.
Chapters
i —3
Cumulative. Review
Multiple Choice
1. tff(x) = 4x2
a) 30
b) 18
c) —6
ci)
—
3x
+
8, thenf(—2)
c)
=
‘
\
S
2
2. Which of the following functions is quadratic?
a) f(x) = 4 + 2x
ii)
y—x3+4
/‘7
46
f(x)6x—3x+12
ci) y(2x2—4)(x+6)
c)
il)
3. Which of the following is the graph of
+ 5)2
y = (x
a)
7
3
.
II.IIITII,i
.5
10 20 30
4.
NJ
ha
.
—á :4
x
là 20 30-
—30--b—b
“302010
.1
Which function has the following domain and
range:
D{xER}
io}
R {yERIy
a)
B
6
4,
3x
—
lj
2
—
ha
,—
.-i
‘0
I A I
6. 1dcntif’ the equation that corresponds to the
following transformations applied to the graph
ofy = x: stretched vertically by a factor of 7,
then translated left 7 units.
I
Li)
.
: ‘o
a)
4
—1
5) y
—2
c)
(13, —2.25)
=
_x2_7
y
d) y
7(x + 7)2
=
—7(x
—
7)2
7
7. ldenri5’ the equation that corresponds to the
Following cnnsformations applied to the graph
ofy = x2: reflected about the x-axis, stretched
vertically by a factor of 7, then translated to the
right 7 units and down 7 units.
c)
a)
yx2+7
5) y
I,.,,,
iIJ
1
—3—2—1
2
3ç
c)
= 7(x
+
7)2
y—x2—7
7)2
= —7(x
d) y
—
—
7
8. ldenri& the relation that is not a function.
d)
12- y=1O—4.9x2
.
y
a)
:
3
71:
5)
I
4.
5. IdentiFy the equation that corresponds to the
following transformations applied to the graph
ofy = x: reflected about the x-axis, then
translated down 7 units.
: ‘_i_S4/’
a) yx2+7
b) y7(x+7)2
c)
y
d)
y = —7(x
—
jl
—
7
d) (8. 9), (3, 2), (5, 7). (1, 0), (4.6)
•
9. Expand and sirnplth? 3x(2x
a) Zv4
1,) 6x2
19x + I
2
14
c)
11x
19x
d) 2x2
—
5)
—
(lv + i).
—
—
—
—
10. ldenrifr the missing factor:
IIx— 10 = (3x+ 2)(?)
—
a)
lv+5
h)
Zv—5
c) 5x±2
d) 5x—2
11. For the expression &2 + 6x + 8. identit the
values of k that make the trinomial unEicrorable.
a) k1
5) k=—2
c) k2
d) k = 3
12. A model rocket is launched straight upward
with an initial velocity of 22 mIs. The height of
the rocket h, in metres, can be modelled by
b(t) = 52 + 22t, where t is the elapsed time
in seconds. Whar is the maximum height the
rocke( reaches
a)
19.5m
—
5)
lO.2m
24.2 m
d) 29.6m
c)
13. Identify the apressions that cannot he factored.
12x + 9
a) 41
5) x2 + 3x + 2
c) x2—3x+5
—
d) ioo—1
14. A rectangular enclosure has an area in square
metres given byA(Wfl = 2w2 + 36w,
where w is the width of the rectangle in metres.
Determine the width that would create a
rectangular enclosure of 130 in2.
—
a)
5
6) 13
c)
to
d) 7
15. ‘Which of the following functions is equivalent
—2(x— 5)2 + 3
cof(x)
a) g(x) =
21
5x + 3
5) g(x) =1— IOx+28
c) g(x) = —2,? + 20x
47
47
d) g(x) = 2v2
—
—
—
16.
Analyzing Quadratic Fuiictions
Analyze the funaionf(x) = 3(x 4)2 + 51n-deprh. Include
a) the domain and range
b) the relationship to the ftincrionf(x)
x2, including all applied
trans formations
c) a sketch of the Rincrion
—
—
17. Coast Guard Rescue
Over the ocean, an inflatable raft is dropped from a coast guard
helicopter to a sinking ship below. The table shows the height oldie
raft above the water at different times as it Falls.
t(s)
ol
h(rn) 320
z
ii
275
315 1300
4
3
240
I
195
a) Draw a scatter piot of the data.
b) What type of model represents the relationship between the height
of the raft and rime? Explain how you know.
c) Use first and second differences to extend the cable of values until
the raft reaches the water.
ci) Draw a curve of good fir. Is the height of the raft a Function of
time? Explain.
e) Use your graph to determine the location of the vertex, the axis of
symmern’, and the zeros. Use this information to help you
determine a function that models this relationship.
fl Stare the domain and range of your Function in this context.
& Use your function to determine
I) the height of the raft at 7.5 s
ii) the time it takes the raft to reach a height of 50 m
l.A
2.C
3.A
4.D
S.C
6.B
7.D
D
l0.B
1l.A
12.C
13.C
14.A
15.C
9.
