Practice Test on Quadratic Expressions
Chapter
Chapter 5
Section
Practice Test on Quadratic Expressions
Purchase this Material for $4
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^205m + 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 square—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 9x3 - 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