Algebra 3H MYP --- 12 Week Study Guide
L1: Graphs of Absolute Value Equations
A = 4 pts
B = 3 pts
C = 2 pts
D = 1 pt
Given a word problem, I can write an absolute value equation or inequality, graph the function and use each to answer
additional questions.
I can graph an absolute value equation or inequality both by hand and using a calculator.
Given a graph, I can write the equation of an absolute value equation or inequality.
I can identify the vertex of an absolute value equation, including those represented in graphical form and as an equation.
1. Identify the parts of the equation.
Graph the function.
y=−
2. Write the equation of the function.
Identify the parts of the equation.
1
x−3 +2
2
3. A company’s guidelines call for
each can of soup produced not to vary
from its stated volume of 14.5 fluid
ounces by more than 0.08 ounces.
Write and solve an absolute value
inequality to describe acceptable can
volumes.
4. A school system is buying new computers. They will buy desktop computers costing $1000
per unit, and notebook computers costing $1200 per unit. The total cost of the computers
cannot exceed $80,000.
a. Write an inequality that describes this situation.
b. Graph the inequality.
c. If the school wants to buy 50 of the desktop computers and 25 of the notebook
computers, will they have enough money?
L2: Solve Linear Inequalities including Absolute Value Inequalities
A = 4 pts
B = 3 pts
C = 2 pts
D = 1 pt
I can solve an absolute value inequality and write the correct solutions in interval notation and draw the solution on a
number line.
I can solve an absolute value inequality, and draw the correct solutions on a number line.
I can solve an absolute value inequality, providing two correct answers.
I can solve an absolute value inequality, providing one correct answer.
1. Solve.
1
3
2x − + 9 ≤ 22
3
4
2. Solve.
2
2
3x − ≤ 10
5
3
3. A certain scholarship and student loan fund uses a
formula to determine whether or not a student
qualifies for college funding. The formula is
3k + 6 > 15 where k is a need score determined by an
interview. What are the possible need scores?
L3: Write Equations of Graphs
A = 4 pts
B = 3 pts
C = 2 pts
D = 1 pt
I can graph data points, find a line of best fit and write the equation of that line with and without a calculator.
I can write the equation of a linear function in slope-intercept form, given one point and a line perpendicular.
I can write the equation of a linear function in slope-intercept form, given one point and a line parallel.
I can write the equation of a linear function in slope-intercept form, given two points.
1. Write the equation of the line passing through the given
points.
(12,5 ) and ( −4,1)
4. Make a scatter plot and draw a line of fit for the data.
2. Write the equation of the line.
3. Write the equation of the line.
Use the line of best fit to predict the amount of whole
milk consumed per person in 2010.
L4: Piecewise Functions
A = 4 pts
B = 3 pts
C = 2 pts
D = 1 pt
Given a word problem, I can write the equations and graph a piecewise function and use them/it to answer questions.
I can write a piecewise function given a graph.
I can graph a piecewise function.
I can evaluate a piecewise function.
1. Evaluate each function for the given (½ point each)
𝑓 𝑥 =
3𝑥 + 5 ; 𝑥 < −7
−2𝑥 + 1 ; 𝑥 ≥ −7
𝑔 𝑥 =
2𝑥 ; 𝑥 < −2
ℎ 𝑥 = 5𝑥 − 2 ; −2 < 𝑥 ≤ 3
!
𝑥 + 5 ; 𝑥 > 3
𝑥 ! + 3𝑥 − 2 ; 𝑥 ≤ 6
2𝑥 − 8 ; 𝑥 > 6
!
( )
1.
f ( −9) = ____
2.
g ( 4) = ____
3.
h −3 = _____
4.
f (5) = ____
5.
g (12 ) = ____
6.
h 6 = ____
2. Graph the piecewise function, by hand.
()
3. Write the piecewise function.
⎧⎪ 3x − 5; x ≤ −2
f ( x) = ⎨
⎩⎪ −2x − 2; x > −2
4. You go to Smart and Final to
buy some candy. You decide to
buy snickers because they have
a special deal on snickers. A
bag of snickers costs $3.45, but
if you buy 4 or more bags, they
only cost $3.00 per bag. Write
a piecewise function to
represent this situation.
a)
Write the piecewise functions.
b)
Graph the function.
c)
What is the price of eight Snickers barg?
L5: Systems of Linear Equations and Inequalities
A = 4 pts
B = 3 pts
C = 2 pts
D = 1 pt
Given a word problem, I can write the equations and solve a system of linear equations and use them to answer a question.
I can solve a system of linear inequalities by hand and/or using a calculator
I can solve a system of linear equations and use the solutions to answer another question.
I can solve a system of linear equations by hand and/or using a calculator.
1. Use any method to solve the system.
3x + y = 6
−x + 2 y = 5
2. What is the sum of the x and y coordinates of the solution of the
system of linear equations?
5x + y = 2
2 y = 6x − 4
4.