I
8.C
16.A)xER,
v>=S
.—
tLXAS INST..UMENm
17b) Quadratic,
2nd
differences are constant c)
——_________________
it reaches the water at 8 sec
d) vertex (0, 320) axis of sym: x=0; zeros: 8 and -8; y=-0.5x’+320 f) x>=0; y<=320 g)i)y38.75 ii) 7.3 sec
Multiple Choice
1. AT-ball player hits a baseball from a tee char
is I m tall. The flight of th ball can be modelled
I, where b(t) is the
by h(r) = 5r + lOt
height in metres andt is the time in seconds.
When does the ball reach its maximum
height?
c) 1.60s
a) O.5s
ci) 1.5s
b) 1.OOs
—
—
2. A rock is dropped from theedgeofa 18Dm
52
5 + 5o
cliff The function h(t)
gives the approximate height oldie rock, h(r),
in metres tscconds after it was released. How
long does it take ior the rock to reach a ledge
80 m from the base of the cliff?
c) 35
a) 5s
ci) 4s
b) 6s
—
—
3. The &mctionf(x)
vertex form is
a) f(s)
h f(s)
c) f(x)
d) f(s)
4.
=
long. The angle of elevation
28°. How tall is the satellite
c)
a) 24.41m
d)
6) 18.2m
7. Two airplanes leave the same airport in opposite
directions. Ar 2:00 p.m. the angle of elevation
from the airport to the first plane is 48° and
to the second plane 59°. The elevation of the
first plane is 5.5 lan. and the elevation of The
second plane is 7.2 km. Determine the air
distance between the two airplanes to the
nearest renth of a kilometre.
c) [5.7km
a) 9.4 km
d) 7.8km
5) 8.5 km
S. Determine the length oIAB to the nearest metre.
A
—5x2 + 20x + 2 in
500 m
5(s
—5(x—
2) + 18
2)2 + 22
=
__5(x+2)2_22
1.8
= —5(x + 2)2
=
of the longer wire is
dish tower?
6m
8.45m
C
—
Which of the following quadratic equations has
no solution?
4x = Zr 3
a) Zr2
6) Zr2— 15x—80
j)2
= 0
c) 16(x +
5)2
+ 7 = 0
ci) 3(x +
—
B
—
5. Identifr which parabola does
5— ax is
6s + 7
a) f(s) =
b) f(s) = 9
)2
c) f(s) = (4 ±
d) f(s)
—2(x— 1)2_
flO(
intersect the
c 574.m
4) 564m
524 m
5) 544m
a)
9. Use this diagram to determine th4height, h,
of the mountain.
A
—
-.
—
6. ‘iwo support wires are fastened to the top ola
TV satellite dish tower from two points on the
ground. A and B, on either side of the tower.
One wire is 18 m long, and the other is 12 in
\(72.41w
4.35
B
a)
2.5 km
6) 1.98km
1.5 km
ci) 1.87km
c)
10. Which functions are both periodic and sinusoidal?
13. IdentiFy the correct amplitude and period.
a)
y
A1
‘XX
fl
i RYt
5)
a) amplitude: 1. period: 360°
b) amplitude: 3, period: 90°
c) amplitude: —5. period: 180°
4) amplitude: 3.perioth 1800
14. IdentiFy the transformations you would apply to
f(x) = sinx to graphf(x) = 0.5 sin(x
30°).
a) vertical stretch by 0.5, shift left 30°
b) vertical compression by 0.5, shift left 300
c) vertical stretch by 0.5, shift right 300
4) vertical compression by 0.5, shift right 30°
—
c)
x
.
F
—
I
I
r
I
15. IdentiFy the transformations you would apply to
f(x) = sin x to graphf(x)
sin x + 3.
a) reflection in the x-axis. shift down 3
5) reflection in they-axis, shift up 3
c) reflection in the x-axis, shift up 3
4) reflection in they-axis, shift down 3
I
J)
16. The ftmctionf(x)
standard form is
‘0
a) (b)
b) (a) and (d)
12. What is the rangeoff(x)
a) IyER 1—6 y
5) IyC.R 1—2
c) lyCR I —4 y
4) jyER I —4 y
a) f(x) = _2 +
5) f(x) = _.2 +
c) f(x) = Zt2 +
4) f(x)t—2x2±
c) (b) and (c)
d) (a)
11. ldenrifjr the amplitude and equation of the axis
off(x) = 2 sin x + 5.
a) amplitude: 2, eqtmtion olaxis:y = 5
b) arnpUrude: 5, equation of axis: y = 2
c) amplitude: 2. equation of axis:y
ci) amplirude 5, equation oIaxis:y =2
61
4J
S
2
—4sinx— 2?
=
17.
—2(x
—
3)2
+ 5 in
tO
6x + 10
12x+ IS
12x
13
12x
—
—
For the parabola defined by
f(x) = —3x + 1)2
4, which of the
following statements is nor true?
a) The vertex is (—1, —4).
5) The axis of symmetry is x = 1.
c) The parabola opens down.
4) The domain is (x C R}.
—
18. Giveny = —x2 + 12x 16, state the
coordinates of the vertex and the maximum or
minimum value of y.
a) vertex (6, 20), maximum 20
b) vertex (—6, 20), minimum —6
c) vertex (6, 20), minimum 6
d) vertex (6, —20), maximum —20
—
19.
