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Solutions
49 Videos

Sketch models to represent each of the following algebraic expressions. The variables `x`

and `y`

are not equal.

```
\displaystyle
y^2
```

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0.19mins

Q1a

Sketch models to represent each of the following algebraic expressions. The variables `x`

and `y`

are not equal.

```
\displaystyle
y^3
```

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0.35mins

Q1b

Sketch models to represent each of the following algebraic expressions. The variables `x`

and `y`

are not equal.

```
\displaystyle
2x
```

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0.21mins

Q1c

`x`

and `y`

are not equal.

```
\displaystyle
(2x)^2
```

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0.16mins

Q1d

Rob is finishing a floor with square tiles. Each tile has an area of `412 cm^2`

. Estimate the length of the side of each tile.

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0.24mins

Q2

Why do you get the same result for each of the following expressions? Show your work using Exponent Laws.

**(a)** `\displaystyle \frac{5^7}{5^4}`

**(b)** `\displaystyle \frac{5^6}{5^3} `

**(c)** `\displaystyle\frac{(5^4)(5^5)}{5^6} `

**(d)** `\displaystyle\frac{(5^4)(5)}{(5)(5)} `

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0.35mins

Q3

Simplify, and then evaluate for `x = -2`

and `y = 3`

```
\displaystyle
\frac{(x^3)(x^4)}{x^6}
```

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0.15mins

Q4a

Simplify, and then evaluate for `x = -2`

and `y = 3`

```
\displaystyle
\frac{(y^6)(x^4)}{(x^2)(y^4)}
```

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0.28mins

Q4b

Simplify, and then evaluate for `x = -2`

and `y = 3`

```
\displaystyle
\frac{-32x^6}{16x^3}
```

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0.26mins

Q4c

If you know that the product of two numbers is `9^6`

and quotient is `9^2`

, which of the following could be the two numbers?

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0.51mins

Q5

About how long does it take for light to travel from one end of our galaxy to the other?

- It is about
`9.5 \times 10^6 km`

from one end of our galaxy to the other. - Light travels at about
`1.1 \times 10^9 km/h`

.

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0.50mins

Q6

Simplify.

```
\displaystyle
(a^3)^2
```

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0.11mins

Q7a

Simplify.

```
\displaystyle
(4x^3)^4
```

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0.19mins

Q7b

Simplify.

```
\displaystyle
\frac{(2^3y^4)^3}{(2^4y^3)^2}
```

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0.42mins

Q7c

Which of the following is equal to `0`

?

- a)
`(10^3)^5 -(10^5)^3`

- b)
`(9^2)^2-(3^4)^2`

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0.34mins

Q8

Express each of the following as a power with a prime base.

`8^3`

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0.22mins

Q9a

Express each of the following as a power with a prime base.

`25^4`

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0.13mins

Q9b

Express each of the following as a power with a prime base.

`9^3`

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0.13mins

Q9c

The length of the side of a cube is `5^3`

. Express its surface area (SA) and volume (V) using powers and simplify each expression.

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0.45mins

Q10

Simplify.

```
\displaystyle
5y -4y
```

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0.09mins

Q11a

Simplify.

```
\displaystyle
3xy^2 + 3xy^2
```

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0.15mins

Q11b

Simplify.

```
\displaystyle
2x^2 - 5x + 5x^2 -x
```

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0.17mins

Q11c

Simplify.

```
\displaystyle
y^2 + 5xy + y^2 - xy
```

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0.14mins

Q11d

Simplify.

```
\displaystyle
\frac{4}{5}a - \frac{1}{5}a
```

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0.14mins

Q12a

Simplify.

```
\displaystyle
2\frac{1}{2}a + \frac{2}{3}b + \frac{1}{2}a-\frac{1}{3}b
```

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0.28mins

Q12b

Simplify.

```
\displaystyle
-1.75m + 2.7 -2.25m + 2.3
```

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0.21mins

Q12c

Mindy and Kimberly have a picture framing business. Mindy cuts the wooden frames. She charges `\$ 25`

for each one plus `\$10/h`

for her labour. Kimberly cuts the picture mats and assemblies the product. She assembles $ 8 for each mat plus `\$ 9/h`

for her labour.

