BCSD Mathematics
Algebra 1/Foundations/Intermediate Assessment Item Bank
AAPR
Algebra - Arithmetic with Polynomials and Rational Expressions
AAPR.1
AREI.1
FIF.1
ACE.1
ACE
Algebra – Creating Equations
ACE.2
ACE.4
AREI.2
AREI
Algebra – Reasoning with Equations and Inequalities
AREI.3
AREI.4
AREI.5
AREI.6
AREI.10
AREI.11
ASE.1
ASE
Algebra – Structure and Expressions
ASE.2
ASE.3
FBF.1
FBF
Functions – Building Functions
FBF.2
FBF.3
FIF.2
FIF
Functions – Interpreting Functions
FIF.4
FIF.5
FIF.6
FIF.3
FIF.7
FIF.8
FLQE
Functions – Linear, Quadratic, and Exponential
FLQE.2
FLQE.3
FLQE.1
FLQE.5
NQ.1
NQ
Number and Quantity - Quantities
NQ.2
NQ.3
NRNS.1
NRNS
Number and Quantity – Real Number System
NRNS.2
NRNS.3
SPID
Statistics and Probability – Interpreting Data
SPID.6
SPID.7
SPID.5
SPID.8
SPMJ
Statistics and Probability – Making Inferences and Justifying Conclusions
SPMJ.1
SPMD.4
SPMJ.2
SPMD
Statistics and Probability – Using Probability to Make Decisions
SPMD.5
NCNS
Number and Quantity – Complex Number System
NCNS.1
NCNS.7
SPMD.6
AREI.12
FIF.9
A1.AAPR.1* Add, subtract, and multiply polynomials and understand that polynomials are closed under
these operations. (Limit to linear; quadratic.)
Simplify the following polynomials:
a. (4x2 – 11) + (-8x2 + 20)
b.
(x2 + 6x – 4) – (2x2 – 3)
c. (2x – 5)(7x + 1)
d.
(3x + 4)2
A1.AAPR.1
Simplify the following polynomials:
a. (2x2 – 5x + 10) – (-3x + 4)
b. (x + 5) (x – 7)
A1.AAPR.1
The perimeter of a pentagon is 20x + 7. Four sides have the following lengths: 6x, 2x, 4x – 5, and 5x + 1.
What is the length of the fifth side?
A1.AAPR.1
Simplify each expression:
a. x2(x – 9) + x(x³ + 5x)
b. (2y + 3)2
c. 2(3x – 4)(x + 1)
A1.AAPR.1
Simplify each expression:
a. (5x4 + 7x + 2) – (3x² - 2x + 9)
b. (4x² + 9x + 1) + (2x² + 7x + 13)
A1.AAPR.1
Simplify each expression:
a. 3x² - 4x - 2x² - 5x
b. 3(2r + 4r² - 7r + 4r²)
c. -2(m + 1) + 9(4m – 3)
A1.AAPR.1
A1.ACE.1*
Create and solve equations and inequalities in one variable that model real-world problems
involving linear, quadratic, simple rational, and exponential relationships. Interpret the solutions and
determine whether they are reasonable. (Limit to linear; quadratic; exponential with integer exponents.)
Jessica’s family gave her a lot of money for her graduation. Her parents gave her $150 and her other
relatives gave her $75 each. In total, she received $1,050 for her graduation. Write an equation that models
this situation using r for the number of relatives.
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
1
Bill ran 8 miles more than 3 of the number of miles that Jack ran. If they ran the same distance, how far did
they run?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
Optimus Prime can transform no more than 10 times a day. If he transformed 4 more times than twice the
number of times he did last week, what’s the greatest number of times he could have transformed last
week?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
Rachel and Rhoda are twin sisters, and they’re leaving for college. If Rhoda’s major will take 2 years more
than one third the time needed for Rachel’s major, how many years does Rachel’s major take to complete if
their parents can afford no more than a total of 10 years of education?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
George’s dad’s age is 5 years more than 3 times George’s age. His dad is also 15 years less than 5 times
George’s age. How old is George? How old is George’s dad?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
Officer Bob likes jelly donuts. Today he ate 8 fewer than 6 times the number of donuts he ate yesterday. If
he had at most 10 donuts today, what is the largest number of donuts he could have eaten yesterday?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
Bill’s weight is 68 kilograms. This is 10 kilograms more than one-half of his father’s weight. How much does
Bill’s father weigh?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
Three times a number is no more than six times that number plus nine. What is the number?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
Three times a number plus 12 minus the quantity 5 times that same number is 22. What is the number?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
There are 96 members of the marching band. The vans that the band uses to travel to games each carry no
more than 14 passengers. How many vans does the band need to reserve for each away game?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
John wants to make at least $800 working this summer. He earns $12 per hour and gets a bonus of $90 at
the end of the summer. How many hours does he need to work to reach his goal?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
A blank CD can hold 70 minutes of music. So far you have burned 25 minutes of music onto the CD. You
estimate that each song lasts 4 minutes. What are the possible numbers of additional songs that you can
burn onto the CD?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
Betty went shopping for school clothes. She bought 13 shirts, which was 4 less than three times the number
of pants she bought. How many pants did she buy?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
Bert and Ernie are comparing ages. Ernie is 32, and Bert says that his age is 4 years more than three-fourths
of Ernie’s age. How old is Bert?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
Optimus Prime transformed 11 times yesterday, which is six more than 1/3 the number of times he
transformed today. How many times did he transform today?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
Jack and Jill went shopping and spent the same amount of money. Jill says that she spent $8 more than half
of what Jack spent. How much money did they each spend?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
Mike bought a soft drink for $4 and four candy bars. He spent a total of sixteen dollars. How much did each
candy bar cost?
A1.ACE.1 (linear)
Write an algebraic equation/inequality to represent the scenario and solve:
Keith has $500 in a savings account at the beginning of the summer. He wants to have at least $200 in the
account at the end of the summer. He plans to withdraw $25 each week for spending money. How many
weeks can Keith withdraw this money from his account so that he still has $200 left?
