MCR 3U
Chapter 1 : Rational Expressions Review
1. Simplify
8mn 2
a) mn
6x 2 6x
b) 18 x
x 2 4x 5
2
d) x 3 x 10
2( x 1)
c) (1 x )(3 x)
3 x 2 5 xy 2 y 2
4x 2 9 y 2
e)
2. Simplify
x 2 y xyz
2
z
xy
a)
2ab 14a 2 b 2
15c 2
b) 5c
x 2 x2 4
2
c) x 3 x 9
x 2y x y
a
MCR 3U FINAL REVIEW
CHAPTER 5: TRIGONOMETRY 2
1. Given y = sin , -360360, find the period, amplitude, and range
2. Question 1 for y =cos
3. a)
b)
c)
d)
Find the period of y = sin 3x _
Find the phase shift: y = sin(3x-90) _
Find the max value: y = 4 cosx -
MCR 3U FINAL REVIEW
CHAPTER 7: DISCRETE FUNCTIONS
1. Find the general term
a) -1,1,3,5
b)
2 4 8
, ,
3 9 27
2. Find t 8 if 4,11,18
3. Find the number of terms a) 3,12,48, 49 152
b) 24,12,6
3
8
4. Find n if t1 = -3, d=4 and Sn = 1650
5. find S6 of a geometr
MCR 3U FINAL REVIEW
CHAPTER 3: QUADRATIC FUNCTIONS
1. Given y = 4(x-3)2 +1, find the vertex, equation of the axis of symmetry, opening, domain and range
2. If f(x) = x2 +5, find the range of the inverse _
3. Find the zeros of the function y = 3(x+4) (x-2)
MCR 3U FINAL REVIEW
CHAPTER 2: FUNCTIONS AND RELATIONS
1. Given the relation (1,9),(2,7),(3,5),(4,3)
Find
a) domain and range
b) Is this a function ? Explain
2. Name the transformations on y=f(x)
a) y = 2 f(x)
b) y = - f(x+2)
3. If point (2,4) f(x), find
MCR 3U - Discrete Functions L
Shapter Expectations: By the end of the chapter, students should be able to:
DFl) Demonstrate an understanding of recursive sequences, represent recursive sequences in a variety of ways,
and make connections to Pascals Tria
_ A) Given the trigonometric function, state the following: a) Amplitude: (7
c) Maximum Value: 2
d) Minimum Value: ,
6) Equation :1 g .4 CM of (16.41 0) .2.
ofCosine: 5:4WLCK+53)"L-
f) .7710): 0
g) Equation of axis: J 2 2
h) Range:cfw_j at?! ~19 5 #2:
i)
May 2nd, 2017
.QR 3U - Exponential Functions Name: w
Chapter Expectations: By the end of the chapter, students should be able to:
EFl Evaluate owers with rational ex orients, sim lif ex ressions containin ex onents, and describe
. P . P P Y P _ g P
prop
MCR 3U - Characteiistics of Functions 4/ ct
Name:
Expectations: By the end of the course, students should be able to:
CF3) Demonstrate an understanding of equivalence as it relates to simplifying polynomial, radical and rationa
expressions.
November 16 2016
MCR 3U - Characteristics of Functions (t-m
Expectations: By the end of the course, students should be able to:
CFl) Demonstrate an understanding of functions, their representations, and their inverses
MCR 3U FINAL REVIEW
CHAPTER 4: TRIGONOMETRY
1. Solve the following triangles
a) ABC where B=90, b= 5,2m , a= 3,1m
b) ABC where a=9.6cm, b=20.6cm , c=14.7cm
c) ABC where B=115 , a=12cm, c=11cm
d) ABC where A=48 ,B=25 and c=121cm
2.
Find the value of the va
Sequences and Series ISU
Sequences Vocabulary
p. 428
define: sequence, term
write ex 1a, 2b, 3
knowledge p. 433 #1aef, 2adi, 3adgj, 4be
A number sequence is a set of numbers, usually separated by commas, arranged in an order.
The first term is referred to
1.)
A scientist has 100 female fish and 100 male fish. She measures their lengths to the nearest cm.
These are shown in the following box and whisker diagrams.
(a)
Find the range of the lengths of all 200 fish.
(3)
(b)
Four cumulative frequency graphs are
1.)
(a)
correct end points
(A1)(A1)
max = 27, min = 4
(b)
range = 23
A1
N33
Graph 3
A2
N22
[5]
2.)
(a)
fx = 1(2) + 2(4) + . + 7(4), fx = 146 + 5x (seen anywhere)
fx
evidence of substituting into mean =
(M1)
f
(b)
A1
correct equation
146 5 x
e.g.
= 4.5, 14
21
Chapter
Linear modelling
Syllabus reference: 5.4
cyan
magenta
95
100
50
75
0
5
95
yellow
25
Correlation
Pearsons correlation coefficient
Line of best fit
The least squares regression line
Interpolation and extrapolation
A
B
C
D
E
100
50
75
25
0
5
95
10
Repetition in Java
While Loops Recall: Simple Selection
One Action
The simplest selection statement tests a single
condition, and has a single action if the condition
is true.
int age = In.getInt();
if (age >= 18)
cfw_
System.out.println("You can vote!");
Repetition using Java Simple for Statements
The following is a practical example to illustrate the while statement. Depending upon the
condition at the beginning ofthe while loop, the code inside the loop may be executed zero, once, or
many times.
while (
Repetition in Java
Do Loops
(check condition at end) Recall: Simple Selection
One Action
The simplest selection statement tests a single
condition, and has a single action if the condition
is true.
int age = In.getInt();
if (age >= 18)
cfw_
System.out.pri
Repetition
One of the greatest strengths of computers is their
ability (and willingness) to do the same task over
and over again.
In addition, the computer will always perform the
task in exactly the same way for the same input,
provided the programmer (y
Repetition using Java do Statements
The following is a practical example to illustrate the while statement.
while (there are lumps in the gravy
give the gravy a stir
end while
First we check for lumps. If there are any lumps, start stirring. The idea is t
Making Decisions in Java
For our programs to become more useful, we
need to start making decisions.
Suppose we want to decide, Is the user old
enough to vote?
Conditions
Conditions are statements that can be tested as
either TRUE or FALSE.
input age
if (a
Assignment Repetition Scoring a Baseball Game
For this assignment, you will create a program to track the score of a baseball game. A standard
baseball game has 9 innings, but you may use a shorter game if you prefer (e.g, 3 innings is sufficient).
Regard
ICS 3U Assignment 3 Baseball Scoring
Example Output for Level 3
What is the name of the first team:
Royals
What is the name of the second team:
Blue Jays
Inning: 1
Current Score:
Royals: 0
Blue Jays: 0
How many runs for Royals:
1
How many runs for Blue Ja
Assignment Selection Statements
Feb 25, 2015
Problem Statement
One way of giving a direction is to simply use one of the letters N, E, S,
or W, indicating the nearest compass point. Another way is to give a
bearing as a number from 0 to 359 (since 360 wou
2016
Canadian
Computing
Competition:
Senior
Division
Sponsor:
1
Canadian Computing Competition
Student Instructions for the Senior Problems
1. You may only compete in one competition. If you wish to write the Junior paper, see the
other problem set.
2. Be