2017
AP Calculus BC
Free-Response Questions
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AP
Chapter 4
Demand
Deriving Demand Curves
Effects of an Increase in Income
Effects of a Price Increase
1
Deriving Demand Curves
If we hold peoples tastes, their incomes, and the prices of other goods
constant, a change in the price of a good will cause a m
6/14/2016
IEB Wireframe
APPENDIX 1B: EMPLOYMENT IN THE ACCOUNTING PROFESSION TODAY
Since 1900, accounting has attained the stature of professions such as law, medicine, engineering, and
architecture. As with all recognized professions, accounting is subje
Chapter 2_Part III
qSupply and Demand Analysis
Government Intervention
1
Sales Tax
1. Why do governments implement taxes?
2. What effect does a sales tax have on a products equilibrium price and
quantity?
3. Can the government determine who pays the tax
Chapter 3
A Consumers Constrained Choice
Part II
Budget Constraint
Optimal Choice
1
Budget Constraint
Assumptions:
Fixed budget or endowment.
No borrowing allowed.
No savings allowed.
Purchase of fractional amounts possible.
Consumers must pay price (ex
Chapter 4_Part II
Demand
Effects of a Price Increase
1
Price Changes
Holding tastes, other prices, and income constant, a change in the price of a
good has two effects on an individuals demand:
Total effect = Substitution effect + Income effect
Substi
Chapter 3
A Consumers Constrained Choice
Objectives
1. Represent Preferences
2. Utility Functions
3. Budget Constraint
4. Optimal Choice
1
Why study consumer choice or behaviour?
Study of how consumers with limited resources
choose go
Chapter 4
Demand
Deriving Demand Curves
Effects of an Increase in Income
Effects of a Price Increase
1
Deriving Demand Curves
If we hold peoples tastes, their incomes, and the prices of other goods
constant, a change in the price of a good will cause a m
Chapter 4_Part II
Demand
Effects of a Price Increase
1
Price Changes
Holding tastes, other prices, and income constant, a change in the price of a
good has two effects on an individuals demand:
Total effect = Substitution effect + Income effect
Substi
Chapter 2_Part II
Supply and Demand Analysis
3. Elasticities
1
Elasticities
The shape of demand and supply curves influence how much shifts in
demand or supply affect market equilibrium.
Shape is best summarized by elasticity.
2
Elasticity indicates h
Math 119
Assignment #6
Winter 2016
Solutions
1. The correspondence is as follows:
(a) (iv)
(b) (ii)
(c) (i)
(d) (iii)
1
x2 + y 2
f (x, y) = x2 + y 2
f (x, y) =
f (x, y) = (x2 + y 2 )2
f (x, y) = x2 + 2y 2
2. (a) First we find the corresponding output valu
Math 119
Assignment #6
Winter 2016
Due: Friday March 4th by 1:00pm (execpt for Monday tutorial)
Hand in #2, 4, and 6
1. Match each picture with the appropriate function below. Note the plots correspond to the
level curves f (x, y) = k.
(a)
(c)
(b)
(d)
(i)
MATH 119
Solutions to Assignment #3
Winter 2016
1. First we will find a polynomial for g(u) = sin(u) where u [0, 3] and then do a substitution u 3t2 .
Taking the derivatives and evaluating at u = 0 (since we are to use a Maclaurin polynomial) we get
g(u)
Math 119
Assignment #4
Winter 2016
Solutions
1. Assume that |r| < 1, that N is an integer (possibly negative), and that a is
any old real number. Write down a closed form expression for
X
ark
k=N
in terms of r, N , and a. Using what you just did, write do
Math 119
Assignment #5
Winter 2016
Solutions
1. Find the radius of convergence, as well as the interval of convergence for the following
power series.
(a)
X
(x 1)n
n=1
5n
Apply the ratio test:
n
an+1
(x 1)n+1
(x 1)
5
= lim
= lim
lim
n an
n
5n+
MATH 119
Assignment #2
Winter 2016
1. Find a polynomial of degree 6 passing through the points (2, 3), (3, 0), (4, 3), (5, 1), (6, 2), (7, 6), (8, 0).
Solution: When making the homework, this seems like a good question. Until you actually have to
do it. A
Math 119
Assignment #5
Winter 2016
Not for Submission
Solutions to be posted on February 13th
1. Find the radius of convergence, as well as the interval of convergence, for the following
power series.
(a)
X
(x 1)n
5n
n=1
(b)
X
nxn
n+1
n=1
(c)
X
3n n
x
n!
Assignment #3
Math 119
Winter 2016
Due: Friday, January 29th by 1:00pm (except for Monday Tutorial)
1
Z
sin(3t2 ) dt by using the Maclaurin polynomial of degree
1. Approximate the value of
0
11 of the function
x
Z
sin(3t2 ) dt.
f (x) =
0
Calculate an uppe
MATH 119
Assignment #1
Winter 2016
Mon, Wed & Thurs Tutorials: due Friday, January 15th at 12 p.m. in drop boxes
Friday Tutorial: due Monday, January 18th at 12 p.m. in drop boxes
Please include your full name, student ID, and tutorial section on the fron
Math 119
Assignment #4
Winter 2016
Due: Friday, February 5th
Hand in #1, #2a-f, #3 (the rest of #2 is just for practice).
1. Assume that |r| < 1, that N is an integer (possibly negative), and that a is
any old real number. Write down a closed form express
MATH 119
1.
Solutions to Assignment #1
Winter 2016
q
2
2
2
(a) E = (pc) + (mc2 ) can be written as E = E0 1 + x, where E0 = mc2 and x = (p/(mc) is considered small
1/2
when c is large. For f (x) = 1 + x we have f (0) = 1 and f 0 (x) = 21 (1 + x)
, giving
Chapter 5
Consumer Welfare and Policy
Analysis
1
Consumer Welfare
Expenditure Function and Consumer Welfare
Market Consumer Surplus
Effects of Government Policies on Consumer
Welfare
2
Child-care Subsidies
Background:
Government child-care subsidies are