Chapter 5 Practice Test
1. What binomial product does each diagram
5. Factor.
illustrate?
a) 9d2e2 " 6d3e
a)
b) 15p2qr3 ! 25p3q2r " 5pqr
c) 5(x " 6) ! 2(x " 6)
d) 16x2 " 8x ! 6x ! 3
KNOWLEDGE
6. a) Find an algebraic expression for the
surface area of the square-based prism.
x
APPLICATION
3x + 4
3x + 4
b)
x
b) Expand and simplify your expression
4
from part a).
c) Factor the resulting expression from
part b).
x
7. Factor.
3
2. Simplify.
a) x2 " 11x " 24
KNOWLEDGE
a) 4x2(3x ! 5y " 8z)
b) 3m(6m2 ! 5m " 4) ! (4m3 ! 8m2 " 9)
3. Expand and simplify.
c) n2 ! n ! 90
KNOWLEDGE
d) x2 ! 14x " 49
e) h2 ! 100
f) d2 " 16d " 64
a) (y " 5)(y " 9)
KNOWLEDGE
8. Factor.
b) (4x ! 7)(3x " 2)
c) (6k " 1)(6k ! 1)
b) y2 ! 15y " 56
KNOWLEDGE
d) (w ! 8)2
e) (4c " 5d)2
f) 2(x ! 4)(x ! 7) ! 5(8x ! 9)(8x " 9)
4. 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.
a) 3k2 " 12km ! 36m2
b)
8y2
" 19y " 6
c)
9w2
! 24w " 7
d)
25a2
" 60a " 36
e) 121w2 ! 144
f) 10x2 ! 7xy ! 6y2
NOTE: For #9, do NOT
list all possible factors...
just explain the process
you would go through to
determine if the
expression can be
factored.
9. Explain how to determine whether or not
you can factor 9x2 ! 10x " 18 over the
integers.
COMMUNICATION
10. The area of a rectangle is given as
x2 " 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
THINKING/INQUIRY
sense?
258 MHR • Chapter 5
11. Determine all values of k so that each
16. Factor to evaluate each difference.
trinomial is a perfect square.
a)
36x2
! kx ! 121
b)
49d2
" 56d ! k
c)
25x2
d)
ka2
" 60xy !
a) 342 " 312
b) 1272 " 1262
THINKING/INQUIRY
ky2
c) 522 " 482
17. The first three diagrams in a pattern are
! 30ab ! 9b2
shown.
12. a) Write an algebraic expression for the
area of the shaded region.
x+5
x—5
APPLICATION
x+9
a) Write a formula for the total number of
small squares in the nth diagram.
b) Write a formula for the number of
x+9
b) Write the area expression in factored
form.
APPLICATION
small squares in the nth
NOTE: #12bshaded
-- Expand,
diagram.
simplify, then factor.
c) Substitute x # 7 into both forms. Are
c) Write a formula for the number of
the results the same? Why? COMMUNICATION
13. A parabola has equation y # 2(x ! 6)2 " 2.
a) Expand and simplify to write the
b) Factor your equation from part a).
d) Write your formula from part c) in
KNOWLEDGE
equation in the form y # ax2 ! bx ! c.
KNOWLEDGE
c) Do the three equations represent the
unshaded small squares in the nth
diagram.
factored form.
e) Show that both forms of the formula
give the same results for the 15th
diagram.
same parabola? Justify your response. COMMUNICATION
Achievement Check
14. The volume of a rectangular prism is given
18. a) Find all values of b so that x2 ! bx ! 10
as 9x3 " 30x2 ! 25x.
can be factored over the integers.
a) Determine algebraic expressions for the
b) Find all values of b so that 4y2 ! by ! 5
dimensions.
can be factored over the integers.
b) Describe the faces of the prism.
c) Write an algebraic expression for the
shaded area. Then, write the expression
15. Determine two values of k so that each
in factored form.
trinomial can be factored as a difference
of squares.
x+2
a) km2 " 25
b) 16d2 " k
c) a2 " kb2
4
x+1
3
Chapter 5 Practice Test • MHR 259
15. a) y ! (x " 6)(x # 3)
c) x ! 1.5; (1.5, "20.25)
b) 6, "3
y
4
x = 1.5
(—3, 0)
(6, 0)
—4
0
4
12 x
8
—4
12.
2
y = x — 3x — 18
—16
—20
10.
11.
—8
—12
8. a) 3(k # 6m)(k " 2m)
b) (8y # 3)(y # 2)
c) (3w " 7)(3w " 1)
d) (5a # 6)2
e) (11w # 12)(11w " 12)
f) (5x " 6y)(2x # y)
9. If there are two integers whose product is 9 $ 18 and
13.
