2011-2012 ADVANCED MATH
SEMESTER 2 FINAL Exam Topics
Chapter 3
Symmetry
Given a graph, sketch the point for its given symmetry
Determine odd or even when given a function
Sketch and transform families of graphs
Determine if a point is a solution to an inequality
Understand and be able to solve for inverses of functions
Determine continuity of a function
Describe end behavior
Find critical points by looking at the graph
Find the holes and asymptotes when given a function
Chapter 4
Solve problems involving i
State the number of complex roots in a polynomial
Given the roots, write a polynomial
Find the discriminant, state the number of roots
Use the remainder theorem to find the remainder, determine if the binomial is a factor.
List all possible rational roots
Final all real and imaginary roots
Solve rational equations
Decompose into partial fractions
Solve radical equations and inequalities (EXCLUDED VALUES)
Chapter 12
Find the nth term of an arithmetic sequence.
Find the sum of an arithmetic series.
Find the nth term of a geometric sequence
Find the limit of terms and the sum of an infinite series
Use sigma notation
Use Pascal’s Triangle to expand binomials
Chapter 13
Solve problems use the basic counting principle
Solve problems with combinations and permutations
Solve problems with reflection and repetition
Find the probability of an event
Find the odds of an event
Find probability of dependent, independent, inclusive, exclusive and conditional events
Use the binomial theorem to find the probability of binomial experiments
Monday / Tuesday / Wednesday / Thursday / FridayStudy for Quarterly / Quarterly Exam / Most Missed Quarterly 3 / Most Missed Quarterly 4
Hand in books / No School—Institute Day
11:11-12:44 Senior Math Final
Advanced Math Name: ______
Semester 2 Review
Chapter 3: The Nature of Graphs
1) Which is the graph of y x3 + 1?
a) b) c) d)
2) Which is the graph of f(x) = |x| - 4 and its inverse?
a) b) c) d)
3) Use a graphing calculator to graph g(x) = x3 - x + 1 and to determine and classify its extrema.
a) relative min: b) relative max: c) relative min: d) relative max:
(-0.6, 1.38); (-0.6, 1.38); (1.38, -0.6); (1.38, -0.6);
relative max: relative min: relative max: relative min
(0.6, 0.62) (0.6, 0.62) (0.6, 0.62) (0.6, 0.62)
4) If the point (5, -8) is reflected over the x-axis, what are the coordinates of the new point?
a) (5, 8) b) (-5, -8) c) (-8, 5) d) (-5, 8)
5) What translation occur from the parent graph y = x3 to y = -(x+6)3
a) Right 6, b) Left 6, c) Right 6, d) Left 6,
flip over x axis flip over y-axis flip over y-axis flip over x-axis
6) Determine the discontinuity of
a) point discontinuity at x = 0 b) infinite discontinuity at x = 0
c) jump discontinuity at x =0 d continuous
7) Describe the end behavior of y = 3x2 – x3 + 2
a) b)
c) d)
8) Use the parent graph to sketch the graph of each function.
a) b)
c) d)
9) Graph the following inequalities. **Remember to shade!**
a) b)
10) Consider
a) Is the inverse a function?
b) Find
c) Graph and
12) Determine whether or not each function is continuous at the given value.
a) b)
c)
13) Use a graphing calculator to graph f(x) = 2x3 - 14x2 + x + 15 and to determine and classify the extrema.
14) Describe the end behavior of f(x) = -4x5 + 5x2 - 1
15)
16)
Chapter 4: Polynomial and Rational Functions
1) Solve:
a) -2 b) -6 c) 6 d) 2
2) Decompose into partial fractions:
a) b) c) d)
3) What is the remainder when 4x3 + 5x + 2 is divided by (x + 1)?
a) 1 b) 0 c) -7 d) 11
4) The equation y = -2x3 + 4x5 – 3 has how many complex roots?
a) -2 b) 3 c) 5 d) 1
5) Find all complex roots of f(x) = x4 - 81
a) b) c) d)
6) Divide: ( x3 – 5x2 + 6x – 3 ) ( x – 1 ) 7) Solve
8) Examine the following equation: 3x3 – 4x2 – 5x + 2 = 0
a. How many complex roots ______b. Possible Rational Roots:
c. Determine the rational roots. d. All Complex Roots ______
9) Examine the following equation: 3x3 – 2x2 + 27x -18= 0
a.How many complex roots ______b. Possible Rational Roots:
c. Determine the rational roots. d.All Complex Roots ______
10) Use synthetic division to find all the factors of if -2 is a double root.
