Download Math B30 Final

Page 1 of 17
Math B30
Final Exam
You will have 2.5 hours to complete the exam.
Please record all answers to the multiple choice questions
on the answer sheet provided.
Show all your work.
Name: ____________
Mark:
Page 2 of 17
Part 1: Multiple Choice: Circle the letter of the best choice on the answer
sheet provided. (1 mark each)
1)
If a single card is drawn from a bridge deck of 52 cards, what is the probability of a jack
or a heart?
A.
B.
C.
D.
2)
From an urn containing 3 red balls and 4 white balls, two balls are drawn in succession from the
urn with replacement. What is the probability that both balls are red?
A.
B.
C.
D.
3)
10
81
540
810
The mean of a set of data is *****.
A.
B.
C.
D.
5)
9/49
1/7
3/7
6/7
The coefficient of the second term of (3x + 2y)5 is *****.
A.
B.
C.
D.
4)
17/52
17/26
7/13
4/13
the range divided by two.
a value such that half of the data are greater than this value and half of the data are less.
the sum of all the values divided by the number of values.
the most frequent value.
The mode of a set of data is *****.
A.
B.
C.
D.
the range divided by two.
a value such that half of the data are greater than this value and half of the data are
less.
the sum of all the values divided by the number of values.
the most frequent value.
Page 3 of 17
6)
The median of a set of data is *****.
A.
B.
C.
D.
7)
The set of complex numbers is the set of real numbers combined with the set of *****
numbers.
A.
B.
C.
D.
8)
the range divided by two.
a value such that half of the data are greater than this value and half of the data are
less.
the sum of all the values divided by the number of values.
the most frequent value.
irrational
whole
imaginary
rational
The number 3  24 written in the form a + bi is *****.
A.
B.
C.
D.
3  2i 6
3  2i 6
2 6  3i
2 6  3i
9)
To simplify 5 - 3i , we multiply the numerator and the denominator by the ***** of
5 + 3i
the denominator.
A.
inverse
B.
converse
C.
reciprocal
D.
conjugate
10)
If a + bi = (3 + 2i)(5 - 7i), then b = *****
A.
B.
C.
D.
-14
-11
14
29
Page 4 of 17
11)
2
One root of x - 6x + 13 = 0 is *****.
A.
B.
C.
D.
12)
If the discriminant of a quadratic equation is 24, the roots of the equation are *****.
A.
B.
C.
D.
13)
3 - 2i
5 - 3i
7 + 2i
9 + 5i
real, unequal, irrational.
real, unequal, rational.
real, equal, rational.
complex.
The graph of the solution set of x2 - x - 6 > 0 is *****.
A.
-2
0
3
B.
-3
0
2
C.
-2
0
3
D.
-3
14)
The value of 22/3 • 41/6 is *****.
A.
B.
C.
D.
15)
½
2
4
8
3-3x-4y5 is equal to *****.
6x-8y-2
A.
2x4y3
B.
x2y3
162
C.
x4y7
162
D.
x4y3
33
0
2
Page 5 of 17
16)
The value of x in the equation 3x
A.
B.
C.
D.
17)
-72
-172
-3,096
-24,564
equal
less than one
greater than one
different
How many terms are there in the sequence 12, 21, 30, 39, ..., 372?
A.
B.
C.
D.
21)
20
90
625
109
In a geometric sequence, the ratios of any two successive terms are always *****.
A.
B.
C.
D.
20)
9
4
1/8
1/64
The sum of the first 43 terms in the series 12 + 8 + 4 + 0 + ..... is *****.
A.
B.
C.
D.
19)
= 48 is *****.
The value of x in log 5 + log 4 = log x is *****.
A.
B.
C.
D.
18)
-2/3
21
31
41
51
The sum of the geometric series where the first term is 24, the common ratio is 3, and the
number of terms is 12 is *****.
A.
B.
C.
D.
1 723 514
2 125 764
3 188 640
6 377 280
Page 7 of 17
22)
The sum of the geometric series 1 - ½ + ¼ - ... is *****.
A.
B.
C.
D.
23)
Which of the following has no vertical asymptote?
A.
B.
C.
D.
24)
x 2  3x  7
x2
2
x  3x  7
f (x) 
2
2
x  3x  7
f (x) 
x2
2
x  3x  7
f (x) 
x2  2
f (x) 
In the polynomial y = 4x3 - 3x2 + 5x – 2, which term determines the end behaviour of the
graph?
A.
B.
C.
D.
25)
3
2/3
½
0
5x
-3x2
4x3
-2
For the polynomial f(x) = x3(2x – 1)4(x + 2)8, which is of the following is true?
A.
B.
C.
D.
End of Part I
Zero is root of multiplicity 3.
2 is a root of multiplicity 4.
There are no multiple roots.
x = 2 is a horizontal asymptote.
Page 8 of 17
Part II:
Show all necessary calculations in the space provided.
Chapter 1: Probability and the Binomial Theorem
1)
Two cards are drawn at random without replacement from a standard deck of 52 cards.
( 6 marks)
a)
Find the probability both are kings.
b)
Find the probability both are red.
c)
Find the probability both are kings or both are red.
2)
Two dice are rolled. What is the probability that they total 11? ( 2 marks)
3)
Expand and simplify. (x + 2y)4
( 3 marks)
Page 9 of 17
Chapter 2: Complex Numbers and Quadratic Equations
1)
2)
Simplify the following. ( 8 marks)
a)
(3 – 2i)(4 + 5i)
b)
5
2i
c)
3  2i
4i
d)
i93
State the nature of the roots for the following quadratic equation. ( 2 marks)
x2 + 5x + 4 = 0
3)
State the sum and product of the roots of 4x2 + 11x - 3 = 0. ( 2 marks)
Sum =
Product =
Page 10 of 17
4)
Write the equation whose roots are {6,-1}. ( 2 marks)
Chapter 3: Matrices
1)
Consider the following matrices: ( 9 marks)
3 7 
A  0 2
6 1 
1 3 5 
B

