Grade:
Last Name:
First Name:
ID Number:
Question 1: On the axes provided, sketch the graph of y = log; (3:). Label at least two
points on the graph. (2 marks)
Question 2: On the axes provided, sketch the graph of y = 311:2 — 63: + 5. Complete the
1
More Practice Questions for January 14
a) Factor the following:
(i) x3 + 5x2 8x 48
(ii) x3 4x2 25x + 28
(Answers:
(i) (x 3)(x + 4)2 ;
(ii) (x 1)(x 7)(x + 4)
b) Solve the following for x: x3 + 2x2 9x 18 = 0
(Answer:
Three solutions: x = 2, x = 3, x = 3)
1
Practice April 3
a) Compute the following sums using the formula for the sum of a geometric series:
10
3(1.5)i
(i)
i=0
20
(0.86)j
(ii)
j=0
40
300(1.02)k
(iii)
k=5
2(0.3)m
(iv)
m=0
2(1.3)n
(v)
n=0
Solutions: (i) 512.99;
(ii) 6.84;
(iii) 17221.79;
(iv) 2.
1
Practice Final Exam
Part A: Quick Answer 20 marks
For each of the following, please ll in your nal answer in the box provided at the
right side of the page. Each correct answer is worth 1 mark.
A1. The price of gas was $1.19 per litre, but then increase
The multiple choice questions are worth 2 marks each, and the written response questions are worth 5
marks each. There are 39 marks available in total.
1. What is the value of
n=0
4
5 ( )n ?
5
(a) 20
3
(b) 35
(c) 175
4
(d) 1
(e) 25
2. The series
31
n
n=72
MATH*1030 F12
Test 1 (White Version)
October 12 2012
This page is included to satisfy the U of Gs privacy policy. Please ll out your rst and last names on
this page, but not your ID number or any other information.
Last Name:
First Name:
On the next page,
The multiple choice questions are worth 2 marks each, and the written response questions are worth 5
marks each. There are 39 marks available in total.
1. If 4(x
(a)
(b)
(c)
(d)
(e)
1/3 +3)
= 1024, then x is closest to:
1.1
1.3
1.5
1.7
1.9
2. At what poin
MATH*1030 F13 Homework Exercises
You should be able to do most of the exercises in the text. This document gives a
reasonable subset for you to work on. (You can also work on other text questions if
youre looking for more practice.) You will not need to h
MATH*1030 F13
Questions for Quiz 7
2
e3(x+h) e3x
h
h0
2
1. What is lim
?
(a) 0
(b) 1
(c) e3x
2
(d) 3e3x
(e) 6x e3x
2
2. Consider the function f (x) =
e8x
3x12 .
This function:
(a) Has a vertical asymptote at x = 0 and no horizontal asymptote.
(b) Has a ve
1
Practice Questions for January 30
a) Solve the system of equations given by
3x1 + x3 = 3
1
x1 2x2 + 2x3 = 12
2
4x1 + x2 + x3 = 1.
3
2
4
Answer: cfw_x1 = , x2 = , x3 = 5
3
3
b) Solve for x, if 2x3 + 11x2 + 7x 20 = 0.
5
Answer: x = 4, x = , or x = 1.
2
c)
1
Practice Questions for February 4
a) Consider the piecewise function given by
10,
if x < 2
f (x) = 1,
if 2 x < 0 .
x + 1, x 0.
(0.1)
(i) Draw the graph of y = f (x).
(ii) Evaluate
lim f (x) and
x2
lim f (x).
x2+
(iii) Does lim f (x) exist? Is f continuo
1
Practice Questions for January 9
a) A nameless math prof weighed 179 pounds just before he left for the holidays and 190
pounds when he came back. He then lost 1% of his body weight during his rst week
back at work.
(i) What is the overall percentage in
1
Practice Questions for January 7
1. Simplify the following:
a)
4
10
7 2 + 2(3)2
(Answer:
1
)
14
b)
1 + (1 + (1 + 12 )2 )2
(Answer:
26)
c)
1 2
+
2 3
(Answer:
3
4
4
5
13
)
30
d) Suppose that a, b, and c are all positive real numbers. Then, write the foll
1
Practice February 27
a) Find the derivatives of the following:
(i) y = e2x
(ii) y = 3x
1
(iii) y = + 1
x
1
(iv) y =
x+1
(v) y = x10 + (x9 x8 + 1)7
(vi) y = ln(x + ex )
(vii) y = (x 1)2/3 (x 2)4/3
x
(viii) y =
1 + ln(x)
1
(ix) y = x
1
(3 + x2 + ln(2x) +
1
Practice February 25
a) Find the equation of the secant line joining points on the curve y =
x at x = 1 and
x = 9.
Answer:
3
1
y = x+ .
4
4
b) Find the equation of the secant line joining points on the curve y = x4 at x = 1 and
x = 1.
Answer:
y=1
(its a
1
Practice Questions for February 15
a) Prove that there is a root in the interval [1, 3] for the function
f (x) = (x 3) ln(x) + x 2.
Answer:
This function is only discontinuous at x = 0 (because of the ln), and so it is
continuous on [1, 3]. Also, f (1)
1
Practice Questions for February 13
a) Evaluate the following:
lim
x5
Answer:
x41
x5
1
2
b) Graph the function given by y =
x2 +4x+3
x+3 .
Answer:
c) Evaluate the following:
i)
ii)
iii)
iv)
v)
Answers: i) 0;
ii) ;
iii) 1;
5
x 2 x
lim
lim x2
x
x2 + 1
x x2
1
Practice Questions for February 11
a) Evaluate the following:
i)
ii)
lim
x0+
lim
x20
iii)
ii) ;
iii) ;
20 + x
20 x
lim ln(x)
x0+
1
xa+ a x
iv)
Answers: i) ;
1
x
lim
iv)
b) Evaluate the following:
i)
x5
ex4
x3
lim
x4
ii)
iii)
lim x
x 1
2
lim
x64
iv)
An
MATH*1030 F13
Questions for Quiz 9
3
x?
1. What is
(a)
1
x
3
(b) x2
3
(c) x2 + C
(d) ln(x) + C
(e) 3ln(x) + C
2. Which one of the following is the indenite integral of x4 ?
(a) x4 + C
(b)
(c)
(d)
(e)
x4
4
x5
4
x4
5
x5
5
+C
+C
+C
+C
3. Which one of the fol
MATH*1030 F13
Questions for Quiz 5
1. Let H(x) be the Heaviside function as dened in class. What is lim H(3x 9)?
x3+
(a)
(b)
(c)
(d)
(e)
6
0
1
3
2. Let H(x) be the Heaviside function as dened in class. What is lim 3H(x) 9?
x3+
(a) 6
(b) 0
(c) 1
(d) 3
(e)
DEPARTMENT OF MATHEMATICS AND STATISTICS
Math 1030, F16
Midterm 1
1. This is a 50 minute test. Do NOT start until instructed.
2. Please fill out your personal details on the cover of the Examination Booklet(s). If
you use more than one booklet, please ind
DEPARTMENT OF MATHEMATICS AND STATISTICS
Math 1030, F15
Midterm
1. This is a 50 minute test. Do NOT start until instructed.
2. Please fill out your personal details on the cover of the Examination Booklet(s). If you
use more than one booklet, please indic
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