The profit Rincrion for a new product is given
byP(x) = —4x2 + 28x— 40,wherexis the
number sold in thousands. How many items
must be sold for the company to break even
a) 2000 or 5000
c) 5000 or7000
1,) 2000 or 3500
d) 3500 017000
20. Which of the foliowing statements is not true
for the equation of a quadratic function?
a) In standard form, they-intercept is clearly
visible.
5) In vertex form, the break-even points are
clearly visible.
c) In factored form, the x-intercepts are clearly
visible.
d) In vertex form, the coordinates of the vertex
are clearly visible.
21. Which of the following is not a step required to
complete the square lory = 7x2 + 21x
a) 7(x2±3x)2
5) 7x(x+3)—2
—
c)
d)
7(x2+3X+)_74
7(x2+3x+_)_2
22. Which of the following statements is not true
for a given quadratic function?
a) They-coordinate of the vertex represents the
minimum or ma’dmum value.
b) The axis of symmetry is given by the
x-coordinate of the vertex.
c) The axis of symmetry is given by the
y-coordinate of the vertex.
d) The midpoint between the x-intercepts is
the x-coordinatc of the vertex.
1.
23. A quadratic function in standard form will have
two distinct real roots when
a) b24ac<0
5) a2—4bc>0
c) b4ac
d) b2—4ac>0
24. Which value of k will produce one toot for
y= —2(x+7)2—k?
a) k1
c) k1
b) k=0
d) k=—2
25. The period of a periodic graph is
a) the length of one cycle
5) the distance from the maximum to the
minimum values of the relation
c) the same as the domain
d) the same as the range
26. The equation of the axis of the curve is
a) y6
5) y = nix + 6
maximum value + minimum value
c) y
2
d)y
maximum value
—
minimum value
2
27. Parallelogram ABCD has sides of length 35 cm
and 27cm. The contained angle is 130°. The
length of the longer diagonal is
a) 27.2cm
c) 22.5cm
5) 5&.3cm
d) 20.7 cm
28. In AABC, LA = 850, c = 10 cm,.and
6 = 15cm. The height ofABCis
a) 17.3cm
c 13.8cm
5) 8.6cm
d) l2.5cr
29. In APQR, LP = 70°, r = 5 cm, and q
The area of PQR is
a) 13cm2
c) 18.8cm2
b) 20 cm2
d) 19.2 em2
=
8 cm.
b 2. D 3. B 4. D 5. d 6. 0 7. 0 8. C 9. C 10.d 11.a 12.a 13.b 14.d 15.c 16.d 17.b 18.a 19.a 20.b
21.b 22.c 23.d 24.b 25.a 26.a 27.b 28.??? 29.c
F.
Review
Multiple Choice
1. Which expression has a value o164?
a)
I,)
c)’
1&
—4
2. If the value of the variable is 3, which of the
following is true?
a) (p X p3)3 = 39
c) (,,2)3 + n = 243
b) (c1)2x?= I0000d)
= 512
3. Which number is equivalent to
:
:
4. Identify the expression which is false.
a) (9)(4i) = (9 X 4)
b)
c)
d)
9+4L(9+4)
r(’)()r
= 9242
5. Which expression does not have a value of 9
when a = 1, b = 3, and c = 2?
a) (—ab)
c) (abr
5) aebe
ci) (a’b”)
6. Identif’ the exponential function whose
equation of the asymptote isy = 2.
a)
c)
LJC
b)
d)
l.a 2.c 3.b 4.c 5.d 6.a 7.d 8.c 9.a lO.c ll.a 12.b
7. A bacteria cukwe doubles in size eveiy 15 minutes.
Given the fonrndap(n) = 20(2)i. how long
will it take for a culture o120 bacteria to grow to a
popWation of 163 840?
a) 2048 minutes
c) 65 minutes
5) 12 hours
d) 195 minutes
8. Thorium-227 has a half-life of 18.4 days. Given
the firmulaftf(:) = 5OQc)iT4,howmany days,
will a 50 mg sample cake to decompose to lOmg?
a) 73.6
c) 42,72
5) 21.09
d) 7.36
9. Four years ago, Sam invested a sum of money at
5%/a, compounded semiannually. Today there is
$921.35 in Sin’s account. How much did she
invest?
a)
$756.19
c)
$920.00
1,) $46.06
d) 875.29
10. How much will $7500 be worth if it is invested
now for 10 years at G%/a, compounded annually?
a) $12000
c) $13431.36
5) $16637.84
d) $4500
11. Phong wants to purchase a motorcycle. He can
borrow $6500 at IO%/a, compounded quarterly,
if he agrees to repay the loan by making equal
quarterly payments for four years. Qetermine a
reasonable quarterly payment.
a) $500
c
$650
5) $300
d) $65 ‘ii
12. In order to repay a loan in less time, you could
a) increase the periodic payment and increase
the interest rate
5) increase the periodic payment and decrease
the interest rate
c decrease the periodic payment and increase
the interest rate
d) noneoftheabove