__Polynomial Functions and Equations__

·
Factoring types

à
common, difference of squares, sum & difference of cubes, Trinomial (Type I
and II), grouping, and factor theorem.

·
Solving equations

à
quadratic equations: with and without the linear term, using factoring where
possible and the quadratic formula where factoring is not possible, with real
and complex solutions.

à
non-quadratic equations (i.e. linear, cubic, and quartic)

·
Graphing polynomials with degrees 2, 3,
and 4

·
Solving non-linear inequalities

1.
How do you know if you can use
trinomial factoring on an expression?

2.
How can you tell if a quadratic
expression is factorable without actually factoring?

3.
How can you identify a difference of
squares pattern?

4.
Explain how to identify a sum of cubes
and provide an explanation as to how to factor it.

5. Identify
what type of factoring you would use on each of the following expressions and
explain why you would use that method:

a) _{} b) _{} c)** _{}**

**6.
**Factor Fully.** **

a) ** _{}** b)

d) _{} e)
_{} f)
_{}

g) _{} h) _{} I)
_{}

7. Factor
each of the following fully. (Do NOT expand before factoring!)

a) _{} b) _{}

8.
What are the things you think is
important to remember when solving a polynomial equation? If you were asked
what type of factoring you would use first, what order would you put the
different factoring skills in?

9.
Solve each of the following using the
most efficient method. _{} (No decimals)

a) _{} b)
_{} c) _{} d) _{}

e) _{} f) _{} g) _{} h) _{}

i) _{} j) _{} k)
_{} l) _{}

m) _{} n) _{} o) _{}

10. Explain
the steps required to sketch a polynomial function using its roots.

11. Sketch
each of the following functions using the x-intercepts, and basic shape of the
curve.

a) _{} b)
_{} c) _{}

12.

a) Find the family of quartic functions whose x-intercepts
are –2, –1, 1 and 3.

b) Find the specific quartic function that has the intercept
in a) and passes through the point (2, –6).

13.

a) Find the family of
cubic functions whose roots are –2, –1 and 0.

b) Find the specific
function that has the roots in part a) and passes through the point (2, 6).

14. Find
the specific function that passes through the points (3, 0), (–2, 0), (4,0) and (0, –4)

__Exponents
and Logarithms__

· Simplifying using exponent rules

·
Evaluating (EXACT VALUES) of
exponential expressions

· Solving exponential equation à Using same base, factoring, and logs.

· Evaluating (EXACT VALUES) of logarithmic expressions

· Convert from log to exponential form and from exponential to log form

· Write as a single logarithm/ expanding logs

·
Solve Logarithmic equations à
Using same base, and exponential form

· Exponential Growth and Decay problems using logarithms

1. Evaluate
without a calculator:

a) _{} b) _{} c) _{} d) _{}

2. Simplify
each of the following.

a) _{} b)
_{} c) _{}

3. Express
as a single power with base 5: _{}

4. Write
each logarithm in exponential form.

a) _{} b) _{} c) _{}

5. Write
each exponential in logarithmic form.

a) _{} b)
_{} c) _{}

7. Evaluate
each logarithm without a calculator.

a) _{} b) _{} c) _{} d) _{}

e) _{} f)
_{} g) _{}

h) _{} i) _{}

8. Expand
each of the logarithms.

a) _{} b) _{}

9. Write
Each as a *Single* Logarithm:

a) _{} b)
_{}

10. Solve
for the unknown. (Give to one decimal place if needed.)

a) _{} b) _{} c) _{} d) _{}

e) _{} f) _{} g) _{}

h) _{} i)_{}

j) _{} k) _{}

11. If *x* equals _{} , *y *equals _{}, and *z *equals _{} simplify the following
into terms of *m *and *n.*

_{}

12. Show
that _{}

13. What
are the restrictions on the following logarithms, and explain how you would
convert them to exponential form.

a) _{} b)_{} c)_{}

14. The
population of a bacteria grows at 17% per day.

a) How
many days will it take for the bacteria to double in size?

b) After
30 days, the bacteria have grown to a population to a size of 1.45 x 10^{4}.
Approximately how many bacteria was there initially?

15. In
1992, the population of the

a) Write
an equation to represent the population of the

b) Calculate
the approximate year that the population will be double that of 1992.

16. In
1976, a research hospital bought half of a gram of radium for cancer research.
Assuming

the hospital still exists, how much of
this radium will the hospital have in the year 6836,

if the half life of the radium is 1620
years?

17. There are 50 bacteria present
initially in a culture. In 3min., the count is 204800.

What is the doubling period?

18. In a recent dig, a human skeleton was
unearthed. It was later found that the amount of ^{14}C

in it had decayed to _{} of its original
amount. If ^{14}C has a half life of 5760 years,

how old was the skeleton?

