MATH 12 F EXAM REVIEW
TOPICS COVERED
1. SEQUENCES
· Explore and develop understanding for three types of sequences - arithmetic, quadratic and geometric
· Use a formula to generate terms in a sequence
· Explore graphs of the different kinds of sequences
2. QUADRATICS
· Explore the pattern and properties of the basic y = x2 function
· Explore graphs using transformations
· quadratics in applications (real life situations)
· become proficient with using the TI-83 calculator for graphing, changing the window, tracing, finding values, vertex, intercepts and a table
3. EXPONENTIAL GROWTH
· Explore the pattern and properties of the exponential function y = a(b)x, including base changes
· Explore the graphs
· Applying exponential relationships (compound interest)
· Some properties of exponents (the “laws”)
4. CIRCLE GEOMETRY
· Distance and midpoint
· Properties and relationship theorems
· Finding angles using the theorems
5. PROBABILITY
· Fundamental principle of counting
· Tree and area diagrams
· Simulations
· Distinguish between permutations and combinations
· Understand factorial notation
· Combine permutations and probability
Terminology/Vocabulary/Concepts to know
You should be able to define/explain, recognize and give an example of the following terms and concepts. Do this on your own to be sure you understand. It is a great way to study.
Chapter 1: Arithmetic sequence (including the formula)
Geometric sequence
Quadratic sequence
Common difference
Common ratio
Second level difference
Term
Fibonnacci sequence
Chapter 2: Parabola
Vertex
Axis of symmetry
x-intercepts (all possibilities for a quadratic)
y-intercept
maximum/minimum point
vertical/horizontal translation (how the equation affects the graph)
reflection in the x-axis
vertical stretch
Chapter 3: FIVE laws of exponents
Exponential growth
Exponential decay
How does the base in y = abx dictate growth or decay
Compound interest formula and what all the variables mean
Exponential regression on the TI-83 (finding the equation from a table of values)
Chapter 4: Midpoint formula
Distance formula
Complementary/supplementary angles
F and Z theorems
Diameter, radius, chord, arc, tangent
4 properties of circles
Chapter 5: probability of an event
Combination
Permutation
Outcome
Theoretical/experimental probability
Complement
Factorial notation
Practice Problems
Do these on your own as best you can; get help from a friend if you need help.
Problems: Chapter 1 - Sequences
1. Complete the next three terms of the following sequences:
a. {2,4,6,8…______
b. {6,10,14…______
c. {1,4,2,4,3,4…______
d. {1,2,4…______
e. {2,2,3,3,4,4…______
2. Given the following sequence, {1,3,9,27….}, determine:
a. The type of sequence______
b. The third term______
c. The pattern (in words)______
d. The next three terms______
3. Write the first four terms of the following sequences:
a. tn = 4n b. tn = 2n + 5 c. tn = n – 4
4. Make an arithmetic sequence of four terms where:
a. t1= 5 and d = 2
b. t1= -6 and d = 4
Now write the formula for these two sequaence. Compare the a and d values.
Use the four terms you created to show the graph for each sequence. Remember, DO NOT join the points on a sequence graph. Compare their shapes.
5. Make a geometric sequence of four terms where:
a. t1 = 1 and r = 3
b. t1 = 4 and r = 2
6. Numbers that can be shown in the shape of a triangle are called triangular numbers. The first four triangular numbers are shown.
· · · ·
· · · · · ·
· · · · · ·
· · · ·
1 3 6 10
a. Make a sequence of ten terms, where the terms show the number of dots needed to draw the first ten triangular numbers.
b. Write a sequence for the first level difference
c. Write a sequence for the second level difference
d. Name the type of sequence created in part (a). ______
7. Describe the type of sequence in each of the following:
a. {1,1,2,3,5,8,…______
b. {1,8,27….______
c.
______
d.
______
e) {1,4,9,16….______
PROBLEMS: Chapter 2 - Quadratics
1. For the following quadratic equations, draw a sketch and identify (next page):
a) the coordinates of the vertex
b) the value of the max/min point
c) the x-intercepts
d) the y-intercepts
e) the equation of the axis of symmetry
TRY TO DO THIS USING TRANSFORMATIONS, WITHOUT A TI-83!
i) y = (x – 2)2 – 1 ii) y = 2(x – 3)2 – 5 iii) y = -(x + 4)2 + 2
a)______a)______a)______
b)______b)______b)______
c)______c)______c)______
d)______d)______d)______
e)______e)______e)______
2. A sniper shoots at a target from a raised platform 2m high. The height ‘h’ of the bullet in meters can be described by the quadratic equation
h = -4.9t2 + 259t + 2, where ‘t’ is the time measured in seconds. When does the bullet finally hit the ground? (assuming that the bullet missed its target)
a) Using the graphing calculator, sketch the graph labeling the vertex and all intercepts. Use an appropriate window so you can see the parabola. (Do NOT use the race button for the x-intercepts. Use 2nd calc, zero, left bound, right bound, etc.)