A1.ACE.1 (linear)
Find the balance in an account after 7 years when a $2500 principle earns 3% interest compounded
annually.
A1.ACE.1 (exponential)
The number of bacteria on a computer keyboard triples every hour. If there were 2,542 bacteria on the
keyboard, how many would there be in 5 hours?
A1.ACE.1 (exponential)
A1.ACE.2*
Create equations in two or more variables to represent relationships between quantities.
Graph the equations on coordinate axes using appropriate labels, units, and scales. (Limit to linear;
quadratic; exponential with integer exponents; direct and indirect variation.)
Write the equation of the graph in each different form.
a. Slope-Intercept:
b. Point Slope:
c. Standard Form:
A1.ACE.2 (linear)
A relation contains this set of ordered pairs: {(0, 0), (2, 1), (6, 3), (10, 5), (24, 12)}.
Write the equation for this relation in slope-intercept form.
A1.ACE.2 (linear)
Write the function that defines this table of values.
x
f(x)
1
4
2
7
3
10
4
13
A1.ACE.2 (linear)
Write an equation in slope intercept form given that m = -4 and the line passes through the point (-2, 9).
A1.ACE.2 (linear)
A line passes through the points (-3, 10) and (-4, -8).
a. Write the equation of the line in point-slope form:
b. Write the equation of the line in slope-intercept form:
c. Write the equation of the line in standard form:
A1.ACE.2 (linear)
Explain the differences between equations of vertical lines and equations of horizontal lines.
A1.ACE.2 (linear)
Suppose y varies directly with x.
a. Write a direct variation equation that relates x and y when y=10 and x=2.
b. What is the value of y when x is 8?
A1.ACE.2 (linear)
Write the equation of the graph in each different form.
a. Slope Intercept:
b. Point Slope:
c. Standard Form:
A1.ACE.2 (linear)
A computer repair service charges $50 for diagnosis and $35 per hour for repairs. Let the domain be the
number of hours it takes to repair a computer. Let the range be the total cost of the repair. Write the
equation that models this situation and be sure to define the variables.
A1.ACE.2 (linear)
Write an equation in slope-intercept form given that m = -4 and the line passes through the point (-2, 9).
A1.ACE.2 (linear)
A car rental company charges $40 per day plus $2 per mile driven. Write the equation for the total cost of
the car rental depending on the number of miles driven. Be sure to define the variables you use.
A1.ACE.2 (linear)
The table shows the average body temperature in degrees Celsius of 9 insects at a given air temperature.
Use the data to determine which equation represents the relationship between air temperature and insect
body temperature.
Air,(x)
Body,(y)
a.) 𝑦 =
c.) 𝑦 =
3
5
5
3
25
20
30
23
35
26
40
29
𝑥 + 5
b.) 𝑦 = 5𝑥 + 35
𝑥 + 20
d.) 𝑦 =
3
5
45
32
50
35
𝑥 + 35
A1.ACE.2 (linear)
Write an equation that represents the relationship between the values in the table below:
x
-1
0
1
2
3
1
y
1
3
9
27
3
A1.ACE.2 (exponential)
Write an equation that represents the relationship between the values in the table below:
x
-1
0
1
2
3
5
y
5
10
20
40
2
A1.ACE.2 (exponential)
Write an equation that represents the relationship depicted in the graph below:
A1.ACE.2 (exponential)
Which equation matches this graph?
A. y = -2(2)x – 4
B. y = -4(2)x – 2
C. y = 2(2)x – 4
D. y = -4(2)x + 2
A1.ACE.2 (exponential)
A population of 50 wolves in a wildlife preserve doubles in size every 12 years.
a. Create an equation that models the population growth. Define your variables.
b. How many wolves will there be after 36 years?
A1.ACE.2 (exponential)
Jerome invests $5000 into an account that earns 5% interest compounded quarterly.
a. Create the equation that models how much money is in Jerome’s account. Define your variables.
b. Find the balance in the account after 12 years.
A1.ACE.2 (exponential)
The population of a city is 25,000 and decreases 1% each year.
a. Write an equation that models the population (p) based on the number of years from now (t).
b. What will the population of the city be in 6 years?
A1.ACE.2 (exponential)
A town had a population of 65,000 in 2005. Since then the population has increased by 2% each year.
Write a function that models the population over time. Then, use this function to estimate the population
in 2014.
A1.ACE.2 (exponential)
The attendance at an indoor waterpark steadily declined between the years of 2000 and 2005. The
attendance in 2000 was about 18,000, and each year the attendance decreased by 7.5%. Write a function
that models the attendance over time. What was the attendance in 2005?
A1.ACE.2 (exponential)
The value of a new pair of shoes is $60. If the price depreciates 1% each month the shoe is worn, write an
equation to show the value of the shoes after x months. What does the initial value tell you about the
graph of your equation?
A1.ACE.2 (exponential)
Complete the table below for the quadratic equation. Then use the table to graph.
y = x2 + 2x + 1
x
y
-2
-1
0
1
2
A1.ACE.2 (quadratic)
Create a quadratic equation to model the data in the table below:
x
1
2
3
4
5
y
1
4
9
16
25
A1.ACE.2 (quadratic)
Suppose 𝑦 varies inversely with 𝑥 and 𝑦 = 20 when 𝑥 = 5. Write an equation for the inverse variation.
A1.ACE.2 (rational)
A1.ACE.4*
Solve literal equations and formulas for a specified variable including equations and
formulas that arise in a variety of disciplines.
Solve each of the following equations for y.
1
a. 4(x + y) = z
b. 6x + 3y = -12
c. 8x + 2y = 50
A1.ACE.4
1
Solve A = 2bh for b.
A1.ACE.4
Solve each equation for the indicated variable.
1
a. 4(x + y) = z; solve for y.
9
b. F = 5C + 32; solve for C.
A1.ACE.4
Solve each equation for x:
a. 2𝑥 − 3𝑦 = 6𝑧
A1.ACE.4
b.