At an ice cream parlor, ice cream cones cost $1.10 and
sundaes cost $2.35. One day, the receipts for a total of
172 cones and sundaes were $294.20. How many cones
were sold?
Part A: Define the variables needed to model this
situation.
Part B: Create a system of equations to model this
situation.
Part C: Solve the system.
3. You can work at most 20 hours next week. You need to earn at least $92 to cover you weekly expenses. Your dog- walking job pays
$7.50 per hour and your job as a car wash attendant pays $6 per hour. Write a system of linear inequalities to model the situation.
Q1: Complex Numbers
A = 4 pts
B = 3 pts
C = 2 pts
D = 1 pt
I can divide complex numbers, including rationalizing the denominator.
I can rationalize the complex number in the denominator.
I can multiply complex numbers and substitute -1 for (i)2.
I can add and subtract complex numbers, writing the complex numbers in standard form. (a + bi)
1. Simplify the expression.
( 2 − 5i ) + ( −4 − 3i )
a.
b.
(3 + 6i ) − (8 −10i )
2. Simplify the expression.
3. Simplify the expression.
( 4 + 2i )(6 − 5i )
4.
Simplify the expression.
2
3 + 5i
3 − 2i
1 + 3i
Q2: Factoring Quadratic Equations
A = 4 pts
B = 3 pts
C = 2 pts
D = 1 pt
I can solve a quadratic equation by factoring.
I can factor a quadratic equation that has a leading coefficient that is not one.
I can recognize and factor difference of perfect squares and factor by grouping.
I can factor out the Least Common Multiple (LCM) and factor a quadratic equation that has a leading coefficient of one.
1. Solve by factoring.
3. Solve by factoring.
12 x − 8 x = 0
8 x 2 − 14 x + 3 = 0
2
2. Solve by factoring.
a. 25 x − 9 = 0
2
4.
Solve by factoring.
a. 7 x 2 + 38 x + 35 = 0 b. 6 x 2 + 11x − 72 = 0
b. 12x + 20x + 3x + 5 = 0
2
Q3: Solve Quadratic Equations
A = 4 pts
B = 3 pts
C = 2 pts
D = 1 pt
I can solve a quadratic equation that has real or non-real roots using any method.
I can use the Quadratic Formula to solve a quadratic equation that has non-real roots and is not written in standard form.
I can use the Quadratic Formula to solve a quadratic equation that has real roots.
I can use the discriminant to determine the numbers of solutions of quadratic equation.
1. How many solutions will this function have?
a. y = 3x − 2 x − 8
2
3. Solve using the quadratic formula.
2
a. 3x − x + 5 = 0
b. y = 3x − 2 x + 5
2
2. Solve using the quadratic formula.
2
2
a. 2 x + 7 x + 3 = 0 b. 2 x − 11x + 5 = 0 4.
2
b. x − x + 5 = 0
Solve.
a. 6 x 2 − 3x = 0
2
b. 12 x − 9 x = 0
Q4: Complete the Square
A = 4 pts
B = 3 pts
C = 2 pts
D = 1 pt
I can write a quadratic equation that does not have a leading coefficient of one in vertex form using completing the square.
I can solve a quadratic equation that does not have a leading coefficient of one by completing the square.
I can write a quadratic equation that has a leading coefficient of one in vertex form using completing the square.
I can solve a quadratic equation with a leading coefficient of one by completing the square.
1. Solve by completing the square.
x2 + 4 x − 6 = 0
3. Solve by completing the square.
2 x 2 + 12 x − 10 = 0
2. Write in vertex form by completing the square.
y = x 2 − 4 x + 1 4.
Write in vertex form by completing the square.
y = 4 x 2 + 14 x − 6
Q5: Analysis of Quadratic Graphs
A = 4 pts
B = 3 pts
C = 2 pts
D = 1 pt
Given a word problem, I can write the equation and use the calculator to find the minimum, maximum or zeros and use
that information to answer additional questions.
Given a word problem and an equation, I can use the calculator to find the minimum, maximum or zeros and use that
information to answer additional questions.
Given a word problem and an equation, I can use the calculator to answer a question requiring the minimum, maximum or
zeros.
Given a quadratic equation, I can find the maximum and/or minimum and the zeros, using a calculator.
1. Find the minimum (or maximum) and the zeroes.
3.
A model rocket is launched from the roof of a building.
The rocket’s path is modeled by ℎ = −5𝑡 ! + 30𝑡 + 10
where h is the height in meters and t is the time in
seconds since launch. What is the maximum height of
the rocket?
4.
You are trying to dunk a basketball. You need to jump
2.5 ft. in the air to dunk the ball. The height that your
feet are above the ground is given by the function
ℎ 𝑡 = −16𝑡 ! + 12𝑡
Part A: What is the maximum height your feet will be
above the ground?
Part B: Will you be able to dunk the basketball? Explain.
y = x2 + 6 x − 3
2. The woodland jumping mouse can hop surprisingly long distances
given its small size. A relatively long hop can be modeled by
!
!
