Chapter

Chapter 5
Section

Practice Test on Quadratic Expressions

Purchase this Material for $4

You need to sign up or log in to purchase.

Subscribe for All Access
You need to sign up or log in to purchase.

Solutions
44 Videos

What binomial product does each diagram illustrate?

Buy to View

Q1a

What binomial product does each diagram illustrate?

Buy to View

Q1b

Simplify.

```
\displaystyle
4x^2(3x -5y + 8z)
```

Buy to View

Q2a

Simplify.

```
\displaystyle
3m(6m^2-5m + 4) -(4m^3 - 8m^2 + 9)
```

Buy to View

Q2b

Expand and simplify.

```
\displaystyle
(y + 5)(y+ 9)
```

Buy to View

Q3a

Expand and simplify.

```
\displaystyle
(4x -7)(3x + 2)
```

Buy to View

Q3b

Expand and simplify.

```
\displaystyle
(6k + 1)(6k -1)
```

Buy to View

Q3c

Expand and simplify.

```
\displaystyle
(w -8)^2
```

Buy to View

Q3d

Expand and simplify.

```
\displaystyle
(4c + 5d)^2
```

Buy to View

Q3e

Expand and simplify.

```
\displaystyle
2(x -4)(x - 7)-5(8x -9)(8x + 9)
```

Buy to View

Q3f

The minimum stopping distance, after a delay of 1 s, for a particular car is
modelled by the formula `d = 0.006(s + 1)^2`

, , where `d`

represents the stopping distance, in metres, and s represents the initial speed, in kilometres per hour.

a) Expand and simplify the formula.

b) Compare the results in both versions of the formula for an initial speed of 60 km/h.

Buy to View

Q4

Factor.

```
\displaystyle
9d^2e^2 +6d^3e
```

Buy to View

Q5a

Factor.

```
\displaystyle
15p^2qr^3-25p^3q^2r + 5pqr
```

Buy to View

Q5b

Factor.

```
\displaystyle
5(x + 6)-2(x + 6)
```

Buy to View

Q5c

Factor.

```
\displaystyle
16x^2 + 8x -6x -3
```

Buy to View

Q5d

a) Find an algebraic expression for the surface area of the squareâ€”based prism.

b) Expand and simplify your expression from part a).

c) Factor the resulting expression from part b).

Buy to View

Q6

Factor.

```
\displaystyle
x^2 + 11x + 24
```

Buy to View

Q7a

Factor.

```
\displaystyle
y^2 -15y + 56
```

Buy to View

Q7b

Factor.

```
\displaystyle
n^2 - n - 90
```

Buy to View

Q7c

Factor.

```
\displaystyle
x^2 -14x + 49
```

Buy to View

Q7d

Factor.

```
\displaystyle
h^2 -100
```

Buy to View

Q7e

Factor.

```
\displaystyle
d^3 + 16d + 64
```

Buy to View

Q7f

Factor fully.

```
\displaystyle
3k^2 + 12km -36 m^2
```

Buy to View

Q8a

Factor fully.

```
\displaystyle
8y^2 + 19y + 6
```

Buy to View

Q8b

Factor fully.

```
\displaystyle
9w^2-24w + 7
```

Buy to View

Q8c

Factor fully.

```
\displaystyle
25a^2 + 60a + 36
```

Buy to View

Q8d

Factor fully.

```
\displaystyle
121w^2 - 144
```

Buy to View

Q8e

Factor fully.

```
\displaystyle
10x^2 -7xy - 6y^2
```

Buy to View

Q8f

Explain how to determine whether or not you can factor `9x^2 - 10x + 18`

over the integers.

Buy to View

Q9

The area of a rectangle is given as `x^2 + 13x - 30`

.

a) Determine polynomials that represent the length and width of the rectangle.

b) What is the smallest integer value of `x`

for which this area expression makes sense?

Buy to View

Q10

Determine all values of `k`

so that each trinomial is a perfect square.

```
\displaystyle
36x^2 + kx + 121
```

Buy to View

Q11a

Determine all values of `k`

so that each trinomial is a perfect square.

```
\displaystyle
49k^2 -56d + k
```

Buy to View

Q11b

Determine all values of `k`

so that each trinomial is a perfect square.

```
\displaystyle
25x^2 -60xy + ky^2
```

Buy to View

Q11c

Determine all values of `k`

so that each trinomial is a perfect square.

```
\displaystyle
ka^2 +30ab + 9b^2
```

Buy to View

Q11d

a) Write an algebraic expression for the area of the shaded region.

b) Write the area expression in factored form.

c) Substitute `x = 7`

into both forms. Are the results the same? Why?

Buy to View

Q12

A parabola has equation ```
\displaystyle
y = 2(x + 6)^2 -2
```

a) Expand and simplify to write the equation in the form `y =ax^2 + bx + c`

.

b) Factor your equation from part a).

c) Do the three equations represent the same parabola? Justify your response.

Buy to View

Q13

The volume of a rectangular prism is given as `9x^3 - 30x^2 + 25x`

.

a) Determine algebraic expressions for the dimensions.

b) Describe the faces of the prism.

Buy to View

Q14

Determine two values of `k`

so that the trinomial can be factored as a difference of squares.

```
\displaystyle
km^2 -25
```

Buy to View

Q15a

Determine two values of `k`

so that the trinomial can be factored as a difference of squares.

```
\displaystyle
16d^2 -k
```

Buy to View

Q15b

Determine two values of `k`

so that the trinomial can be factored as a difference of squares.

```
\displaystyle
a^2 -kb^2
```

Buy to View

Q15c

Factor to evaluate the difference.

```
\displaystyle
34^2-31^2
```

Buy to View

Q16a

Factor to evaluate the difference.

```
\displaystyle
127^2-126^2
```

Buy to View

Q16b

The first three diagrams in a pattern are shown.

a) Write a formula for the total number of small squares in the nth diagram.

b) Write a formula for the number of shaded small squares in the nth diagram.

c) Write a formula for the number of unshaded small squares in the nth diagram.

d) Write your formula from part c) in factored form.

e) Show that both forms of the formula give the same results for the 15th diagram.

Buy to View

Q17

a) Find all values of b so that `x^2 + bx + 10`

can be factored over the integers.

b) Find all values of b so that `4y^2 + by + 5`

can be factored over the integers.

c) Write an algebraic expression for the shaded area. Then, write the expression in factored form.

Buy to View

Q18