𝑥+𝑦
2
=𝑧
A1.AREI.1* Understand and justify that the steps taken when solving simple equations in one variable
create new equations that have the same solution as the original.
4𝜋𝑥
Explain the step-by-step process you use to solve the equation 12 =
for x.
3
A1.AREI.1
IA.AREI.2*
Solve simple rational and radical equations in one variable and understand how extraneous
solutions may arise.
Use Pythagorean Theorem to solve for the missing side length of the right triangle:
1.) leg = 1.1 cm, leg = 6 cm
2.) leg = 6 in, hypotenuse = 7.5 in
IA.AREI.2 (radical)
A construction worker is cutting along the diagonal of a rectangular board that is 15 feet long and 8 feet
wide. What is the length of the cut?
IA.AREI.2 (radical)
A park has two walking paths shaped like right triangles. Path A has legs of 75 yards and 100 yards long.
Path B has legs of 50 yards and 240 yards long. Which path has the longest diagonal and what is its length?
IA.AREI.2 (radical)
Solve the following equations and identify any extraneous solutions.
1.) 4 + √𝑦 = 7
2.) √𝑤 − 2 = 4
3.) √𝑑 + 2 = 𝑑
4.) 2√𝑟 = √3𝑟 + 1
IA.AREI.2 (radical)
𝐴
The length s of one edge of a cube is given by 𝑠 = √6 , where A represents the cube’s surface area.
Suppose a cube has an edge length of 9 cm. What is its surface area?
IA.AREI.2 (radical)
𝑛
The formula 𝑡 = √16 gives the time t in seconds for an object that is initially at rest to fall n feet. What is
the distance an object falls in the first 10 seconds?
IA.AREI.2 (radical)
Solve for y and identify any extraneous solutions:
5
𝑦+2
𝑦
+5=
𝑦+5
5
IA.AREI.2 (rational)
A1.AREI.3* Solve linear equations and inequalities in one variable, including equations with
coefficients represented by letters.
Solve each of the following for the value of x:
5
a. - 3 x + 2 = -3
b. -4(2x – 1) = -10(x – 5)
c. 8(x + 2) = 16
3
d. 4 x = 9
e. -3(2x – 3) = -5(x – 1)
A1.AREI.3
Solve each of the following for the values of x:
a. -5x + 13 ≥ -7
(𝑥−5)
b. 3 ≥ 12
c. 12 > 8 – 6x
d. 2( x – 3) > -12
e. -3x – 7 > 23
A1.AREI.3
Solve each of the following for the value of x:
a. 7 – 3x + 4 = 5x – 1 + 4x
b. 3(x – 5) – x = 3 + 2(x – 3)
c. 3(x + 1) - 5 = 3x – 2
A1.AREI.3
Solve each of the following for the values of the variables:
a. -2(4x + 3) +5(x + 4) ≤ 2
b. -6 < 3n + 9 < 21
c. 16 < -x – 6 or 2x + 5 ≥ 11
d. |𝑑 + 4| ≥ 3
A1.AREI.3
Solve each of the following for the value of x:
3
1. − 2 𝑥 = 15
2. 2𝑥 = −8
4. 𝑥 − 2 = 𝑥 + 5
5. −3(𝑥 − 2) = 18
3. −4𝑥 − 7 = 13
6. −2𝑥 + 6𝑥 + 4 = −12
A1.AREI.3
Solve each of the following for the values of x:
3
1. − 2 𝑥 > −15
2. 𝑥 + 1 < 3𝑥 − 3
4. −2𝑥 > 2𝑥 − 16
3. −8 + 6𝑥 ≥ −14
5. −18 > 𝑥 + 2 or 3𝑥 − 2 > 40
6. 12 < 2𝑥 − 4 < 44
A1.AREI.3
A1.AREI.4* Solve mathematical and real-world problems involving quadratic equations in one variable.
(Note: A1.AREI.4a and 4b are not Graduation Standards.)
a. Use the method of completing the square to transform any quadratic equation in x into an
equation of the form (𝒙 − 𝒉)𝟐 = 𝒌 that has the same solutions. Derive the quadratic formula
from this form.
b. Solve quadratic equations by inspection, taking square roots, completing the square, the
quadratic formula and factoring, as appropriate to the initial form of the equation. Recognize
when the quadratic formula gives complex solutions and write them as a+bi for real numbers a
and b. (Limit to non-complex roots.)
Solve each of the following equations by factoring. Show all work.
a. x2 + x – 12 = 0
b.
3n2 + 9n = 0
c. 36k2 = 49
d.
3x2 + 2x = 5
A1.AREI.4
Solve the following equations by factoring.
a. x2 – 8x + 12 = 0
b. 5n2 + 10n = 0
A1.AREI.4
Solve each of the following by factoring:
a. x² + 11x – 26 = 0
b. x² - 25 = 0
c. 5x² - 8x = 8 – 5x
A1.AREI.4
Solve each of the following for the value(s) of n:
a. 2n2 + n  1 = 0
b. n2 + 9n  10 = 0
A1.AREI.4
c. n2  6n = 0
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic, then rewrite
the expression as a squared binomial.
a. v2  6v +
= ____________
b. t2 + 8t +
= ____________
A1.AREI.4
Solve by completing the square: t2 + 6t = 3
A1.AREI.4
Solve using the method of your choice. Show all work.
s2 + 16s + 39 = 0
A1.AREI.4
A1.AREI.5
Justify that the solution to a system of linear equations is not changed when one of the
equations is replaced by a linear combination of the other equation.
A1.AREI.6* Solve systems of linear equations algebraically and graphically focusing on pairs of linear
equations in two variables.
(Note: A1.AREI.6a and 6b are not Graduation Standards.)
a. Solve systems of linear equations using the substitution method.
b. Solve systems of linear equations using linear combination.
Solve each system of equations by graphing.
{
𝑦 = 2𝑥 + 4
– 3𝑥  2𝑦 = 6
{
𝑦 = −𝑥 + 3
4𝑥 − 2 = 𝑦
A1.AREI.6
Solve each system of equations by substitution.
