THE UNIVERSITY OF NEW SOUTH WALES
SCHOOL OF MATHEMATICS AND. STATISTICS
Semester 1 2012
MATH1151
Mathematics for Actuarial Studies
and Finance 1A
(1) TIME ALLOWED 2 HOURS
(2) TOTAL NUMBER OF QUESTIONS A 4
(3) ANSWER ALL QUESTIONS
(4) THE QUESTIONS ARE OF
Math 1151. Calculus 2009. S1. Test 2 Version 1b. (1) Determine all a, b such that the function
R
f (x)
=
ax + b ln x
if x 1 if x > 1
is differentiable at x = 1. Solution. For f to be differentiable at x = 1, we require
x1-
lim f (x)
=
x1+
lim f (x)
f (1 +
School of Mathematics and Statistics
University of New South Wales
MATH1151
Mathematics for Actuarial Studies and Finance 1A
MATLAB Computing Exercises 2014
The purpose of this handout is to help you prepare for the MATLAB Computing Test in week
10. Model
MATH1151 Calculus Test 1 Solutions
c UNSW MATHSOC 2013
These solutions were written by Johann Blanco and typed up by David Ong. Please be
ethical with this resource. It is for the use of MATHSOC members, so do not repost
it on other forums or groups witho
Faculty of Science
School of Mathematics and Statistics
MATH1151
Mathematics for Actuarial Studies
and Finance 1A
Calculus Problems
Semester 1 2014
CRICOS Provider No: 00098G
2014, School of Mathematics and Statistics, UNSW
1
CONTENTS
Introduction .
Calc
Chemistry
Stage 6
Syllabus
Amended October 2002
2002 Copyright Board of Studies NSW for and on behalf of the Crown in right of the State of New South Wales.
This document contains Material prepared by the Board of Studies NSW for and on behalf of the Sta
page 1
Mathematics Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
The Trigonometric Functions
14
7
14
11
e
How many solutions of the equation (sin x 1)(tan x + 2) = 0 lie between 0 and 2?
(A) 1
(B) 2
(C) 3
(D) 4
2
Evaluat
Mathematics Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
page 1
Probability
14
10
Three runners compete in a race. The probabilities that the three runners finish the
1 1
2
race in under 10 seconds are
,
and
respectivel
Mathematics Ext 1 Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
page 1
Linear Functions and Lines
14
4
The acute angle between the lines 2x + 2y = 5 and y = 3x + 1 is .
What is the value of tan ?
1
1
(A)
(B)
(C) 1
(D) 2
page
Page
1 1
General Mathematics HSC Examinations by Topics compiled by projectmaths.com.au
Prel :AM1: Algebraic Modelling Algebraic manipulation
SP
7
11
12
13
5
Which of the following expresses
(A) 5x2
10
12T 2
in its simplest form?
3T 2W
8T
(B) 2TW
(C)
page
Page
1 1
General Mathematics HSC Examinations by Topics compiled by projectmaths.com.au
Prel: DS3: Data and Statistics - Summary Statistics
14
14
Twenty Year 12 students were surveyed. These students were asked how many
hours of sport they play per w
Mathematics Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
page 1
Applications of Calculus to the Physical World Kinematics (x, v, a)
14
9
The graph shows the displacement x of a
particle moving along a straight line as a
Mathematics Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
page 1
Geometric Applications of Differentiation
14
11
f
The gradient function of a curve y = f(x) is given by f (x) = 4x 5. The curve
passes through the point (2
Mathematics Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
page 1
Integration
14
14
14
13
11
d
12
d
Find
1
(x 3)
2
dx.
The parabola y = 2x2 + 8x and
the line y = 2x intersect at the
origin and at the point A.
(i)
Find th
page 1
Mathematics Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
Logarithmic and Exponential Functions
14
14
3
4
What is the solution to the equation log2(x 1) = 8?
(A) 4
(B) 17
(C) 65
Which expression is equal to
(A) e2
Mathematics Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
page 1
Combined Topics
10
10
a
Solution
In the diagram, ABC is an
isosceles triangle AC = BC = x.
The point D on the interval AB is
chosen so that AD = CD.
