Math 2 Spring 2021 Study Guide. CHAPTER FOUR: FACTORING Due Thursday, May 20

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Math 2 Spring 2021 Study Guide

CHAPTER FOUR: FACTORING

Due Thursday, May 20

4-A

Monomial Factors

factor • common monomial

➊

Factor a common monomial out of each term of a polynomial.

➊ 40x5 _{– 8x}3 _{+ 20x}2

➋

_{Factor a polynomial by grouping.}

➋ 2x3 _{– 8x}2 _{+ 5x – 20}

4-B

Binomial Factors

perfect square • difference of squares

➊

Factor ax

_{+ bx + c.}

➊ 18x2 _{+ 27x + 4}

➋

Factor x

_{+ bx + c.}

➋ x2 _{– 13x + 22}

➌

_{Identify and factor a perfect square trinomial.}

a) 16x2 _{– 24x + 9 b) x}2 _{+ 10x + 100}

➍

_{Factor a difference of squares.}

➍ 16x2 _{– 9}

➎

_{Factor a polynomial.}

4-C Solving

➊

_{Solve an equation in factored form.}

➊ 3x2_{(x + 6)(2x – 9)(x}2 _{– 16)(x}2 _{+ 7x + 10) = 0}

➋

_{Solve an equation by factoring.}

➋ 18x3 _{= 50x}

CHAPTER FIVE: GRAPHS OF QUADRATIC FUNCTIONS

Due Tuesday, May 25

5-A Parabolas

quadratic function • parabola • axis of symmetry • vertex • minimum • maximum

➊

_{Identify the vertex, minimum or maximum value, axis of symmetry, domain, and range of a graphed}

quadratic function.

➊

➋

_{Graph f(x) = ax}

_.

➋ Graph f(x) = -0.5x2_.

➌

_{Sketch the graphs of y = ax}

_{for different values of a.}

➌ Sketch the graphs of f(x) = x2_{, g(x) = 0.1x}2_{, h(x) = -0.1x}2_{, and i(x) = -5x}2 _{on the same set of axes.}

5-B

Vertex Form

vertex form

➊

_{Identify the vertex of a parabola in vertex form.}

➊ y = -3(x + 4)2 _{+ 12}

➋

Sketch f(x) = a(x – h)

_{+ k.}

➋ Sketch f(x) = -0.5(x – 2)2 + 8 and g(x) = -0.1(x – 2)2 + 8.

➌

_{Identify the x-intercepts of a parabola in vertex form.}

➌ Find the x-intercepts of f(x) = -0.5(x – 2)2 _{+ 8}

5-C

Intercept Form

intercept form

➊

Identify the vertex of a parabola in intercept form.

➊ f(x) = 1₅(x – 4)(x + 6)

➋

_{Sketch f(x) = a(x – p)(x – q).}

➋ f(x) = 1₅(x – 4)(x + 6)

5-D Standard Form

standard form

➊

Identify the vertex of a parabola in standard form.

-25 0 25

-25 25

(0, -1) (0, 7)

(3, -32)

➋

_{Convert standard form to vertex form.}

➋ f(x) = 0.25x2 _{+ x – 3}

➌

Convert vertex form or intercept form to standard form.

➌ f(x) = 0.25(x + 2)2 _{– 4}

➍

Write, in standard form, the equation of a parabola from a graph.

➍

CHAPTER SIX: SQUARE ROOTS

Due Thursday, May 27

6-A

Classification of Numbers

natural • integer • rational • irrational • real • complex • imaginary

➊

Identify a number as natural, integer, rational, real, or complex.

➊ Sort the following numbers into the smallest set that includes each.

a) 2 b) -2 c) √2 d) √-2

e) -22 f) 2.2 g) 2 – √-2 h) 2 x 1022

6-B Radicals

radical • radicand

➊

_{Add and subtract radical expressions.}

➊ (3 + 5√7) – 2(3√2 – 11√7)

➋

_{Multiply radical expressions.}

➌

_{Simplify the square root of a positive integer.}

➌ √800

➍

Simplify the square root of an algebraic term.