2𝑥 − 3𝑦 = 13
𝑥 = −2𝑦 + 14
1
7
{
{
−3𝑥 + 𝑦 = −14
𝑦= 𝑥−
2
𝑥 + 𝑦 = −24
𝑦 = 2𝑥
{
2
A1.AREI.6
Solve each system of equations by elimination.
𝑥 − 2𝑦 = −2
{
−𝑥 + 𝑦 = 3
A1.AREI.6
{
2𝑥 − 4𝑦 = −6
𝑥 − 𝑦 = −1
At an all-you-can-eat barbeque fundraiser that you are sponsoring, adults pay $6 for the dinner and children
pay $4 for the dinner. You know that 212 dinners were served and that you raised $1128, and you want to
find the total number of adults and the total number of children that attended.
a. Write the system of equations that you would use to solve this problem. Be sure to define the
variables.
b. What method would you use to solve this problem and why?
c. Solve the system and answer the question, how many adults and how many children attended the
fundraiser?
A1.AREI.6
Describe the solution of each system of equations shown in the graphs and explain how you know.
A1.AREI.6
Solve the system by graphing.
𝑦 = 3𝑥 − 2
𝑦 = −𝑥 + 2
A1.AREI.6
Solve the system of equations by substitution. 𝑦 = 5𝑥
𝑥 + 𝑦 = 12
A1.AREI.6
Solve the system of equations by elimination. 5𝑥 + 7𝑦 = 3
2𝑥 + 3𝑦 = 1
A1.AREI.6
Explain the difference between the following types of systems: one solution, no solution, infinitely many
solutions.
A1.AREI.6
Johnny went to Target to buy new pencils and markers for his class. At Target he bought a total of 8 items
(pencils and markers). Markers are $6.50 apiece and the pencils are $0.25 each. He spent a total of $20.75.
How many pencils and how many markers did he buy?
A1.AREI.6
The difference of two numbers is 3. Their sum is 27. Find the two numbers.
A1.AREI.6
Graph each system of equations. Then determine whether the system has no solution, one solution, or
infinitely many solutions. If the system has one solution, name it.
a. y = -x + 4
b. x + y = 0
y=x–4
x+y=2
A1.AREI.6
Barbara bought some salt water tuna for $9.00 each and fresh water bass for $7.50 each. If she bought a
total of 34 fish and spent $285.00, how many of each fish did she buy?
A1.AREI.6
Solve each system by elimination or substitution:
a. -x + 4y = 5
-x - 2y = -19
b. x = 8y + 4
3x + y = -13
3
x+2
4
y = 2x – 3
d. y =
c. 5x + 9y = -89
7x – 3y = -31
e. y = -4x
x + 2y = -16
A1.AREI.6
A1.AREI.10* Explain that the graph of an equation in two variables is the set of all its solutions plotted
in the coordinate plane.
Determine if (-3, 2) is a solution to the equation 3y – 2x = 0, and explain how you know.
A1.AREI.10
Determine if the ordered pair (2, -3) is a point on either of these graphs:
1
a. 𝑦 = − 2 𝑥 + 1
b. 2𝑥 − 𝑦 = 10
A1.AREI.10
Determine three solutions of the equation graphed below:
A1.AREI.10
Use the graph to complete the table.
x
f(x)
3
3
11
5
A1.AREI.10
A worker finds that it takes 16 tiles to cover one square foot of floor. Make a table and draw a graph to
show the relationship between the number of tiles and the number of square feet of floor covered.
Number of
Tiles
Number of
Square Feet
How many square feet of floor will be covered by 208 tiles?
A1.AREI.10
A painter finds that it takes 2.25 hours to paint one room. Make a table and draw a graph to show the
relationship between the number of hours and the number of rooms painted. Construct an equation
to help determine how many rooms can be painted in 40.5 hours.
Number
of Rooms
Total
Amount
of Time
Painting
A1.AREI.10
Bob, the builder, is planning on building a new neighborhood. He figures it will take his team two and
a half months to build each house. If he has 2 and a half years to build his neighborhood, how many
houses will it have? Make a table and draw a graph to show the relationship between the number of
months worked and the number of houses built.
Number of
Months
Worked
A1.AREI.10
Number of
Houses Built
Megan is making holiday gifts for her family and friends. She has calculated that it will take her 45
minutes to make each gift. If she has thirteen and a half hours over the next few weeks she can spend
working on her gifts, how many gifts can she make? Make a table to show the relationship between
the number of hours spent working and the number of gifts made. Graph your results.
Number of
Hours Worked
Number of
Gifts Made
A1.AREI.10
Bernice is training for a marathon. She figures that she can run one mile every 8 minutes. If she has an
hour and 20 minutes to train today, how many miles can she run? Use the table to show the
relationship between the number of minutes and the number of miles ran. Graph your results.
Number of Number of
Minutes
Miles Ran
A1.AREI.10
Bob is mowing lawns for a summer job. After many calculations he figures he can mow a lawn in 55 min.
He charges $20 per lawn. Bob wants to buy a new skateboard that cost $240. How many lawns does Bob
have to mow this summer to earn enough for the skateboard? Use the table to show the relationship
between the number of lawns mowed and the amount of money earned. Graph your results.
Number of
Lawns
Mowed
A1.AREI.10
Amount
Of Money
Earned
A1.AREI.11* Solve an equation of the form f(x)=g(x) graphically by identifying the x-coordinate(s) of the
point(s) of intersection of the graphs of y=f(x) and y=g(x). (Limit to linear; quadratic; exponential.)
1 𝑥
Find the value(s) of x that satisfy the equation −2𝑥 + 4 = (2) − 3. Round to the nearest tenth if
necessary.
A1.AREI.11
1 𝑥
Given the two functions 𝑓(𝑥) = 3𝑥 + 2 and 𝑔(𝑥) = (2) − 3, find the values of x for which f(x) = g(x)
rounded to the nearest tenth.