PROBLEMS: CHAPTER 3 – EXPONENTS
1. Simplify each of the following:
a) 3p3 x p5 = ______b) (4x6)(2x4) = ______
c) (a3b6)3 = ______d) (-4x2y3z)(-5xy2z5) = ______
e) ( x15)¸(x10) = ______f) (12p4)¸(3p) = ______
g) (2a2b5c3)4 = ______h) 32 + 32 = ______
i) (3a2b4)(2x2y6) = ______j) 15a2b5¸ 5 a5b2= ______
k) (a2b) ¸ (ab2) = ______l) (41)(50)(30) = ______
m) (x8)(x2) ¸ (x3) = ______n) (10p4) ¸ (2p) x (3p3) = ______
2. If x = 2 and y = 3, calculate each of the following. Show all work!!!
a) (2x2 )( y2) b) 15x5 ¸ 5x3 c) (x2y4)(x3y) ¸ x5y5
3. Identify the following as linear, exponential growth or exponential decay:
a) b) c)
______
Graph, using a table of values:
a) y = 0.5x b) y = 6x
2a. Which graph shows growth? ______
b. Which graph shows decay? ______
c. In the equation, what determines growth or decay? ______
d. What point is common to both graphs? Why? ______
e. For the graph y = 0.5x, what is the value of x when y = 4? ______
f. For the graph y = 6x, what is the value of x when y = 4? ______
1. Jim deposits $550.00 into a fund that pays 6% interest compounded annually. How much will he have after 3 years?
2. Carlee invests $2500.00 into a bank account that pays 4% per year compounded quarterly. If she doesn’t touch the account, how much will she have in 5 years?
3. Jessica wants to save up for a trip to Florida. She deposits $100.00 into a fund that pays 5% per year compounded monthly. How much money will she have in 4 years?
PROBLEMS CHAPTER 4: CIRCLE GEOMETRY
1. Using the midpoint formula, find the midpoint of each line that contains the following endpoints:
a) (6,10) & (12, 14) b) (4,9) & (16,6)
c) (12,5) & (16,10)
2. Find the length of the line that contains the following endpoints:
a. (8,7) & (10,14)
b. (-5,12) & (10,24)
3. Give the value of each missing angle:
a) b) c)
d) e) f)
a° = ______b° = ______c° = ______
d° = ______e° = ______f° = ______
g° = ______h° = ______i° = ______
j° = ______
PROBLEMS – CHAPTER 5 – PROBABILITY
1. What is the probability of drawing a heart from a deck of cards?______
2. A dice is rolled. What is the probability that the number obtained is the following?
a) 5 ______b) 0 ______
c) an odd number ______d) a number greater than 4______
3. A bag contains 3 black cubes, 6 red cubes and 6 white cubes. What is the probability of choosing each of the following?
a) a black cube______b) a white cube ______
c) a red or white cube______d) not a black cube______
4. Based on the results thus far in the season, the Flyers have a 0.25 chance being first in their division. What is the probability that they will not finish first in their division? ______
5. The Flyers have won 2 out of the past 10 games.
a) What is the probability of winning the next game? ______
b) What are the odds of winning the next game? ______
6. A golf bag has 50 golf balls in a pocket.
· 25 are Topflight golf balls.
· 15 are Pinnacle golf balls.
· 20 are no name brands.
Topflight Pinnacle
20
a) Determine the probability of picking either a Topflight or a Pinnacle golf ball from the bag.
P(T or P) = P(T) + P(P) – P(T & P)
7. The cafeteria is having a lunch special. You can choose from a hamburger or a cheeseburger. Along with this you get your choice of fries, salad or rice. For your drink you can have pop, water, milk or juice.
a) What is the total number of different combinations available to you?
b) Draw out a tree diagram to verify your answer.
8. Write out the meaning of 8! ______
a) What is the value of 8! ______
9. Determine the value of each of the following.
a) 4P3 b) 10C5 c) 10P3
10. Determine if the following are permutations or combinations. Calculate each possibility.
a) There are 15 players on a hockey team. 4 players are to be sponsored for a summer hockey camp. How many possibilities are there?
b) On the same team, a captain and an assistant captain are to be chosen. How many possibilities are there?