 2 3 4
a)
State the dimensions of B.
b)
If possible, find B + C.
c)
If possible, find A + B.
d)
Find 3C.
e)
If possible, find AB.
0 6 8 
C

3 6 9
Page 11 of 17
Chapter 4: Polynomial and Rational Functions
1)
Use division to find the quotient and the remainder. You may use long division or
synthetic division. ( 3 marks)
2x 3  x 2  4x  2
x2
2)
For the polynomial f(x) = -2x4 + x3 – 4x2 – 1, state: ( 3 marks)
a)
the degree
b)
the leading coefficient
c)
the leading term
d)
the constant term
e)
the beginning quadrant
f)
the ending quadrant
Page 12 of 17
3)
4)
For the function y = 3x – 2:
a)
Find the equation of the inverse. ( 2 marks)
b)
Find the equation of the reciprocal. ( 2 marks)
Factor the following polynomial function, identify all zeros, their multiplicity, the
behaviour of the graph at each zero, and sketch the graph of the function: ( 6 marks)


y  x 2 x  5 x  3 x 2  9 .
5
Zeros
Multiplicity
Behaviour
Page 13 of 17
Chapter 5: Exponential and Logarithmic Functions
1)
Solve the following equations for x. (3 marks each)
a)
6x = 63x – 12
b)
92x =
c)
2x = 17
d)
2
log x    1
3
e)
log3 (x – 4) + log3 (x + 4) = 2
27
Page 14 of 17
Chapter 6: Sequences and Series
1)
Find the tenth term of the following arithmetic sequence. ( 3 marks)
25, 33, 41, …
2)
If a = 96 and the second term of the geometric sequence is 48, find the fifth term.
( 3 marks)
3)
Find the following sums. ( 6 marks)
10
a)
 2k  1
k 1
7
b)
 5(2)
j1
j1
Page 15 of 17
Problem Solving: Answer any 2 of the following problems. Use methods studied in this course
for full marks. Remember to answer with a sentence. ( 8 marks)
1.
The half life of a certain radioactive substance is 4.5 days. How much of a 123 mg
sample of the substance will be left after 7 days?
2.
Billy Single deposits $1000 at the end of each year for a period of 10 years in an account
paying 8% interest compounded annually. How much will be in Bill’s account after the
final deposit?
3.
Find two consecutive odd integers whose squares have a sum of 514.
Page 16 of 17
Chapter 7: Data Analysis
1)
The masses of 12 people are given, in kilograms.
112
110
112
118
114
119
118
121
120
128
132
130
a) Calculate the mean, median, mode and range for the data. ( 4 marks)
Mean =
Median =
Mode =
Range =
b) Calculate the standard deviation of the data. Show all your work. (4 marks)
2) If the test scores are normally distributed, how many out of a class of 85 will have a zscore of 2 or better? (2 marks)
________________________
Page 17 of 17
Multiple Choice - Answer Key
1. _______
2. _______
3. _______
4. _______
5. _______
6. _______
7. _______
8. _______
9. _______
10. ______
11. ______
12. ______
13. ______
14. ______
15. ______
16. ______
17. ______
18. ______
19. ______
20. ______
21. ______
22. ______
23. ______
24. ______
25. ______
25
Total:
Multiple
Choice
25
Long
Answer
+
95
=
120