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REVIEW FOR EXAM
Cumulative Review Questions from Textbook
Chapter 1-3 – Pg. 214 #1-33
Chapter 4-5 – Pg. 348 #1-19
Extra Questions
CHAPTER 1
1. Determine if each relation is a function.
a)
Chapter 6-8 – Pg. 468 #1-23
b)
2. State the domain and range of each relation. Determine if each relation is a function.
1
a) {(17, 2), (11, 14), (2, 2), (5, 45), (117, 118)}
b) y = x2 + 1
c) y = x  3
2
3. If f(x) = 5x2, find
a) f(4)
b) f(0)
c) f(10)
4. Simplify.
a)
b)
98
5. Simplify.
a) 54  20 
405
c)
15
24 +
6
25
d) 8 3  5 11
e) 4 10  3 5
b)  252 + 162 + 112 –
80

f)
14  147
7
50

6. Expand and simplify 4 5 6 10  3 35 .
7. Simplify.
1
a) 
5 3


b) 2 5  7 6 2 5  7 6

c)
4
14  4 3
8. Find the maximum or minimum value of the following functions by completing the square.
a) y = 5x2  10x + 14
b) y = 0.7x2  11.2x  25.6
c) y = 6x2  7x + 2
9.
Solve 10x2  3x = 2x + 2 by factoring. Check the solution.
10. Solve 2x2 + 7x + 9 = 0 using the quadratic formula.
11. Solve. Express answers as exact roots and as approximate roots, to the nearest hundredth, if necessary.
a) x2  11x  26 = 0
b) 3x2 + 8x  2 = 0
c) 2x2  x + 3 = 0
12. Solve each system of equations.
a. y  x 2  7 x  15 and y  2 x  5
b.
y  13 x  3 and x 2  y 2  25
c.
y  3x 2  16 x  37 and y  8 x  1
CHAPTER 2
13. Simplify each of the following. State any restrictions on the variables.
14 x 4  28 x 3  7 x 2
6  4x
2x 2  x  1
a)
b)
c) 2
7x
2x  3
x  4x  3
8
2
5
x

4
12 c
x

x

2
2x 2  4x
x2  4
15d
d)

e)

f)

x 1
36c 9
5d 2
x 2  x  20
x 2  4 x  3 x 2  2 x  15
14. Simplify each of the following. State any restrictions on the variables.
10
7
2 5
2
2x  7
x  1 3x  1
8
6
4
6
a)

+
b)
+
c) 3 +  2 e)
+
g) 2
 2
3
2
s 5s
5
1  2 x 2 x  1 3s
3w  9 4w  12
v  7v  10 v  4v  5
15. How do the graphs of y =
1
1
1
+ 4 and y =  1 compare with the graph of y = ? Graph the first two functions.
x
x
x
16. How do the graphs of y =
1
1
1
and y =
compare with the graph of y = ? Graph the first two functions.
x
x5
x8
17. Sketch the graph of y =
x  1  2.
18. a) Given the graph of y = f(x), as shown, graph y = f(x) and y = f(x) on the same axes.
b) Describe how the graphs of y = f(x) and y = f(x) are related to the graph of y = f(x).
19. If f(x) = x  2 + 1, write an equation to represent each of the following functions,
describe how the graph of each function is related to the graph of y = f(x), sketch each graph, state the domain
and range, and identify any invariant points.
a) y = f(x)
b) y = f(x)
20. a) Find the inverse f1 of the function f whose ordered pairs are {(3, 10), (1, 9), (8, 4)}.
b) Graph both functions.
21. For each of the following functions i) f(x) = 2x + 5
ii) f(x) = x2 + 2
a) find the inverse b) graph f(x) and its inverse c) Is the inverse is a function d) domain and range of f(x) and f-1(x)
1 2
x on the same grid.
4
1
b) Describe how the graphs of y = 3x2 and y = x 2 are related to the graph of y = x2.
4
22. a) Graph y = x2, y = 3x2, and y =
23. a) Given the graph of y = f(x), sketch the graphs of y =
1
f(x), y = 2f(x), y = f(3x)
3
1 
and y = f  x  .
4 
b) Describe how the graph of each of the functions in part a) is related to the graph of y = f(x).
x , sketch the graphs of y = f(x) and y = 3f(x + 1) + 1.
1
25. The graph of y = x2 is compressed vertically by a factor of , reflected in the x-axis, and translated 4 units to the
5
right and 2 units upward.
a)Write the equation of the transformed function. b) Graph it.
24. If f(x) =
CHAPTER 3 – EXPONENTIAL FUNCTION
26. Simplify.
a) (14m7n2)(3m2n4)
b) (z12)5
27. Simplify
16 x
3