**(a)** Represent Mindy's bill as a polynomial.

**(b)** Represent Kimberly's bit las a polynomial.

**(c)** Write a new polynomial that represents their total charge to dream a picture. Assume that they both work h hours on the frame.

**(d)** Calculate the cost for a frame if they both work 5 h on it.

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1.14mins

Q13

Expand. check one of your answer using a different tool or strategy.

`3(y - 2)`

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0.12mins

Q14a

Expand. check one of your answer using a different tool or strategy.

`x(2x+ 4)`

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0.14mins

Q14b

Expand. check one of your answer using a different tool or strategy.

`5m(3m^3 + 2n)`

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0.29mins

Q14c

Expand. check one of your answer using a different tool or strategy.

`-3x(x^2 -x)`

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0.26mins

Q14d

Expand. check one of your answer using a different tool or strategy.

`2y^3(y^3 + 3y^2 - y)`

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0.30mins

Q14e

Expand. check one of your answer using a different tool or strategy.

`-a^2(2a -5a^2+4a^3)`

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0.36mins

Q14f

Expand.

```
\displaystyle
\frac{1}{3}(3x +12)
```

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0.16mins

Q15a

Expand.

`\displaystyle \frac{2}{5}(\frac{5}{8}a +10b)`

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0.24mins

Q15b

Expand.

`-1.5m(2.8m + 2.2)`

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0.29mins

Q15c

Rick runs a pet store and is building rectangular pens for the animals. The length of the pens is always 20 cm longer than the width.

**(a)** One way of determining the perimeter is to use `P = 2(l + w)`

. Use this formula to create an expression for the perimeter in terms of x.

**(b)** Simplify your formula in part (a).

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0.26mins

Q16ab

Rick runs a pet store and is building rectangular pens for the animals. The length of the pens is always 20 cm longer than the width.

- Find the perimeter of a pen with a width of 45 cm.

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0.22mins

Q16c

Expand and simplify. Check one of your answers using a different tool or strategy.

`2(x - 3) + 3(x + 2)`

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0.16mins

Q17a

Expand and simplify. Check one of your answers using a different tool or strategy.

`3(y^2 + y-2)-(y^2+2y+4)`

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0.37mins

Q17b

Expand and simplify. Check one of your answers using a different tool or strategy.

`2x(3x - 2) + x^2 + 2(x^2+3)`

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0.33mins

Q17c

Expand and simplify. Check one of your answers using a different tool or strategy.

`3x(4x^2-5x) + x^3 -x^2`

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0.27mins

Q17d

Ms. Smith needs fabric pieces for an art project for her students. The pieces will be cut to two rectangular sizes, as shown.

Determine a simplified expression for the area of fabric needed if 14 students choose the larger size and 12 choose the smaller size.

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1.00mins

Q18a

Ms. Smith needs fabric pieces for an art project for her students. The pieces will be cut to two rectangular sizes, as shown.

The class decides that the width of each piece of fabric will be 20 cm. Use your answer from part a) to determine how much material will be needed.

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0.40mins

Q18b

Expand and simplify.

`\displaystyle \frac{1}{4}(8x - 12) -\frac{1}{2}(6 - 14x)`

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0.30mins

Q19a

Expand and simplify.

`\displaystyle \frac{5}{6}(6x - 18y) +\frac{2}{3}(21x - 6y)`

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0.42mins

Q19b

Expand and simplify.

`\displaystyle \frac{5}{6}(6x - 18y) +\frac{2}{3}(21x - 6y)`

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1.13mins

Q19c

Mike has a baseball card collection. He is wondering about the future value of his rookie and big star cards.

Write an expression that represents the combined value of these cards in y years.

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1.38mins

Q20a

Mike has a baseball card collection. He is wondering about the future value of his rookie and big star cards.

Determine the combined value of the cards in 6 years.

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0.22mins

Q20b