__Trigonometry
in the Coordinate Plane__

·
Exact Values

Evaluate
Expressions

·
Solving Trigonometric Equations à
Special Triangles and Unit Circle

à
Cast Rule

à
Factoring

à
Using Radians

·
Prove Identities

·
Graphing Trigonometric Functions ( _{} or _{} )

·
Domain / Range

·
Amplitude, Period, Phase Shift,
Vertical Translation, Reflection (Vertical and Horizontal)

1. Evaluate the
following: a) _{} b) _{} c) _{}

2. If _{} , make a diagram and
find the other five ratios, if Ðq is
acute.

3. If _{} and Ðq is
obtuse, find the exact values of the other five ratios

and the
approximate value of q ,

4. Determine the exact value.

a) _{} b) _{} c) _{} d) _{}

e) _{} f) 5sec30°tan60°

5. If _{} , find all possible
values of 0° £ q £
360° .

6. Solve each of the following for _{}. Where necessary, round to one decimal place.

a) _{} b) _{} c) _{}

d) _{} e) _{} f) _{}

g) _{} h) _{} i) _{}

j) _{} k) _{}

- Prove the following identities.

a) _{} b)
_{}

c) _{} d) _{}

e) _{} f)
_{}

g) _{} h) _{}

- State
the domain, range, period, amplitude, vertical translation and phase shift
of each of the following:

a) _{} b) _{} c) _{}

d) _{} e) _{} f) _{}

- Sketch
two cycles of each function in #2.

__Applications
of Trigonometric Ratios and Vectors__

·
Pythagorean Theorem

·
Primary Trig ratios (sin x , cos x, and
tan x) and Inverse Trig Ratios (cscx, secx, tanx)

à
Solving for the angle and solving for the side

·
Sine Law à
Solving for the angle and solving for the side

·
Cosine Law à
Solving for the angle and solving for the side

·
Ambiguous Case of Sine Law

·
Application questions -> Angle of
elevation and depression.

·
Multi-step questions (Indirect
Measurement) à you need to find more than one thing to get to the final
answer

·
Resultant and Equilibrant Vectors

·
Resolving Vectors

·
Applications of Vectors

1. State
the formula for each and describe when you should use them:

a) a
primary trig ratio

b) the
Pythagorean theorem

c) the
sine law

d) the
cosine law

2. Solve
for the unknown side. (Round to 2 decimals if necessary.)

a) b)

3. Solve
each of the triangles. (Round your angle to the nearest degree and the side
length to 1 decimal place.) Give ALL possible solutions.

a) Given
DRST
where ST = 9.0 m, ÐS = 90^{o},
and ÐT =
46^{o}.

b) DJKL
is given with JL = 5.0 cm, JK = 2.7 cm and ÐK =
57^{o}.

c) Given
triangle ABC where AB = 9.8 cm, ÐA =
27^{o} and ÐC = 112^{o}.

d) DPQR
has PQ = 7 cm, QR = 6 cm, and PR = 9 cm.

4. Explain
how you know when solving a triangle that you must check for the ambiguous
case.

5. A
triangular park measures 250.0 m along one side. The other two sides form
angles of 32^{o} and 56^{o} with the first side. Calculate the
area of the park.

6. Two
boxes are 65 cm apart. The angle of depression from the top of taller box to
the top of the shorter box is 22^{o}. How high is the taller box given
that the shorter box is 25 cm tall?

7. Two
office towers are 31.7 m apart. The angle of elevation from the top of the shorter tower to the top of the taller tower
is 27^{o}. The angle of depression from the top of the shorter tower to
the base of the taller tower is 48.2^{o}. Calculate the height of each
tower.

8. Explain
the difference between vectors and scalars.

9. How
does a vector sum result in the zero vector? Explain using diagrams.

10. Label the following vector in two different
ways:

11. Find the resultant vector of the forces 50 N at [E35°N] and 65N at
[W40°N] **graphically.**

12. Given the following diagram, use
components to determine the magnitude and direction of the resulting force:

13. The pilot of an airplane that flies at 800 km/h wishes to
travel to a city 800 km due east. There is a 80 km/h wind from the north east.

a) What should the plane’s heading be?

b) How long will the trip take?

__Geometry and The Circle__

·
Calculating Perimeter, Area, Volume and
Surface Area

·
Arc Length and Chord of a Circle

·
Determining the equation of a circle
given radius and the coordinates of the centre

·
Solving linear-quadratic systems by
substitution to determine the point of intersection of a line and a circle

·
Determining the equation of a tangent
to a given circle

1. Determine
the equation of the circle with diameter of 8 units and centre at (-8,-1).

2. Solve
each system. No decimals allowed.

a) _{} b)
_{} c) _{}

3. Determine
the point(s) of intersection between the circle _{} and the line _{}

4. What
two numbers differ by 5 and have squares with a sum of 196?

5. For
a circle with radius 7 cm, determine the exact value of the arc length
subtended by an angle of 315°.

6. The
hypotheneuse of an isosceles right triangle is the chord of a circle. The
equivalent sides in the triangle represent the circle’s radius, and the length
of the chord is 12 cm. Determine the length of the arc subtended by the chord.

7. Determine
equations of the tangents with slope -1 to the circle x^{2}+y^{2}=6.