a

For each pair of numbers below:

i) Find all the common factors.

ii) Find the first 3 common multiples.

20, 100

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Q6b

For each pair of numbers below:

i) Find all the common factors.

ii) Find the first 3 common multiples.

25, 75

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Q6c

For each pair of numbers below:

i) Find all the common factors.

ii) Find the first 3 common multiples.

30, 36

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Q6d

a) Find two pairs of numbers for which the lowest common multiple is the product of the numbers.

b) Find two pairs of numbers for which the lowest common multiple is less than the product of the numbers.

c) How can you tell if the lowest common multiple of two numbers is less than or equal to the product of the numbers?

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Q7

Here are the areas of the ten largest lakes in the world, tot he nearest 100 km^{2}.

a) Order the lakes from the greatest area to the least area. Explained how you did this.

b) Which two lakes together have an area approximately equal to that of Lake Superior? How do you know?

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Q8

Write each number in expanded form using powers of 10.

9 337 000

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Q9a

Write each number in expanded form using powers of 10.

977 183

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Q9b

Write each number in expanded form using powers of 10.

106 040 055

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Q9c

Write each number in expanded form using powers of 10.

73 532

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Q9d

Write each number in scientific notation.

1 500 000

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Q10a

Write each number in scientific notation.

42 000

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Q10b

Write each number in scientific notation.

600 000 000

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Q10c

Write each number in scientific notation.

27

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Q10d

Write each number in standard form.

6 x 10^{3}

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Q11a

Write each number in standard form.

8.43 x 10^{6}

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Q11b

Write each number in standard form.

7.2 x 10^{5}

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Q11c

Write each number in standard form.

3.28 x 10^{8}

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Q11d

Evaluate.

\displaystyle83 - 6 x 11

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Q12a

Evaluate.

\displaystyle15 + (3 + 12) x 6

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Q12b

Evaluate.

\displaystyle(20 - 9)^{2} - 3 x 2

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Q12c

Evaluate.

\displaystyle1.3 + 4.1^{2} - 15

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Q12d

A rectangular lot has a river along one side.

The fencing for the other 3 sides has a total length of 30 m. When the width of the lot is w metres, the area of the lot, in square metres, is expressed as \displaystyle30w - 2w^{2}.

What is the area of the lot for each value of w?

a) 5 m

b) 9 m

c) 12 m

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Q13

Solve each equation.

x + 2 = 7

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Q14a

Solve each equation.

x - 3 = 5

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Q14b

Solve each equation.

\displaystyle13 = 4 + x

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Q14c

Solve each equation.

\displaystyle7 = x - 2

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Q14d

Ruby collects foreign stamps. Her friend gives her 8 stamps. Ruby then has 21 stamps.

How many stamps did Ruby have to start with?

Let x represent the number of stamps.

Then, an equation is \displaystyle8 + x = 21.

Solve the equation. Answer the question.

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Q15

Solve each equation. Verify the solution.

\displaystyle3 + 11 = 5 + x

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Q16a

Solve each equation. Verify the solution.

x - 3 = 11 - 8

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Q16b

Solve each equation. Verify the solution.

\displaystyle16 - 9 = x + 4

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Q16c

Solve each equation. Verify the solution.

x - 7 = 8 - 5

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Q16d

Solve each equation. Verify the solution.

\displaystyle6 + 3x = 17 - 2

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Q17a

Solve each equation. Verify the solution.

\displaystyle9 + 12 = 2x - 1

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Q17b

Solve each equation. Verify the solution.

\displaystyle5x - 3 = 9 - 2

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Q17c

Solve each equation. Verify the solution.

14 - 3 = 4x + 7

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Q17d

One paperback book costs $7. How many books can be bought for $133?

Let x represent the number of books.

Then, an equation is \displaystyle7x = 133.

Solve the equation. Answer the question.

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Q18

Leah has 26 hockey cards.

Leah has 1 fewer than 3 times the number her brother, Robert, has. How many cards does Robert have?

Let x represent the number of cards Robert has.

Then, an equation is \displaystyle3x - 1 = 26.

Solve the equation. Answer the question.

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Q19