➍ √50a20_b21_c49_d

➎

_{Rationalize a denominator.}

➎ Simplify.

a) _√2012 b) _{8 – √20}12

6-C

Complex Numbers

i • real number • imaginary number • complex number • standard form • complex plane • complex conjugate

➊

Plot numbers on the complex plane.

➊ Plot the following numbers on the complex plane.

b) 2 – 5i c) 2 d) 5i

➋

Add and subtract complex numbers.

➋ (3 + 5i) – 4(8 + 3i)

➌

_{Simplify the square root of a negative integer.}

➌ Simplify.

a) √-25 b) √-75

➍

_{Multiply complex numbers.}

6-D Completing the Square

➊

_{Solve x}

_{+ bx + c = 0 by completing the square.}

➊ x2 _{+ 10x + 9 = 0}

6-E

The Quadratic Formula

quadratic formula • discriminant

➊

Solve a quadratic equation by using the quadratic formula.

➊ 12x2 _{+ 17x = 7}

➋

Use a discriminant to determine the type of solutions of a quadratic equation.

➋ 2x2 _{= 4x – 5}

➌

_{Use a discriminant to determine the number of x-intercepts of a quadratic function.}

➌ f(x) = 2x2 _{– 4x + 5}

CHAPTER SEVEN: PROBABILITY

Due Tuesday, June 1

7-A

Probability of a Single Event

sample space • mutually exclusive • two-way table • Venn diagram

➊

_{List the sample space of an event.}

➊ a) Roll a 6-sided die. b) Flip a coin and roll a 4-sided die.

➋

_{Use a sample space to find the probability of an event.}

➋ Find the probability of rolling higher than 17 on the dice stated.

➌

_{Find the probability that a specific item is one of the items selected from a group.}

➌ If two random states are selected, what is the probability that one of them is Oregon?

➍

Find the probability that either of two specific events will occur.

➍ A card is drawn from a deck. Calculate the probability of it being as stated.

a) hearts or black b) hearts or a queen

➎

Find probabilities based on given information.

➎ Find the following probabilities for two randomly drawn cards. a) The second card is an ace.

b) The second card is an ace, given the first card is an ace.

c) The first card is an ace, given the second card will be an ace.

➏

_{Use a two-way table to organize data and determine basic probabilities involving two variables.}

➏ In a certain neighborhood, 20 out of 32 of the males and 25 out of 38 of the females are children. Use this information to fill in a two-way table and determine the probability that a random person from the neighborhood meets the stated criteria.

a) a child b) a female c) a child or a female d) a child or a male

➐

_{Use a two-way table to organize data and determine conditional probabilities involving two variables.}

➐ Determine the probability of the following for the scenario above.

a) A random child is female. b) A random female is a child. c) A random person is a female child.

➑

_{Create a Venn diagram representing two variables with two conditions each.}

7-B

Probability of Multiple Events

dependent events • independent events

➊

_{Find the probability of multiple events all occurring.}

➊ Nick rolls three 6-sided dice. Calculate the following probabilities. a) The first roll is a 2, the second roll is a 5, and the third roll is odd.

b) All three rolls are lower than 3.

c) The first roll is a 6 and the third roll is a 4.

➋

Identify whether events are independent or dependent.

➋ Explain whether the following are independent or dependent.

a) drawing two cards b) flipping two coins

➌

_{Calculate the probability of an event that can happen in different ways.}

➌ A class has 9 freshmen, 20 sophomores, and 7 juniors. What is the probability that two random students are in the same grade?

7-C Combinations

combination • choose • fundamental counting principle • permutation

➊

_{Count combinations.}

➊ In how many ways can Naiya choose her 6 favorite songs from a playlist of 9 songs?

➋

_{Find the total number of possible outcomes in a series of events.}

➋ State the number of possible outcomes of the following.

a) Choose 3 representatives out of 9 seniors and 2 representatives out of 8 juniors.

b) Identify the 1st _{place, 2}nd _{place, 3}rd _{place, and 4}th _{place finisher out of 25 racers.}

➌

_{Count permutations.}