A1.AREI.11
A1.AREI.12* Graph the solutions to a linear inequality in two variables.
Graph the linear inequality 𝑦 > 3𝑥 − 4.
A1.AREI.12
1
Graph the linear inequality 𝑦 ≤ 3 𝑥 + 3.
A1.AREI.12
Graph the solutions: 𝑦 ≥
2
3
𝑥 − 4.
A1.AREI.12
Graph the solutions: 𝑦 < −2𝑥 + 5.
A1.AREI.12
Graph the solutions: 2𝑥 − 6 < 2𝑦 + 5.
A1.AREI.12
A1.ASE.1*
Interpret the meanings of coefficients, factors, terms, and expressions based on their realworld contexts. Interpret complicated expressions as being composed of simpler expressions. (Limit to
linear; quadratic; exponential.)
Write an algebraic expression or equation for each word phrase:
a. Five less than the product of 6 and a number q.
b. The quotient of 5 minus x and 12.
c. Three minus the product of a number and four is nine.
d. The product of 6 and the sum of 7 and x is 54.
A1.ASE.1 (linear)
Write an algebraic expression for each word phrase:
a. The product of a number x and 23
b. 9 less than the product of 7 and a number y
A1.ASE.1 (linear)
Write a word phrase for each algebraic expression:
a. 5w + 3
b.
(𝑥−2)
10
A1.ASE.1 (linear)
Write a word phrase for each algebraic expression:
a. 3x + 5
b. 2(x - 4) = 8
A1.ASE.1 (linear)
c.
(𝑥+5)
3
= 12
A1.ASE.2*
Analyze the structure of binomials, trinomials, and other polynomials in order to rewrite
equivalent expressions.
Factor each of these expressions into products of linear binomials:
a. 9x² + 3x – 30
b. 4x² - 36
c. x² + 6xy – 55y²
A1.ASE.2
Factor each of these expressions:
a. x2 – 8x + 12
b. 5n2 + 10n
c. 25k2 – 9
A1.ASE.2
Factor each expression:
a. 2n2 + n  1
d. x² + 5x + 6
b. n 2 + 9n  10
e. x² - 12x + 36
c. n2  6n
f. x² + 18x + 48
A1.ASE.2
A1.ASE.3*
Choose and produce an equivalent form of an expression to reveal and explain properties
of the quantity represented by the expression.
a. Find the zeros of a quadratic function by rewriting it in equivalent factored form and explain
the connection between the zeros of the function, its linear factors, the x-intercepts of its
graph, and the solutions to the corresponding quadratic equation.
b. Determine the maximum or minimum value of a quadratic function by completing the square.
Find the zeros for the function f(x) = -x2 + 8x + 15.
A1.ASE.3
IA.FBF.1*
Write a function that describes a relationship between two quantities.
(Note: IA.FBF.1a is not a Graduation Standard.)
a. Write a function that models a relationship between two quantities using both explicit
expressions and a recursive process and by combining standard forms using addition,
subtraction, multiplication and division to build new functions.
b. Combine functions using the operations addition, subtraction, multiplication, and division to
build new functions that describe the relationship between two quantities in mathematical
and real-world situations.
IA.FBF.2*
Write arithmetic and geometric sequences both recursively and with an explicit formula,
use them to model situations, and translate between the two forms.
A1.FBF.3*
Describe the effect of the transformations kf(x), f(x)+k, f(x+k), and combinations of such
transformations on the graph of y=f(x) for any real number k. Find the value of k given the graphs and
write the equation of a transformed parent function given its graph. (Limit to linear; quadratic;
exponential with integer exponents; vertical shift and vertical stretch.)
Describe how the graph of y = 2(6x) differs from the graph of its parent function f(x) = 6x.
A1.FBF.3 (exponential)
A1.FIF.1*
Extend previous knowledge of a function to apply to general behavior and features of a
function.
a. Understand that a function from one set (called the domain) to another set (called the range)
assigns to each element of the domain exactly one element of the range.
b. Represent a function using function notation and explain that f(x) denotes the output of
function f that corresponds to the input x.
c. Understand that the graph of a function labeled as f is the set of all ordered pairs (x,y) that
satisfy the equation y=f(x).
Use the graph to complete the table:
x
f(x)
3
3
11
5
Identify the domain of the function: ____________________
Identify the range of the function: ______________________
A1.FIF.1
Complete the table of values for the function 𝑦 = −3𝑥 + 2 and identify the domain and range.
x
y
-2
-1
1
2
A1.FIF.1
Make a table of values for the function f(x) = 3x + 4 with the domain {0, 2, 4, 6, 8}. Identify the range of the
function.
A1.FIF.1
A1.FIF.2*
Evaluate functions and interpret the meaning of expressions involving function notation
from a mathematical perspective and in terms of the context when the function describes a real-world
situation.
IA.FIF.3*
Define functions recursively and recognize that sequences are functions, sometimes
defined recursively, whose domain is a subset of the integers.
A1.FIF.4*
Interpret key features of a function that models the relationship between two quantities
when given in graphical or tabular form. Sketch the graph of a function from a verbal description showing
key features. Key features include intercepts; intervals where the function is increasing, decreasing,
constant, positive, or negative; relative maximums and minimums; symmetries; end behavior and
periodicity. (Limit to linear; quadratic; exponential.)
Identify the y-intercept of each line and classify each line as increasing or decreasing:
a.
b.
A1.FIF.4 (linear)
Find the indicated features of the following graph:
a.
b.
c.
d.
e.
A1.FIF.4 (linear)
Domain:
Range:
x-intercept:
y-intercept:
slope:
Identify the following features from the given graph:
a. Slope:
b. X-intercept:
c. Y-intercept:
A1.FIF.4 (linear)
Does the graph represent exponential growth or exponential decay? How do you know?
A1.FIF.4 (exponential)
Use the graph to answer the following:
a. What is the y-intercept?
b. What are the x-intercepts?
c. Where is the maximum or minimum of the function?
d. What is the equation for the line of symmetry?
