Algebra FSA End of Course Exam review Name______
Show all work on separate paper(graph paper when directions say “graph”). Date______Period______
MAFS.912.A-REI.1.1 ***********NO CALCULATOR**************Explain each step in solving a simple equation as following from the equality of numbers asserted at the previous step, starting from the assumption that the original equation has a solution. Construct a viable argument to justify a solution method.
1. A student solved the equation 7 = 3(t – 1) – 2(t – 3) as shown below. Assume there is a value of t for that satisfies the equation.
Provide a justification for each step of the solution process.
7 = 3(t – 1) – 2(t – 3)
a) 7 = 3t – 3 – 2t + 6 Justification:
b) 7 = t + 3 Justification:
c) 4 = tJustification:
Equation Logic
2. Solve the equation. Explain and justify each step in your solution process.
MAFS.912.F-IF.2.4 *****************NO CALCULATOR*******************For a function that models a relationship between two quantities, interpret key features of graphs and tables in terms of the quantities and sketch graphs showing key features given a verbal description of the relationship. Key features include: intercepts; intervals where the function is increasing, decreasing, positive, or negative; relative maximums and minimums; symmetries; end behavior; and periodicity.
Also assesses MAFS.912.F-IF.3.9 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a graph of one quadratic function and an algebraic expression for another, say which has the larger maximum.
4. (Old Standard 2: MA.912.A.2.3)
The students in Adam's science class measure and graph the speed of a slow-moving snail.
A. / f(x) = 3xB. / f(x) = 2xx2
C. / f(x) = −3x
D. / f(x) = 3x + 2
The snail moves at a constant rate, and after the investigation, the students use their data to create the following graph. Based on this graph, what function would best represent the snail's speed if x = time and f(x) = distance?
5. (Old Standard 3: MA.912.A.3.9)
On a coordinate graph, Celeste places a red marble at the point (2, 2) and a green marble at the point (4, 1). If she draws a line that passes through both of these points, what are the coordinates of the x- and y-intercepts of the line?
6. State the x and y intercepts: 3x – y = 3
7.(Old Standard 7: MA.912.A.7.1)
Which of the following is the graph of the function y = x2 − 4x − 12? Label any extrema on the graph. Be sure to indicate whether the point represents a relative minimum or absolute minimum, etc.
A. / / B. /C. / / D. /
8. (Old Standard 7: MA.912.A.7.1)
What equation represents the graph shown below? On what interval(s) is the graph decreasing? Increasing? Identify the extrema.
9. Statethe absolute maximum and/or absolute minimum and list any relative minima or maxima.
11. (Old Standard 3: MA.912.A.3.8)
Ignacio threw 14 pitches during the first two innings of a baseball game. He threw an average of 8 pitches per inning for the next seven innings. Which graph correctly represents the number of pitches Ignacio threw during the game?
A / / C /B / / D /
MAFS.912.F-LE.1.1 *******************NO CALCULATOR*******************
Distinguish between situations that can be modeled with linear functions and with exponential functions.
a. Prove that linear functions grow by equal differences over equal intervals and that exponential functions grow by equal factors over equal intervals.
b. Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
c. Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
Also assesses MAFS.912.F-LE.2.5 Interpret the parameters in a linear or exponential function in terms of a context.
12. Name the type of model suggested by the graph to the below.
[A] linear [B] quadratic[C] exponential [D] absolute value
13. The table gives the number of inner tubes, I, sold in a bike shop between 1985 and 1990.
Determine which model best fits the data.
[A] quadratic [B] linear [C] absolute value [D] exponential
14. A forester has determined that the number of fir trees, N, in a forest can be modeled by the equation where 8000 is the estimated number of trees in 2010 and t is the number of years since 2010. Label and scale the axes appropriately. Then, sketch a graph of this equation for the period 2010-2030. Indicate clearly the coordinates of the points you used to construct the graph.
15. A radioactive kind of nitrogen has a half-life of 10 minutes. If you start with 64 grams of the substance, how much will be left after 20 minutes?
MAFS.912.F-LE.1.3 **********************NO CALCULATORS********************Observe using graphs and tables that a quantity increasing exponentially eventually exceeds a quantity increasing linearly, quadratically, or (more generally) as a polynomial function.