c) (6j2k3)4

y 2 3 y 1 z
. Express the answer with positive exponents.
 8z 2
28. Evaluate.
2
a)  
5
3
b)
2 4
(5) 0  3
c)
5 2  5 1
5 4
1
d) 64 3
4
e)  27  3
 9 
f)  
 49 
 2 .5
29. Use a calculator to evaluate the following, to the nearest hundredth.
7
a) 11 4
b) 62.4
30. A car’s value decreases by 14% each year. The car originally cost $23 500.
a) What is the growth/decay factor?
b) Write an equation to represent the value of the car, V, after x number of years.
c) What is the value of the car in 4 years?
31. A house increases in value by 1.5% each year. The original cost of the house is $369 800.
a) What is the growth/decay factor?
b) Write an equation to represent the value of the house, V, after x number of years.
c) What is the value of the house in 6 years?
32. Solve and check.
a) 65x + 1 = 363 + 2x
b) 7x + 3 + 7x = 16 856
CHAPTER 4 - TRIGONOMETRY
33. Prove the following Trigonometric Identities.
a. sin   cos tan 
b. csc  sec cot 
c. cos  sin  cot 
d. sec  csc tan 
e. 1  csc   csc  (1  sin  )
f. cot  sin  sec  1
g. 1  sin   sin  (1  csc  )
h.
i.
j.
sin x
1
=
2
cos x
cos x tan x
1
cos x
sin x =

sin x
tan x
sin 2 x  cos 2 x
2
1
+
=
1  cos x
1  cos x sin 2 x
34. In XYZ, X = 90, Y = 54.2, and y = 4.1 cm. Solve the triangle by finding
a) the unknown angle
b) the unknown sides, to the nearest tenth of a centimetre
35. In PQR, Q = 90, p = 14.9 m, and r = 18.3 m. Solve the triangle by finding
a) the unknown angles, to the nearest tenth of a degree
b) the unknown side, to the nearest tenth of a metre
36. To calculate the height of a tree, Marie measures the angle of elevation from a point A to be 34. She then walks
10 m directly toward the tree, and finds the angle of elevation from the new point B to be 41. What is the
height of the tree, to the nearest tenth of a metre?
37. To measure the distance from a point A to an inaccessible point B, a surveyor
picks out a point C and measures BAC to be 71. He moves to point C, a distance
of 56 m from point A, and measures BCA to be 94. How far is it from A to B, to
the nearest metre?
38. In ABC, B = 144.9, a = 2.4 cm, and b = 4.4 cm. Solve the triangle, rounding the side length to the nearest
tenth of a centimetre and the angles to the nearest tenth of a degree, if necessary.
39. In DEF, d = 34.6 m, e = 18.4 m, and f = 19.5 m. Solve the triangle. Round each angle measure to the nearest
tenth of a degree.
40. The point (24, 10) is on the terminal arm of an angle  in standard position. Find sin  and cos .
41. The point (6, 8) is on the terminal arm of an angle  in standard position. Find sin  and cos .
42. Evaluate, to four decimal places.
a) sin 64.7
b) cos 153
43. Find A, to the nearest tenth of a degree, if 0  A  180.
a) cos A = 0.2421
b) sin A = 0.7988
44. The point P(5, 2) lies on the terminal arm of an angle  in standard position. Determine the exact values of sin
, cos , and tan .
45. Find the exact values of
a) sin 210
b) tan 210
c) sin 405
d) cos 330
46. Find the values of the sine, cosine, and tangent of an angle that measures
a) 180
b) 270
CHAPTER 5
47. Determine whether each function is periodic. If it is, state the period.
a)
b)
48. The graph has a period of 6. Find the value of
a) f(3)
b) f(21)
49. Sketch one cycle of each function.
a) y = 3cos x
b) y = sin 2x
c) y = 4cos 3x
50. Sketch one cycle of each functions and state the following properties about each function
a. Amplitude
b. Period
c. Phase shift
d. Vertical shift
e. Equation of horizontal axis
f. Maximum value
g. Minimum value
1
3