A1.FIF.4 (quadratic)
State whether the graph displays a maximum or minimum. Draw the line of symmetry and identify the
equation for the line of symmetry.
A1.FIF.4 (quadratic)
What is the value of y of the quadratic equation graphed below when x = 0?
A1.FIF.4 (quadratic)
For the quadratic function shown in the graph, determine the
domain, range, and the intervals for which the function is increasing
and decreasing.
A1.FIF.4 (quadratic)
A1.FIF.5*
Relate the domain and range of a function to its graph and, where applicable, to the
quantitative relationship it describes. (Limit to linear; quadratic; exponential.)
4
Identify the horizontal and vertical asymptotes of the graph of the function (𝑥) = 3+𝑥 .
IA.FIF.5 (rational)
2𝑥+6
State the domain and range for 𝑓(𝑥) = 4𝑥−8.
IA.FIF.5 (rational)
A1.FIF.6*
Given a function in graphical, symbolic, or tabular form, determine the average rate of
change of the function over a specified interval. Interpret the meaning of the average rate of change in a
given context. (Limit to linear; quadratic; exponential.)
A relation contains this set of ordered pairs: {(0, 0), (2, 1), (6, 3), (10, 5), (24, 12)}.
Determine the average rate of change.
A1.FIF.6
A line passes through the points (-3, 10) and (-4, -8). What is the slope of the line?
A1.FIF.6
Explain the differences between the slopes of vertical lines and the slopes of horizontal lines.
A1.FIF.6
Find the slope of the line contain the points (-2, 12) (-9, -2).
A1.FIF.6
Find the rate of change of the relation given in the following table.
X
Y
-2
21
-1
16
0
11
1
6
2
1
A1.FIF.6
Find the rate of change for each function:
A.
X
Y
-3
-5
0
1
3
7
6
13
B.
9
19
A1.FIF.6
A1.FIF.7*
Graph functions from their symbolic representations. Indicate key features including
intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative
maximums and minimums; symmetries; end behavior and periodicity. Graph simple cases by hand and
use technology for complicated cases.
(Limit to linear; quadratic; exponential only in the form 𝒚 = 𝒂𝒙 + 𝒌.)
Graph the equation 5𝑥 − 3𝑦 = −15.
What is the x-intercept of the line?
What is the y-intercept of the line?
A1.FIF.7 (linear)
Find the x- and y-intercepts of the equation 2𝑥 + 3𝑦 = −18.
A1.FIF.7 (linear)
Graph the following equation: 𝑦 = 2𝑥 + 4.
A1.FIF.7 (linear)
For the function f(x) = 2x + 2, make a table of at least 5 ordered pairs, identify the domain and range of the
function, and graph the function.
A1.FIF.7 (linear)
Graph f(x) = 3x + 2.
A1.FIF.7 (linear)
A tee-shirt design company charges $5 for a shirt and $0.50 per letter/symbol printed on the shirt. Create a
table of values and graph the relation between the cost of a shirt and the number of letters and symbols
printed.
A1.FIF.7 (linear)
Graph the function f(x) = -x + 3.
A1.FIF.7 (linear)
Sketch the graph of the function 𝑓(𝑥) = 3𝑥 − 4.
Identify each of these key features of the graph:
x-intercept(s): _______________
y-intercept(s): _______________
domain: ___________________
range: _____________________
interval(s) of increase: _______________
interval(s) of decrease: ______________
interval(s) of positive values: _________________
interval(s) of negative values: ________________
A1.FIF.7 (exponential)
Sketch the graph of the exponential function 𝑦 = 3(2)𝑥 . Identify the key features of the graph listed below.
If needed, round your answers to the nearest hundredth. (10 points)
x-intercept: _______________
y-intercept: _______________
domain: ___________________
range: _____________________
increasing: _______________
decreasing: ______________
positive: _________________
negative: ________________
A1.FIF.7 (exponential)
Graph the function: y = -(½)x + 2.
A1.FIF.7 (exponential)
Graph the functions:
5 𝑥
𝑦 = (2)
𝑦 = 4𝑥
A1.FIF.7 (exponential)
Graph the equation 𝑦 = 2𝑥 . Label the y-intercept and describe the end behavior.
A1.FIF.7 (exponential)
Graph the following equation and identify its domain and range.
y = -5x
A1.FIF.7 (exponential)
Graph the following equation and identify its domain and range.
1 𝑥
y = 2 ∙(5)
A1.FIF.7 (exponential)
Graph the function: y = -2x + 1.
A1.FIF.7 (exponential)
Graph the equation y = x2 – 4.
A1.FIF.7 (quadratic)
Find the x-intercepts and the vertex of the graph of y = x2 + 6x + 5.
Graph the quadratic function using the key features you identified.
A1.FIF.7 (quadratic)
What are the coordinates of the vertex of the quadratic equation y = (x – 2.5)2 – 2.25?
A1.FIF.7 (quadratic)
What are the coordinates of the vertex for f(x) = x2 – 4x – 5?
A1.FIF.7 (quadratic)
What are the coordinates of the vertex for f(x) = x² + 6x – 2, and what is the equation for the function’s line
of symmetry?
A1.FIF.7 (quadratic)
For the function f(x) = x2, make a table of at least 5 ordered pairs, identify the domain and range of the
function, and graph the function.
A1.FIF.7 (quadratic)
Graph 𝑦 =
IA.FIF.7 (rational)
12
𝑥
.
Graph 𝑦 =
4
3+𝑥
.
IA.FIF.7 (rational)
A1.FIF.8*
Translate between different but equivalent forms of a function equation to reveal and
explain different properties of the function. (Limit to linear; quadratic; exponential.) (Note: A1.FIF.8a is
not a Graduation Standard.)
a. Use the process of factoring and completing the square in a quadratic function to show zeros,
extreme values, and symmetry of the graph, and interpret these in terms of a context.
A1.FIF.9*
Compare properties of two functions given in different representations such as algebraic,
graphical, tabular, or verbal. (Limit to linear; quadratic; exponential.)
