BCSD Mathematics
Algebra 1/Foundations/Intermediate Assessment Item Bank
AAPR
Algebra - Arithmetic with Polynomials and Rational Expressions
AAPR.1
ACE
Algebra – Creating Equations
ACE.1 / ACE.2 / ACE.4
AREI
Algebra – Reasoning with Equations and Inequalities
AREI.1 / AREI.2 / AREI.3 / AREI.4 / AREI.5 / AREI.6 / AREI.10 / AREI.11 / AREI.12
ASE
Algebra – Structure and Expressions
ASE.1 / ASE.2 / ASE.3
FBF
Functions – Building Functions
FBF.1 / FBF.2 / FBF.3
FIF
Functions – Interpreting Functions
FIF.1 / FIF.2 / FIF.3 / FIF.4 / FIF.5 / FIF.6 / FIF.7 / FIF.8 / FIF.9
FLQE
Functions – Linear, Quadratic, and Exponential
FLQE.1 / FLQE.2 / FLQE.3 / FLQE.5
NQ
Number and Quantity - Quantities
NQ.1 / NQ.2 / NQ.3
NRNS
Number and Quantity – Real Number System
NRNS.1 / NRNS.2 / NRNS.3
SPID
Statistics and Probability – Interpreting Data
SPID.5 / SPID.6 / SPID.7 / SPID.8
SPMJ
Statistics and Probability – Making Inferences and Justifying Conclusions
SPMJ.1 / SPMJ.2
SPMD
Statistics and Probability – Using Probability to Make Decisions
SPMD.4 / SPMD.5 / SPMD.6
NCNS
Number and Quantity – Complex Number System
NCNS.1 / NCNS.7
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:
  1. (4x2 – 11) + (-8x2 + 20)b.(x2 + 6x – 4) – (2x2 – 3)
  1. (2x – 5)(7x + 1)d. (3x + 4)2
A1.AAPR.1
Simplify the following polynomials:
  1. (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:
  1. x2(x – 9) + x(x³ + 5x) b. (2y + 3)2 c. 2(3x – 4)(x + 1)
A1.AAPR.1
Simplify each expression:
  1. (5x4+ 7x + 2) – (3x² - 2x + 9) b. (4x² + 9x + 1) + (2x² + 7x + 13)
A1.AAPR.1
Simplify each expression:
  1. 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:
Bill ran 8 miles more than 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.
  1. Slope-Intercept:
  1. Point Slope:
  1. 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)
x / f(x)
1 / 4
2 / 7
3 / 10
4 / 13
Write the function that defines this table of values.

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).
  1. Write the equation of the line in point-slope form:
  2. Write the equation of the line in slope-intercept form:
  3. 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.
  1. Write a direct variation equation that relates x and y when y=10 and x=2.
  2. What is the value of y when x is 8?
A1.ACE.2 (linear)
Write the equation of the graph in each different form.

  1. Slope Intercept:
  1. Point Slope:
  1. 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) / 25 / 30 / 35 / 40 / 45 / 50
Body,(y) / 20 / 23 / 26 / 29 / 32 / 35
a.) b.)
c.) d.)
A1.ACE.2 (linear)
Write an equation that represents the relationship between the values in the table below:
x / -1 / 0 / 1 / 2 / 3
y / / 1 / 3 / 9 / 27
A1.ACE.2 (exponential)
Write an equation that represents the relationship between the values in the table below:
x / -1 / 0 / 1 / 2 / 3
y / / 5 / 10 / 20 / 40
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?

  1. y = -2(2)x – 4
  1. y = -4(2)x – 2
  1. y = 2(2)x – 4
  1. y = -4(2)x + 2
A1.ACE.2 (exponential)
A population of 50 wolves in a wildlife preserve doubles in size every 12 years.
  1. Create an equation that models the population growth. Define your variables.
  2. 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.
  1. Create the equation that models how much money is in Jerome’s account. Define your variables.
  2. 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.
  1. Write an equation that models the population (p) based on the number of years from now (t).
  2. 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 varies inversely with and when . 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. (x + y) = zb. 6x + 3y = -12 c. 8x + 2y = 50
A1.ACE.4
Solve A = bh for b.
A1.ACE.4
Solve each equation for the indicated variable.
  1. (x + y) = z; solve for y.b. F = C + 32; solve for C.
A1.ACE.4
Solve each equation for x:
  1. b.
A1.ACE.4
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.
Explain the step-by-step process you use to solve the equation 12 = for x.
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 cm2.) 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 + 2.)
3.) 4.) 2
IA.AREI.2 (radical)
The length s of one edge of a cube is given by , 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)
The formula 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:
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:
  1. - x + 2 = -3
  2. -4(2x – 1) = -10(x – 5)
  3. 8(x + 2) = 16
  4. x = 9
  5. -3(2x – 3) = -5(x – 1)
A1.AREI.3
Solve each of the following for the values of x:
  1. -5x + 13 ≥ -7
  2. ≥ 12
  3. 12 > 8 – 6x
  4. 2( x – 3) -12
  5. -3x – 7 > 23
A1.AREI.3
Solve each of the following for the value of x:
  1. 7 – 3x + 4 = 5x – 1 + 4x
  2. 3(x – 5) – x = 3 + 2(x – 3)
  3. 3(x + 1) - 5 = 3x – 2
A1.AREI.3
Solve each of the following for the values of the variables:
  1. -2(4x + 3) +5(x + 4) ≤ 2
  2. -6 < 3n + 9 < 21
  3. 16 < -x – 6 or 2x + 5 ≥ 11
A1.AREI.3
Solve each of the following for the value of x:
  1. 2. 3.
4. 5. 6.
A1.AREI.3
Solve each of the following for the values of x:
  1. 2. 3.
  1. 5. or 6.
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.)
  1. Use the method of completing the square to transform any quadratic equation in x into an equation of the form that has the same solutions. Derive the quadratic formula from this form.
  2. 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 andb. (Limit to non-complex roots.)

Solve each of the following equations by factoring. Show all work.
  1. x2 + x – 12 = 0b. 3n2 + 9n = 0
  1. 36k2 = 49d.3x2 + 2x = 5
A1.AREI.4
Solve the following equations by factoring.
  1. x2 – 8x + 12 = 0b. 5n2 + 10n = 0
A1.AREI.4
Solve each of the following by factoring:
  1. 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:
  1. 2n2 + n 1 = 0 b. n2 + 9n 10 = 0 c. n2 6n = 0
A1.AREI.4
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic, then rewrite the expression as a squared binomial.
  1. v2 6v + = ______
  1. 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.5Justify 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.


A1.AREI.6
Solve each system of equations by substitution.

A1.AREI.6
Solve each system of equations by elimination.

A1.AREI.6
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.
  1. Write the system of equations that you would use to solve this problem. Be sure to define the variables.
  2. What method would you use to solve this problem and why?
  3. 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.


A1.AREI.6
Solve the system of equations by substitution.

A1.AREI.6
Solve the system of equations by elimination.

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?