Let AD
Mathematics Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
page 1
Linear Functions and Lines
14
5
14
12
b
13
2
Which equation represents the line perpendicular to 2x 3y = 8, passing through
the point (2, 0)?
(A) 3x + 2y =
Mathematics Ext 1 Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
page 1
Parametric Representation
14
10
Which equation describes the locus of points (x, y) which are equidistant from the
distinct points (a + b, b a) and (
Mathematics Ext 1 Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
page 1
Mathematics Course (Prel)
14
11
a
13
11
d
Consider the function f(x) =
(i)
(ii)
12
1
12
13
b
3
2
2
2
Solve x 6 x + 9 = 0.
x
x
x
Solution
Solution
.
4
Mathematics Ext 1 Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
page 1
Apps of Calculus to the Physical World Projectile Motion
14
14
a
Solution
The take-off point O on a ski jump is located
at the top of a downslope. Th
Mathematics Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
page 1
The Tangent to a Curve and the Derivative of a Function
14
11
c
Differentiate
13
11
b
Evaluate lim
x 2
x3
.
x 1
x3 8
x2 4
.
2
Solution
2
Solution
Find the
General Mathematics HSC Examinations by Topics compiled by projectmaths.com.au
page
Page
1 1
Prel: MM2: Measurement Applications of area and volume
SP
2
SP
26
b
For which solid could the volume be calculated using the formula V = Ah?
1
Solution
The diagra
Mathematics Ext 1 Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
page 1
Permutations and Combinations
14
8
In how many ways can 6 people from a group of 15 people be chosen and then
arranged in a circle?
14!
14!
15!
15!
(
page 1
Mathematics Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
Plane Geometry
14
15
b
(i)
(ii)
Show that DEF is similar to DSR.
x
DR
Explain why
=
.
xy
DF
12
16
c
16
a
Show that
(iv)
Using the result from part (iii) an
General Mathematics HSC Examinations by Topics compiled by projectmaths.com.au
page
Page
1 1
HSC: AM4: Algebraic Modelling Modelling linear relations
14
26
f
The weight of an object on the moon varies directly with its weight on Earth. An
astronaut who we
Mathematics Ext 1 Higher School Certificate Examinations by Topics compiled by projectmaths.com.au
page 1
Further Probability
14
11
b
The probability that it rains on any particular day during the 30 days of November
is 0.1. Write an expression for the pr
page
Page
1 1
General Mathematics HSC Examinations by Topics compiled by projectmaths.com.au
SP
26
a
11
25
a
Prel: DS1: Data and Statistics - Statistics and society, data collection and
sampling
A study on the mobile phone usage of NSW high school student
MATH1131 Mathematics 1A
and
MATH1141 Higher Mathematics 1A
CALCULUS NOTES
as additional resource
for MATH1151
CRICOS Provider No: 00098G
c
2017
School of Mathematics and Statistics, UNSW
Sydney
Preface
Please read carefully.
These Notes form the basis for
Faculty of Science
School of Mathematics and Statistics
MATH1151
Mathematics for Actuarial Studies
and Finance 1A
Calculus Problems
CRICOS Provider No: 00098G
c
2017
School of Mathematics and Statistics, UNSW
1
CONTENTS
Introduction .
Calculus problems .
Matrices
Topic and contents
Matrices
Definition (Vector space of Matrices)
School of Mathematics and Statistics
Mm,n (R) = vector space of m by n matrices
A Mm,n (R)
a11 a12
a21 a22
A= .
.
.
.
am1 am2
MATH1151 Algebra
A/Prof Josef Dick
Lecture 05 Ma
MATH1151 Some problems from the Chapter 1 lectures
1. Let xn =
1
1+
n
n
, for n = 1, 2, 3, . . . .
Prove that
1. cfw_xn is increasing.
2. cfw_xn is bounded above.
Solution. 1. We need to show that for any n
n
n+1
1
1
1+
< 1+
n
n+1
Expand out the two ex
MATH1151 Mathematics for Actuarial
Studies and Finance 1A
INFORMATION BOOKLET
Semester 1 2017
CRICOS Provider Code 00098G
c
2017
School of Mathematics and Statistics, UNSW
1
CONTENTS OF THE
MATH1151 COURSE PACK 2017
Your course pack should contain the fol