A1.FLQE.1* Distinguish between situations that can be modeled with linear functions or exponential
functions by recognizing situations in which one quantity changes at a constant rate per unit interval as
opposed to those in which a quantity changes by a constant percent rate per unit interval.
(Note: A1.FLQE.1a is not a Graduation Standard.)
a. Prove that linear functions grow by equal differences over equal intervals and that exponential
functions grow by equal factors over equal intervals.
Determine whether the given functions are linear, exponential, or neither.
1. 𝑦 = −3𝑥 4 + 4
A1.FLQE.1
2. 𝑦 = −3𝑥 + 4
1
3. 𝑦 = 2 𝑥 − 3
A1.FLQE.2* Create symbolic representations of linear and exponential functions, including arithmetic
and geometric sequences, given graphs, verbal descriptions, and tables. (Limit to linear; exponential.)
Sketch a graph that represents the situation below. Be sure to label the axes.
Rachel decided to drive to visit her grandmother. She merged onto the interstate, drove on I-26 for a few
hours on cruise control, and then exited when she reached her destination.
A1.FLQE.2
Sketch a graph that represents the situation below. Be sure to label the axes.
After stopping the bus to pick up Tom, Ms. Ellie drives to the school and drops off all the children.
A1.FLQE.2
For the graph shown, write the equation in each different form.
a. Slope-Intercept:
b. Point-Slope:
c.
Standard:
A1.FLQE.2
Write the function that defines this table of values.
x
f(x)
1
45
2
46
3
47
4
48
A1.FLQE.2
Which equation represents the function depicted in the table of values?
W = Number of weeks
1
2
3
L = Length of ivy plant
7 in
10 in
13 in
A. L = 4W + 16
B. L = 3W+ 7
A1.FLQE.2
Which equation matches this graph?
A. y = -2(2)x – 4
B. y = -4(2)x – 2
C. y = 2(2)x – 4
D. y = -4(2)x + 2
A1.FLQE.2
C. L = 3W + 4
4
16 in
D. L = 4W + 3
A1.FLQE.3* Observe using graphs and tables that a quantity increasing exponentially eventually
exceeds a quantity increasing linearly, quadratically, or more generally as a polynomial function.
A1.FLQE.5*
to linear.)
Interpret the parameters in a linear or exponential function in terms of the context. (Limit
A1.NQ.1*
Use units of measurement to guide the solution of multi-step tasks. Choose and interpret
appropriate labels, units, and scales when constructing graphs and other data displays.
A1.NQ.2*
Label and define appropriate quantities in descriptive modeling contexts.
A1.NQ.3*
Choose a level of accuracy appropriate to limitations on measurement when reporting
quantities in context.
A1.NRNS.1* Rewrite expressions involving simple radicals and rational exponents in different forms.
Simplify each of the following expressions:
a. (5x)²
b. (9b³)²
A1.NRNS.1
Use the properties of exponents to simplify these expressions:
1
a. (−3𝑣 2 )(−3𝑣 2 )
b.
𝑝4 𝑞9
𝑝2 𝑞6
A1.NRNS.1
Simplify the following exponential expressions:
1. 𝑥 7 ∙𝑥 9
2.
𝑦5
𝑦 −3
3. (𝑛9 )7
4.
1
𝑥2
∙𝑥17
5. (𝑥 2 )4 (3𝑥 5 )
6. 10m4 (2m5)6
7. (
3𝑥 5
3
5
) ∙ 𝑥4
10𝑦 2
8. (4x -3y4)-2
A1.NRNS.1
A1.NRNS.2* Use the definition of the meaning of rational exponents to translate between rational
exponent and radical forms.
Write each expression in simplified radical form:
2
a. 𝑥 3
A1.NRNS.2
2
b. (5𝑦 2 )5
1
2
c. (3) (𝑚3 )
1
d. (729𝑦 2 )6
Write each expression in simplified exponential form:
3
a. √𝑧
3
b.
√8𝑥 34
4
3
c. √𝑥 5 ∙ √𝑥 2
A1.NRNS.2
A1.NRNS.3 Explain why the sum or product of rational numbers is rational; that the sum of a rational
number and an irrational number is irrational; and that the product of a nonzero rational number and an
irrational number is irrational.
FA.SPID.5* Analyze bivariate categorical data using two-way tables and identify possible associations
between the two categories using marginal, joint, and conditional frequencies.
There are 17 members in a travel group. The Venn diagram below shows the members that have been to
the United States, Australia, both, or neither. Complete the two-way frequency table.
Have been to Have not
United States been to the
United States
Have been to
Australia
Have not been
to Australia
FA.SPID.5
Gallup polled a random collection of 1,500 adults daily and asked them whether they approve or disapprove
of President Obama’s performance in office. The two-way frequency table below shows the results on April
27, 2009 and September 3, 2014. Were adults polled on April 27, 2009 more likely or less likely to approve
of President Obama’s performance than adults polled on September 3, 2014? Use probability concepts to
verify your solution.
FA.SPID.5
The two-way frequency table below shows the data on behavior of students and the use of candy to provide
a positive incentive for behavior for a group of students at Lion’s Lane Elementary School. Complete the
following two-way table of relative frequencies for receiving or not receiving candy.
Desirable Behavior
Undesirable Behavior
Received Candy
Did Not Receive
Candy
Row Total
1.00
1.00
FA.SPID.5
A 2014 study analyzed what percentage of residents in California were born in-state and what percentage
were born out of state from 1900 until 2012. The two-way table of column relative frequencies below
shows the results of the study. California’s total population was approximately 31 million in 2012.
Approximately how many 2012 California residents were born in California? Round your answer to the
nearest million.
FA.SPID.5
A1.SPID.6* Using technology, create scatterplots and analyze those plots to compare the fit of linear,
quadratic, or exponential models to a given data set. Select the appropriate model, fit a function to the
data set, and use the function to solve problems in the context of the data.
