Question 2 w [Ll
Evaluate (gr (13:3)?
e 63;
a a
Question 3 [E] E]
Evaluate log 100 cfw_100.
e 105
o 103
e 5 PartlA
Question 4
mm
Sohre forthe variable a in logzz = 3.
Queson 5
Evaluate 510353
a 125 PartlA
Question 6
Simplify log32'i' + 10g39.
Mar
k
Tota
l
22
24
14
19
24
103
22
25
16
21
29
113
LESSON 11
33.
R
12 cm
Q
6 cm
8 cm
cosR=
122+6 282
2(12)(6)
cosR=
144+3664
144
cosR=
116
144
R=cos1
( 116
144 )
R=36.3
4
34.
P
[22/22]
Unit
Mark
91%
2
6
A
6
2
A
Good diagram
tanA=
2
6
A=tan 1
( 26 )
A=18.
Note: * will indicate 1 mark on solutions that have not earned full marks.
LESSON 6
10/10 marks
21.
3x
5 6 3
( 4 ) (3 x )
9
( 39 x36 ) ( 315 x 18 )
3915 x 3618
6
3 x
18
1 18
x
36
x 18
36
x 18
729
7
63 a5
511 b 2
x
5 9
6 3
5b
6 a
3
( )( )
621 a35
533 b6
LESSON 16
49.
The next 3 terms are 35, 48, and 63. The pattern is adding successive
odd numbers, starting with 3, to the successive terms.
x
f ( x ) First
Second
Differenc Differenc
es
es
1
0
2
3
3
3
8
5
2
4
15
7
2
5
24
9
2
6
35
11
2
7
48
13
2
8
63
15
2
LESSON 2
a
3 2
4
( 3 a b ) (5 a7 b2 ) ( 4 a3 b6 ) 0
( 32 a4 x 2 b 3 x 2) (5 a7 b2 ) ( 40 a3 x0 b6 x 0 )
( 9 a8 b6 )(5 a7 b2 ) ( 1 a0 b0 )
8 6
7 2
9 a b (5 ) a b ( 1 )
9 (5 ) a 8+7 b6 +2 ( 1 )
15
45 a b
b
8
3 b2
x4 a
y2 a
( )
2
x 4 a (3 b )
2a(3b )
y
1.
a
( 4 a3 ) (9 a5 )
4 ( a3 ) (9 ) ( a5 )
4 (9 ) ( a 3+5 )
8
36 a
b
3
8
17
9x y z
5 5 10
3 x y z
3 x
35
y
85
3 x2 y 3 z 7
3 y 3 z 7
2
x
c
(7 k 8 )
3
7 3 k 8(3)
7 3 k 24
343 k
24
d
( 2 a3 b6 )
5
( 3 a 4 b4 )
2
z
1710
5
3(5)
6 (5 )
2a b
2 4 (2) 4 (2)
3 a
Unit 1 Earning Money
Lesson 1
1. A) Car dealership sales representatives
Insurance policy sales people
B) Retail workers
Skilled trades (ex. Electrician)
C) Hair dressers
Waiters/waitresses
D) Computer software designers
Artists (Ex. Painter)
2. A) There
Unit 4: Saving, Investing and Borrowing
Lesson 16
51. A) A chequing account would be best suited to cover everyday expenses (bill payments,
payroll deposits, cash withdrawal and so on), but if your money will likely just sit there,
use a savings account.
Unit 2 - Purchasing Power
Lesson 6
20. A) Discount two will save more money.
Discount one:
1 3 x 100 = 0.3333 x 100
= 33% discount
A 50% discount is better than a buy two get on free (33% discount), unless you really
needed three of that particular item.
Unit 3: Transportation and Travel
Lesson 11
31. A) Both G1 and G2 drivers must maintain this while driving: zero blood alcohol
B) If a new driver has a G1 license and has completed a driving course, he or she can try the G1 road test
after 8 months, other
Math Key Questions
41.