a) y = 3sin x + 1 b) y = 2cos x  45 c) y = 0.5sin 3x  90 d) y = 5cos  x  30   2
e) y = 2sin x 180
CHAPTER 6 Sequences and Series
51. Find each term described for (3x  6) 8
a. 4th term
b. 2nd term
c. 5th term
52. How many terms are there in the following
expansions:
a. (3a  5) 0
( x  2) 25
c. (t  6)15
d. (5ab  6a) n
b.
53. Complete the following Pascal’s Triangle.
54. Use the Binomial Theorem and Pascal’s Triangle to write the simplified expansion of each of the following.
a. ( x  2) 5
b. ( y  3) 4
c. (4  t ) 6
d. (1  m) 5
e. (2 x  3 y) 4
55. Given the formula for the nth term, write the first four terms of each sequence.
a) tn = 5n – 2
b) f(n) = 3n2 – 2
c) tn = 6n + 1
d) f(n) = –4n + 3
e) tn = –7(3)n  1
f) f(n) = 2(–4)n  1
56. Find the formula for the nth term that determines each sequence.
a) 7, 14, 21, 28, … b) 6, 7, 8, 9, … c) 7, 9, 11, 13, … d) 14, 11, 8, 5, … e) 4, 20, 100, 500, … f) 256, 128, 64, 32 …
57. Find the indicated terms.
a) tn = 4.5n – 8; t6
b) f(n) = –0.8n – 0.4; t20
c) tn = 5(–2)n – 1; t7
d) f(n) = 8(0.1)n  1; t4
58. Find the number of terms in each of the following sequences.
a) 8, 11, 14, …, 50
b) 9, 7, 5, …, –9
c) 9, 18, 36, 72, …, 1152
d) 0.0625, 0.25, 1, 4, …, 4096
59. Find a and d, and write the formula for the nth term, tn, of arithmetic sequences with the following terms.
a) t3 = 22 and t8 = 67
b) t2 = –9 and t10 = 39
60. Find a, r, and tn for each geometric sequence.
a) t3 = –72 and t5 = –2592
b) t4 = 270 and t6 = 2430
61. Determine whether each sequence is arithmetic, geometric, or neither. Then, find the next two terms.
a) 3, 12, 27, 48, …
b) 19, 13, 7, 1, …
c) 4, 2, 1, 0.5, …
d) 0.8, –0.6, –0.4, –0.2, …
62. Find the indicated sum for each arithmetic series.
a) S8 for 15 + 21 + 27 + …
b) S12 for 4 – 1 – 6 – …
63. Find the indicated sum for each geometric series.
a) S5 for 1 + 7 + 49 + …
b) S7 for 3 – 6 + 12 – …
64. A student paid $5500 tuition for her first year attending a university. Tuition at the university is projected to
increase $750 a year for the next four years.
a) How much tuition should the student expect to pay for her fourth year at the university?
b) How much should the student expect to pay in tuition for all four years?
65. In an arithmetic series t3 = 30 and t6 = 54. Find the sum of the first 20 terms.
66. Two friends started a telephone chain. Each person in the chain called three people. Thus, there were six
telephone calls in the first round.
a) How many telephone calls were made in the fifth round?
b) After eight rounds, how many telephone calls had been made in all?
CHAPTER 7 Compound Interest and Annuities
67. To purchase a new computer, Prasanna borrows $4000 at an interest rate of 5.25% per annum, compounded
annually. He has arranged to pay back the loan in 3 years.
a) How much will Prasanna owe after 3 years?
b) How much of this is interest?
68. Gwen wants to invest $20 000. She must decide between a 12-year plan with an interest rate of 8% per annum,
compounded quarterly, and a 12-year plan with an interest rate of 7.75% per annum, compounded monthly.
Which plan earns Gwen more interest, and by how much?
69. What rate of interest, to the nearest hundredth of a percent, compounded semi-annually, would be required for
an investment of $70 000 to grow to $110 000 after 8 years?
70. Marc needs to save $20 000 for a home gym, which he would like to have in 6 years. How much should he invest
today at an interest rate of 7% per annum, compounded quarterly?
71. P. J. needs $14 000 in 5 years to purchase a van. P. J.’s bank has offered her two investment plans: 3.6% per
annum, compounded quarterly, or 3.55% per annum, compounded monthly. Which plan requires a smaller
investment, and by how much?
72. To save money for college, Ronna plans to deposit $250 into an account at the end of every three months for
the next two years. She will begin making payments three months from now. If her account has an interest rate
of 4% per annum, compounded quarterly, how much will Ronna have after she makes her last payment?
73. larence has $20 000 in the bank. He wants to create an investment to pay his $230 monthly car insurance
payments for four years, with the first payment due in one month. How much of his $20 000 should he invest
now at 8.25% per annum, compounded monthly?
74. Half of the $5542 raised in a charity raffle is invested in an account at 7.1% per annum, compounded quarterly.
The winner of the raffle is to receive payments from this account every three months for the next five years,
beginning three months from now. How much are the payments?
75. Jack is purchasing a house that he plans to rent to students attending community college. The price of the house
is $115 000. Jack makes a down payment of 12% of the price and agrees to a mortgage at 6.8%, amortized over
15 years, for the balance of the price.
a) How much is Jack’s mortgage?
b) How much are Jack’s monthly payments?
Answers
1. The points of intersection are:
a. (4,3)(5,5)
b. (3,4) (-24/5,7/5)
c. (12,7)(6,49)
2.  L.S.  R.S , QED
3. The terms are:
a.  2939328x
b.  104976x
c. 7348320x
4. The number of terms are:
a. 1
b. 26
c. 16
d. n  1
5. The simplified expansions are:
a. x  10 x  40 x  80 x  82 x  32
b. y  12 y  54 y  108 y  81
c. 4096  6144t  3840t  1280t  240t
d. 1  5m  10m  10m  5m  m
e. 16x  96x y  216x y  216xy  81y
6. Pascal’s
Triangle
5
7
4
5
4
3
4
3
2
2
2
2
4
3
3
2
2
3
4
5
3
4
4
 24t 5  t 6