Use the table showing the average body temperature of 9 insects at a given air temperature.
Air Temp(oF)
Body Temp (oF)
25
20
30
23
35
26
40
29
45
32
a. Using technology, determine the line of best fit for the data.
b. What is the body temperature of an insect when the air temperature is 38° ?
A1.SPID.6 (linear)
50
35
The table shows the relationship between the time spent studying and the exam grade.
Time, x
Score, y
2
77
5
92
1
70
0
63
4
90
2
75
3
84
a. Create a scatter-plot from the table.
b. Determine the line of best fit for the scatter-plot.
A1.SPID.6 (linear)
The table below shows the average body temperatures of 9 beetles at given air temperatures.
Air Temp(oF)
Body Temp (oF)
25
20
30
22
35
27
40
28
45
31
50
36
a. Using technology, determine the equation of the line of best fit for the data.
b. Using your equation of best fit, predict the body temperature of a beetle when the air temperature
is 38oF.
A1.SPID.6 (linear)
Use the following coordinates and a graphing calculator to create a scatter plot of the data.
(0.2, 2.6), (-0.6, 2.1), (0.8, 2.0), (1.1, 2.1), (-1.7, 2.5), (1.9, 2.8), (-2.2, 3.3), (2.6, 4.4), (3.0, 5.0), (-3.2, 6.8)
a. Does the scatterplot best model a linear or quadratic correlation?
b. What is the equation of best fit for this data set? (round coefficients to the nearest hundredth)
A1.SPID.6
Use the following coordinates and a graphing calculator to create a scatter plot of the data.
(0.2, 4.4), (0.5, 5.2), (0.7, 5.7), (1.1, 6.1), (1.5, 7.0), (1.9, 7.8), (2.3, 8.7), (2.5, 9.0), (2.9, 9.9), (3.4, 10.8)
a. Does the scatterplot model a linear or quadratic correlation?
b. What is the equation of best fit for this data set? (round coefficients to the nearest hundredth)
A1.SPID.6
Identify the following scatterplots as linear, quadratic, or exponential:
a.
b.
y
A1.SPID.6
Jeremy took a survey of his friends’ heights and shoe sizes. Graph the data points on the grid, being sure to
label the axes. Then draw (estimate) a line that best fits the data.
HEIGHT (in) SHOE SIZE
AMY
50
6
BRIAN
55
9
CHARLIE
53
8.5
DEREK
51
7.5
EVAN
58
9.5
FIONA
48
6
A1.SPID.6 (linear)
A1.SPID.7* Create a linear function to graphically model data from a real-world problem and interpret
the meaning of the slope and intercept(s) in the context of the given problem.
A1.SPID.8*
Using technology, compute and interpret the correlation coefficient of a linear fit.
FA.SPMJ.1* Understand statistics and sampling distributions as a process for making inferences about
population parameters based on a random sample from that population.
FA.SPMJ.2* Distinguish between experimental and theoretical probabilities. Collect data on a chance
event and use the relative frequency to estimate the theoretical probability of that event. Determine
whether a given probability model is consistent with experimental results.
You toss a dart at a dart board 500 times. You hit the bull’s eye 80 times. What is the experimental
probability that you will hit a bull’s eye?
FA.SPMJ.2
You flip a coin 5 times. What is the theoretical probability that you will get a heads all 5 times?
FA.SPMJ.2
Sophie is playing with a spinner from a board game. The spinner is divided into five equal spaces with the
numbers 1-5 on them. She has spun the spinner 30 times and landed on 1 and 2 a total of 6 times. Is the
experimental probability consistent with the theoretical probability of hitting a 1 or 2? Use probability
concepts to verify your solution.
FA.SPMJ.2
The Widget Company randomly selects its widgets and checks for defects. If 5 of the 300 selected widgets
are defective, how many defective widgets would you expect in the 1500 widgets manufactured today?
FA.SPMJ.2
FA.SPMD.4* Use probability to evaluate outcomes of decisions by finding expected values and
determine if decisions are fair.
FA.SPMD.5* Use probability to evaluate outcomes of decisions. Use probabilities to make fair decisions.
FA.SPMD.6* Analyze decisions and strategies using probability concepts.
Eliza and Alisha are the two baseball captains. They roll a die and decide that if the die lands with an even
number, Eliza’s team will bat first. Otherwise, Alisha’s team will bat first. Is the method fair? Use
probability concepts to verify your conclusion.
FA.SPMD.6
Maria and Mary are playing with dice. They roll one die. If the die lands on the number 2 then they win 7
candies. If the die lands on the number 5 then they win 4 candies. If the die lands on any other number,
they lose 2 candies. Is the game fair? Use probability concepts to verify your conclusion.
FA.SPMD.6
Your friend Jeff is on a game show hoping to win a car. The host of the game show reveals three doors, and
tells Jeff that the car is behind one of them. Behind the other two doors are goats. The game show host
knows where the car is. The game show host tells Jeff to pick a door and he does. Then, the game show
host opens one of the doors that Jeff did not choose to reveal a goat. The game show host asks Jeff if he
wants to switch doors. Should Jeff switch from the original door he picked or should he stick with his
original decision? Use probability concepts to verify your answer.
FA.SPMD.6
You are at a carnival and decide to play one of the games. You spot a table where a person is flipping a coin,
and since you have an understanding of basic probability, you believe that the odds of winning are in your
favor. When you get to the table, you find out that all you have to do is guess which side of the coin will be
facing up after it is tossed. You are assured that the coin is fair, meaning that each of the two sides has an
equally likely chance of occurring. Before you bet, your friend comes up and tells you that heads has come
up the last 9 times in a row. Would you place your bet on tails? Use probability concepts to support your
answer.
FA.SPMD.6
IA.NCNS.1* Know there is a complex number i such that i^2=-1, and every complex number has the form
a+bi with a and b real.
IA.NCNS.7* Solve quadratic equations in one variable that have complex solutions.
Find the solutions for the equation 3x2 + 27 = 0.
IA.NCNS.7