11) Write a polynomial function of least degree with roots -2, 1, 2i and -2i.
12) Find the discriminant and describe the nature of the roots. Then solve using the Quadratic formula:
.
Chapter 12: Sequences and Series
1) Find the 15th term in the arithmetic sequence 14, 10.5, 7…
a) -21 b) -63 c) 63 d) -35
2) Find the sum of the first 25 terms in the arithmetic series 11 + 14 + 17 + 20 + …
a) 1175 b) 1164 c) 1206 d) 1500
3) Find the 10th term in the geometric sequence -2, 6, -18,…
a) 118,098 b) -118,098 c) 39,366 d) -39,366
4) Find the sum of the first 8 terms in the geometric series -4 + 8 – 16 + …
a) -342 b) -1020 c) -340 d) 340
5) What type of sequence is
a) arithmetic b) geometric c) infinite d) recursive
6) A patterned floor has 6 tiles in the first row and increases by 4 tiles for each following row for a total of 35 rows. How tiles are needed to make the entire floor?
a) 142 b) 146 c) 2590 d) 2660
7) Find for -90 + (-30) + (-10) +
a) -135 b) c) 45 d) does not exist
8) Evaluate
9) Given the sequence for which …
a) Find n b) Find
c) Find d)
10) Given the sequence for which
a) Find r b) Find
c) Find d)
11) Write as a fraction (NO WORK = NO CREDIT!)
12) Use Pascal’s Triangle to expand (2x + 1)5.
13) Use sigma notation to express 5 + 9 + 13 + … + 101
14) Our math class drops a tennis ball off the top of the 90 foot tall PAC. We measure that it rebounds 65% of the height on each bounce. What is the total distance that the ball will travel before coming to rest?
15) Determine if the sequence of the multiples of 6 from 120 to 300 is arithmetic or geometric. Then find the sum.
Chapter 13: Probability
1) How many different ways can 10 different chairs be arranged in a circle?
a) 362,880 b) 120 c) 3,628,800 d) 10,000,000,000
2) One red and one green number cube are tossed. What is the probability that the red number cube shows an even number and the green number cube shows a number greater than 2?
a) b) c) d)
3) A basket contains 3 red, 4 yellow, and 5 green balls. If one ball is taken at random, what is the probability that it is yellow or green?
a) b) c) d)
4) A basket contains 3 red, 4 yellow, and 5 green balls. If two balls are taken at random, what is the probability that you pick 2 green balls?
a) b) c) d)
5) How many distinct ways can the letters of Nintendo be arranged?
a) 20160 b) 6720 c) 40320 d) 5040
6) In a standard deck of cards, what is the probability of drawing an 8 or a red card?
a) b) c) d)
7) How many ways can the letters in the word capitol be arranged if the first letter must be p?
8) A class consisting of 10 boys and 12 girls must select 2 boys and 2 girls to serve on a committee. How many variations of the committee can there be?
9) A bakery’s dessert list consists of 3 kinds of cakes, 9 kinds of pies and 10 kinds of brownies. How many combinations of three desserts will Jana have if she buys one of each kind?
10) If two cards are drawn at random from a standard deck of cards with no replacement, find the probability that both cards are queens.
11) Consider a class with 10 sophomores, 8 juniors and 6 seniors. Two students are selected at random.
a) What is the probability of selecting 1 junior and 1 senior?
b) Find the odds of selecting 2 students who are not seniors.
12) Scotty flips a coin 5 times. Find the probability that he flips heads exactly 4 times.
13) In a jar of 14 scented pencils, 8 are licorice, 4 are bubblegum and 2 are tutti-fruitti.
You randomly grab 4 pencils. Find the probability that you choose at least 2 licorice scented.
14) Jimmy is burning a CD for his girlfriend to give on their one-year anniversary. He wants to put her favorite 11 songs on the CD. How many different ways can he put the 11 songs on the CD?
15) You roll 2 dice. Find the probability of rolling a sum of 8 on the first roll, and then matching dice on the second roll.
16) 70% of seniors drive to school at LZHS; 85% of seniors go off campus for lunch; 62% of seniors do both. Find the odds that a senior drives to school or goes off campus for lunch.