𝑦 = − 𝑥 ! + 𝑥 where x and y are measured in feet.
!
!
Part A: How far can the woodland jumping mouse hop?
Part B: How high can it hop?
Q6: Quadratic Inequalities and Systems
A = 4 pts
B = 3 pts
C = 2 pts
D = 1 pt
I can write the quadratic inequality equations, graph the system and answer questions given a word problem.
I can write the quadratic inequality equations, and graph the system given a word problem.
I can write the quadratic inequality equations given a word problem.
I can graph a system of Quadratic Inequalities on a calculator and determine the solution set.
1. David has learned that the light from the headlights reaches about
3. A ball is thrown upwards with a velocity of 40m/s from a
100 m ahead of the car he is driving. If v represents David’s speed,
in kilometers per hour, then the inequality 0.007v2 + 0.22v ≤ 100
gives the speeds at which David can stop his vehicle in 100m or less.
a. What is the maximum speed at which David can travel and safely
stop his car in the 100 m distance?
b. Modify the inequality so that it gives the speeds at which the
vehicle can stop in 50 m or less.
2. Jennifer hit a golf ball from the ground and it followed the projectile
2
h(t) = -16t + 100t
where t is the time in seconds, and h is the height of the ball. Find
the highest point that her golf ball reached and also when it hits the
ground again.
height of 6m. For what times is the height of the ball greater
than 12m? Use height formula h = -16t2 + v0t + h0 and
round your answers to the nearest hundredths of a second. A
ball is thrown upwards with a velocity of 40m/s from a
height of 6m. For what times is the height of the ball greater
than 12m? Use height formula h = -16t2 + v0t + h0 and
round your answers to the nearest hundredths of a second.
4.
A dog toy is thrown from 5 inches above the ground. After
2 seconds, the toy reaches a maximum height of 9 inches,
and then lands back on the ground 5 seconds after it was
thrown. Find the “a” (coefficient of the x2) and write this
quadratic equation in vertex form, standard form, and
factored form.
P1: Properties of Exponents
A = 4 pts
B = 3 pts
C = 2 pts
D = 1 pt
I can simplify an expression using all of the properties of exponents.
I can simplify an expression using zero and negative exponents.
I can simplify an expression using division properties of exponents.
I can simplify an expression using the multiplication properties of exponents.
⎛ 2x 3 y 3 ⎞
1. ⎜
4
⎝ xy ⎟⎠
10x 8 y15
2. 2 12 5
2 x y
3
⎛ 3x −2 y 3 ⎞
3. ⎜ 3 −4 ⎟
⎝ x y ⎠
−2
4.
(
3x 3 y 2 2x 3 y 6
)
2
20x 3 y 5
P2: Factoring Polynomials
A = 4 pts
B = 3 pts
C = 2 pts
D = 1 pt
I can factor the sum of cubes and difference of cubes.
I can factor a polynomial by grouping.
I can factor a polynomial with a leading coefficient that is not one.
I can factor out the least common multiple of polynomial.
1. 18x 3 + 36x 2 + 54x
2. 10x 2 − 29x − 21
3. 6x 3 + 8x 2 + 9x + 12
4. 125x 3 − 64
P3: End Behavior
A = 4 pts
I can state the degree, describe the end behavior and state the domain and range of a polynomial function.
B = 3 pts
I can describe the end behavior of a polynomial function.
C = 2 pts
I can state the domain and range of a polynomial function.
I can determine the degree of a polynomial function.
D = 1 pt
State the degree of each polynomial function. Describe the end behavior of each function. State the domain and range.
1. f ( x ) =
1 2
x + 5 x − 12
2
3. y = 11x 4 + 3x3 + 3x + 5
as
x → ____,
as
x → ____,
as
x → ____,
as
x → ____,
f ( x ) → ____
f ( x ) → ____
f ( x ) → ____
f ( x ) → ____
2. y = 3x3 − 8x + 4
as
x → ____,
as
x → ____,
4. f ( x ) = −3x 4 + 5x 3 + x − 4
f ( x ) → ____
f ( x ) → ____
as
x → ____,
as
x → ____,
f ( x ) → ____
f ( x ) → ____
P4: Fundamental Theorem of Algebra
A = 4 pts
B = 3 pts
C = 2 pts
D = 1 pt
I can state all possible zeros and find all zeros of a polynomial function.
When given one zero, I can find the zeros of a polynomial function, using synthetic division and factoring.
I can simplify an expression using synthetic division.
I can simplify an expression using synthetic substitution.
1. Use synthetic substitution.
Find f ( −2 ) if
f ( x ) = 5 x + 2 x − 3x + 4
4
2. Use synthetic division.
2x5 + 3x4 − 2x3 + 3x2 − 5x + 1 ÷ ( x − 3)
(
)
2
3. Find the remaining zeros.
Given ( x − 2 ) ,
f ( x ) = x 4 + 3x3 − 11x 2 − 3x + 10
4. Find all zeros.
f ( x ) = x 4 − 5x 2 + 4