Chapter Review
Textbook
9 Math workbook
Chapter
Chapter 3
Section
Chapter Review
Solutions 63 Videos

Use algebra tiles to build a model for each situation. Write an algebraic expression to represent the model. Sheila swam \displaystyle 5 \mathrm{~km} .

Q1a

Use algebra tiles to build a model for each situation. Write an algebraic expression to represent the model. Ursula walked an unknown distance,

three times.

Q1b

Use algebra tiles to build a model for each situation. Write an algebraic expression to represent the model. Tasnia drove \displaystyle 5 \mathrm{~km}  plus an unknown distance.

Q1c

Use algebra tiles to build a model for each situation. Write an algebraic expression to represent the model. Susu read a book twice.

Q1d

a) Build a volume model to represent a cube with side length \displaystyle 4 \mathrm{~cm} .  Sketch the model and label the length,

width, and height.

b) What is the volume of the cube?

Write this as a power.

c) Write an expression for the area of

one face of the cube as a power.

Evaluate the area of one face.

d) Write an expression for the surface

area of the cube. Evaluate the surface

area of the cube.

Q2

Evaluate.

\displaystyle 5^{3}

Q3a

Evaluate.

\displaystyle (-2)^{6}

Q3b

Evaluate.

\displaystyle \left(\frac{3}{4}\right)^{3}

Q3c

Evaluate.

\displaystyle 1.06^{5}

Q3d

Write as a single power. Then, evaluate the expression.

\displaystyle 3^{2} \times 3^{3} \times 3

Q4a

Write as a single power. Then, evaluate the expression.

5^6 \div 5 \div 5^2

Q4b

Write as a single power. Then, evaluate the expression.

4^6 \div 4^5 \times 4^2

Q4c

Write as a single power. Then, evaluate the expression.

4^6 \div 4^5 \times 4^2

Q4d

Write as a single power. Then, evaluate the expression.

[(-3)^2]^3

Q4e

Write as a single power. Then, evaluate the expression.

\dfrac{(5^4)^3}{5^5 \times 5^4}

Q4f

E. coli is a type of bacteria that can cause dangerous health problems. It doubles every 20 min. The initial population of a sample of E. coli is 400.

a) Copy and complete this table.

\displaystyle \begin{array}{|c|c|} \hline Time (min) & \text{Population of E. coli} \\ \hline 0 & 400 \\ \hline 20 & 800 \\ \hline 40 & \\ \hline 60 & \\ \hline 80 & \\ \hline 100 & \\ \hline 120 & \\ \hline \end{array} 

b) Construct a graph of population versus time. Use a smooth curve to connect the points. Describe the shape of the graph.

c) What will the population be after

• 5 h?

• 8 h?

Q5

Simplify.

a^5b^4 \times a^3b^2

Q6a

Simplify.

\dfrac{d^6 \times d^5}{d^7}

Q6b

Simplify.

\dfrac{m^{10}}{m^3 \times m^5}

Q6c

Simplify.

\dfrac{(y^6)^3}{(y^5)^2}

Q6d

Identify the coefficient and variable part of each term.

6x

Q7a

Identify the coefficient and variable part of each term.

-5y

Q7b

Identify the coefficient and variable part of each term.

7

Q7c

Identify the coefficient and variable part of each term.

4a^5b^3

Q7d

Identify the coefficient and variable part of each term.

dm

Q7e

Identify the coefficient and variable part of each term.

\dfrac{2}{3}x^2y^3

Q7f

In a hockey tournament, teams are awarded 4 points for a win and 2 points for an overtime win.

a) Write an expression that describes the number of points a team has.

b) Use your expression to find the number of points earned by a team that has five wins and two overtime wins.

Q8

State the degree of each term.

5x^4

Q9a

State the degree of each term.

-7m^5

Q9b

State the degree of each term.

a^3b^2c

Q9c

State the degree of each term.

5

Q9d

State the degree of each polynomial.

5x+4

Q10a

State the degree of each polynomial.

3y^4-2

Q10b

State the degree of each polynomial.

5m^2+3m+6

Q10c

State the degree of each polynomial.

6a^3-5a^2+4a-3

Q10d

Classify each pair of terms as either like or unlike.

3x and -7x

Q11a

Classify each pair of terms as either like or unlike.

4y and 5z

Q11b

Classify each pair of terms as either like or unlike.

4ab and -2ab

Q11c

Classify each pair of terms as either like or unlike.

3x^2y and 4xy^2

Q11d

Classify each pair of terms as either like or unlike.

5xy and 3yx

Q11e

Classify each pair of terms as either like or unlike.

5m^2 and 8m^2

Q11f

Identify the like terms in each set.

5a^2, -3b, 2d, 6x^2, 7b^3, -5x^2, 4a, 6c

Q12a

Identify the like terms in each set.

6y^2, 5y^2, -4y^3, 3, -4y^2, -2y^3

Q12b

Simplify by collecting like terms.

3x+5y+4x+6y

Q13a

Simplify by collecting like terms.

5d+3m-4d-5m

Q13b

Simplify by collecting like terms.

2a^2-5a+3-a^2+2a-6

Q13c

Simplify by collecting like terms.

3w^2+2wy-y^2-2w^2-2wy+4y^2

Q13d

Simplify by collecting like terms.

4d-8e-6f+3d+5e-10f

Q13e

Simplify by collecting like terms.

6a^3-4ab+5b^2-3+5a^3-3ab

Q13f

Simplify.

(5x+3)+(6x-4)

Q14a

Simplify.

(4y-3)+(5y-2)

Q14b

Simplify.

(3p^2+5p+4)+(7p^2-4p-3)

Q14c

Simplify.

(4m^2-3mn-2n^2)-(m^2+mn-5n^2)

Q14d

Simplify.

(6a+8b)+(3a-4b)-(5a-3b)

Q14e

A rectangular cake has dimensions 4x by 3x+2. Find a simplified expression for its perimeter.

Q15

Expand.

5(x+2)

Q16a

Expand.

-4(y-3)

Q16b

Expand.

2m(3m+4)

Q16c

Expand.

-4g(2g-3)

Q16d

Expand and simplify.

4(2x+3y)+5(3x+6y)

Q17a

Expand and simplify.

3(4y-2w)-3(2y+1)

Q17b

Expand and simplify.

4(3a+2b)+3(2a-3b)-(a+2b)

-4[3-2(c+5)-4c]