Equation:
y=x
Vertex:
Equation of axis
of symmetry:
(0,0)
Transformations
of standard
parabola (
2
y=x ):
0 units
2
2
y=3 x 8
(0,-8)
x=0
y=(x6)2+4
(6,4)
x=0
(-3,-7)
x=6
Vertical
translation of 8
units down
2
y=4 ( x+3 ) 7
x=3
Horiza
Name:_
Quadratic Functions. Practice 5
1. Sketch the following functions:
a. = 4( + 2)2 3
b. = ( 4)2
1
c. = 2 ( 5)2 + 3
d. = 3 2 + 4
2. Determine the equation of the parabola that has
a. a vertex at (3,5) and passes through the point (8,10)
b. an optimum
1.4 TRANSFORMATIONS
polynomial functions f(x) = xn can be transformed by adjusting the
value of four parameters, a, k, d, and c
the general equation is of the form f(x) = a[k(x d)]n + c
a,k,d, and c are real numbers
The role of d and c
Ex. Graph each gr
1.6 TANGET LINES AND INSTANTANEOUS RATES OF CHANGE
An instantaneous rate of change corresponds to the slope of the
tangent line to a point on the graph
A tangent is a line that touches the graph at only one point and
follows the shape of the graph at th
2.1 THE REMAINDER THEOREM
2.2 THE FACTOR THEOREM
The Remainder Theorem
When a polynomial P(x) is divided by ax b, the remainder is
P(b/a), where a and b are integers, and a 0.
Ex. What is the remainder when 4x3+9x-12 is divided by 2x+1
Soln:
P( x) 4 x 3 9
3.2 RECIPROCAL OF A QUADRATIC FUNCTION
The reciprocal of a linear function has the form:
f ( x)
1
ax 2 bx c
The behavior near asymptotes is similar to that of reciprocals of
linear functions
Reciprocals of quadratic functions with two zeros have three
1.2 CHARACTERISTICS OF POLYNOMIALS
Polynomials of Odd-degree
positive leading coefficient - extends from Q3 to Q1
negative leading coefficient - extends from Q2 to Q4
have at least one x-int, up to a maximum of n x-int
the domain of all odd-degree poly is
1.5 SECANTS AND AVERAGE RATES OF CHANGE
a rate of change is a measure of the change in the dep-variable
with respect to the indep-variable
ex. a car leaves Toronto at 12pm and arrives in Ottawa at 5pm, a
distance of 400 km. The average speed would be 80
3.3 RATIONAL FUNCTIONS
The rational functions we will study in this course will have the
form:
f ( x)
ax b
cx d
The equation of the vertical asymptotes can be found by setting
the denominator equal to zero and solving for x
The equation for the horizo
2.6 SOLVE FACTORABLE INEQUALITIES ALGEBRAICLLY
Factorable inequalities can be solved algebraically by:
considering all cases
using intervals and then testing values in each interval
Multiplying or dividing both sides of an inequality by a negative
val
3.1 RECIPROCAL OF A LINEAR FUNCTION
The reciprocal of a linear function has the form:
f ( x)
1
kx c
The restriction on the domain of f(x) is when the denominator is
zero, that is when x = c/k
5y
y =1/x
4
The vertical asymptote
of f(x) has an equation
3.4 SOLVING RATIONAL EQUATIONS AND INEQUALITIES
To solve rational equations algebraically, start by factoring the
numerator and the denominator to find asymptotes and
restrictions.
Next multiply both sides by the factored denominator and simplify
to obt
1.1 POWER FUNCTIONS
A polynomial expression is an expression of the form:
anxn an1 xn1 an2 xn2 . a3 x3 a2 x2 a1 x a0
n is a
whole
number
x is a variable
the coefficients a0,a1,a2, are real numbers
the degree of the expression is n, the exponent of the
1.3 EQUATIONS AND GRAPHS OF POLYNOMIALS
zeros of a polynomials function y = f(x) correspond to the x-int of
the graph and to the roots of the equation f(x) = 0.
for eg. has zeros 2 and 1. These are the roots of (x 2)(x + 1) =
0.
If a polynomial functio
2.3 POLYNOMIAL EQUATIONS
The real roots of a polynomial equation P(x) = 0 correspond to the
x-int of the graph of the polynomial function P(x)
The x-int of the graph of a polynomial function correspond to the
real roots of the related polynomial equatio
Unit 4
Lesson 16 Key Questions
#63
#64
One situation that could be modelled by the given graph could be the
height of a certain cabin of the ferris wheel against time. The static part
of the graph would represent the ferris wheel going out of service.
#65
Unit Two
Lesson 6 Key Questions
#31
Degree: 6
Dominant term : 8 x
6
#32
D omain: cfw_ x R R ange : cfw_ y R ; y 5
#33
i-c
ii - a
iii - b
#34
Negative coefficient and odd exponent, therefore as
x f ( x )
x f (x )
#35
a) x intercepts: two at x = 2, one a