(1.5, —20.25)
16. a) (2x # 3)(x # 2)
b) (2y # 9)(3y # 1)
c) (a " 3)(6a " 5)
d) (4b " 1)(b " 1)
e) 4(3m " 1)(m # 2)
f) (7k # 2)(2k " 5)
17. a) (2x # 3y)(4x " 5y)
b) not possible
c) (4m # 3n)(3m # n)
d) not possible
e) 3(4x # 3y)(2x " y)
f) not possible
18. a) length 4x " 5, width 2x # 3
b) P ! 140 cm, A ! 1161 cm2
19. a) (x # 7)(x " 7)
b) (y # 11)(y " 11)
c) (2k # 3)(2k " 3)
d) 16(1 # 3a)(1 " 3a)
e) (3w # 5x)(3w " 5x)
f) (1 # 9p)(1 " 9p)
20. a) x2 # 14x # 49 ! (x)2 # 2(x)(7) # (7)2; (x # 7)2
b) k2 # 8k # 16 ! (k)2 # 2(k)(4) # (4)2; (k # 4)2
c) y2 " 10y # 25 ! (y)2 " 2(y)(5) # (5)2; (y " 5)2
d) 25y2 " 70y # 49 ! (y)2 " 2(y)(7) # (7)2; (5y " 7)2
e) 36c2 " 108c # 81 ! 9(4c2 " 12c # 9) !
9[(2c)2 " 2(2c)(3) # (3)2]; 9(2c " 3)2
f) 121 # 176y # 64y2 ! (11)2 # 2(11)(8y) # (8y)2;
14.
15.
16.
17.
whose sum is "10, then 9x2 " 10x # 18 can be factored
over the integers.
a) length x # 15, width x " 2
b) 3
a) 132, "132
b) 16
c) 36
d) 25
a) Area: (x # 9)2 " (x # 5)(x " 5)
b) 2(9x # 53)
c) 232 square units; the results are the same because the
expressions are equivalent.
a) y ! 2x2 # 24x # 70
b) y ! 2(x # 7)(x # 5)
c) Yes, because the three expressions give the same
graph when graphed using a graphing calculator.
a) height x, side of base 3x " 5, side of base 3x " 5
b) It is a square-based prism, so the top and bottom are
squares with side length 3x " 5 and area (3x " 5)2,
and the four sides are rectangles with width 3x " 5,
height x, and area x(3x " 5).
Answers may vary. For example:
a) 4, 9
b) 1, 25
c) 9, 16
a) (34 # 31)(34 " 31) ! 195
b) (127 # 126)(127 " 126) ! 253
c) (52 # 48)(52 " 48) ! 400
a) The total number of squares, s, in diagram n is
s ! 4n2.
b) The total number of shaded squares, S, in diagram n
is S ! n # 3.
c) The total number of unshaded squares, u, in diagram
n is u ! 4n2 " n " 3.
d) u ! (4n # 3)(n " 1)
e) 4(15)2 " 15 " 3 ! 882 unshaded squares
(4(15) # 3)(15 " 1) ! 882 unshaded squares
(11 # 8y)2
21. a) 120, "120
22. a) (3wx " 4yz)2
c) not possible
b) 49
b) (20 # y)(30 " y)
d) not possible
Chapter 5 Practice Test, pages 258—259
1. a) (2x # 3)(x # 3) ! 2x2 # 9x # 9
b) (x # 3)(x # 4) ! x2 # 7x # 12
2. a) 12x3 " 20x2y # 32x2z
b) 14m3 " 7m2 # 12m " 9
3. a) y2 # 14y # 45
b) 12x2 " 13x " 14
c) 36k2 " 1
d) w2 " 16w # 64
2
2
e) 16c # 40cd # 25d
f) "318x2 " 22x # 461
4. a) d ! 0.006s2 # 0.012s # 0.006
b) The minimum stopping distance is d ! 22.326 m for
both versions of the formula.
5. a) 3d2e(3e # 2d)
b) 5pqr(3pr2 " 5p2q # 1)
c) (x # 6)(3)
d) (2x # 1)(8x " 3)
6. a) Surface area: 2(3x # 4)2 # 4(x)(3x # 4)
b) 30x2 # 64x # 32
c) 2(3x # 4)(5x # 4)
7. a) (x # 8)(x # 3)
b) (y " 8)(y " 7)
c) (n " 10)(n # 9)
d) (x " 7)2
e) (h # 10)(h " 10)
f) (d # 8)2
Chapter 6 Answers
Get Ready, pages 262—263
1. a)
y
16
(0, 15)
12
x=4
8
4
—4
0
—4
y = (x — 4)2 — 1
4
8
(4, —1)
12 x
Answers • MHR 543