16. Let f(x) = x3and g(x) = 3x + 2. Find solutions of the equation f(x) = g(x) by creating a table of integer values of x for −2 ≤ ? ≤ 3 and finding the corresponding values of f and g. Be sure to clearly indicate all values from the table that are solutions of f(x) = g(x).
17. Two nature parks opened the same year in neighboring towns. Park A’s attendance can be represented by the equation y = 3x2 – 10x + 10, and Park B’s attendance can be represented by the equation y = 1.8x - 1, where x represents the number of years since opening, and y represents the attendance in hundreds. Tables and graphs for both parks are shown below.
19a. In which years does Park A have the greater attendance?
19b. In which years does Park B have the greater attendance?
19c. Describe how the functions are different.
19d. If the trends continue, will Park A’s attendance ever surpass Park B’s attendance again? Explain.
MAFS.912.A-APR.1.1 ************************NO CALCULATOR****************Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
20. Polynomials are closed under all but which of the following operations?
A)Addition
B)Subtraction
C)Multiplication
D)Division
21. (Old Standard 4: MA.912.A.4.2)
Which answer choice is equivalent to the sum of the polynomials shown below?
(10x2 + 3x − 6) + (2x2 − 9x − 12)
A. / 3(4x2 − 2x + 6) / C. / 6(2x2 − x − 3)B. / 6(x − 3) / D. / 18(x3 − 1)
What is the simplified form of each expression?
22A. (5m2 – 6m +12) – (5m – 12 – m2)
22B. (3m – 4)(m – 8 )
22C 4xy2(5x5 – xy + 2y3)
22D. (m – 4)(5m2 + m – 1 )
23.(Old Standard 4: MA.912.A.4.2)
Which of the following expressions is equivalent to (5x − 3)2?
A. 25x2 – 30x + 9 C. 25x2 – 15x + 9
B. 25x2 – 15x – 9 D. 25x2 – 9
24. A heart shaped chocolate box is composed of one square and two half circles. The total number of chocolates in the box is calculated by adding the area of a square given by 4?2 and the area of a circle approximated by 3?2. The company plans to add a small additional box for a promotional campaign containing one row (2?) of chocolates. If the total combined heart shape and small box contain 69 chocolates, which of these equations could be utilized to solve for the number of chocolates in the small box (2?)?
A. 4?2 + 3?2 + 2? = 69
B. 4?2 – 3?2 + 2? = 69
C. 4?2 + 3?2 – 2? = 69
D. 4?2 – 3?2– 2? = 69
25. In the diagram at the right, the dimensions of the large rectangle are (3? − 1) by (3? + 7) units. The
dimensions of the cut-out rectangle are ?by 2? + 5 units. Which choice expresses the area of the shaded region, in square units?
A. ?2 + 23? – 7
B. ?2 + 13? – 7
C. 7?2 + 23? – 7
D. 7?2 + 13? – 7
MAFS.912.N-RN.1.2**********************NO CALCULATORS********************Rewrite expressions involving radicals and rational exponents using the properties of exponents.
Also assesses MAFS.912.N-RN.1.1 Explain how the definition of the meaning of rational exponents follows from extending the properties of integer exponents to those values, allowing for a notation for radicals in terms of rational exponents. For example, we define to be the cube root of 5 because we want ( ) ( ) to hold, so ( ) must equal 5.
Also assesses MAFS.912.N-RN.2.3 Explain why the sum or product of two 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.
26. Which statement is NOT always true?
A. The product of two irrational numbers is irrational.
B. The product of two rational numbers is rational.
C. The sum of two rational numbers is rational.
D. The sum of a rational number and an irrational number is irrational.
27. Consider a quadratic equation with integer coefficients and two distinct zeros. If one zero is irrational, which statement is true about the other zero?
A. The other zero must be rational.
B. The other zero must be irrational.
C. The other zero can be either rational or irrational.
D. The other zero must be non-real.
28. What value of x would make the expression below equal to 8?
29. (Old Standard 4: MA.912.A.4.1)
What is the value of the following expression when x = 3?
4x2x−1
30. Simplify for x≠0:
A. B. C. D.
31.
32.
33A. (Old Standard 4: MA.912.A.4.1)
Simplify the expression below
33B. Simplify
34A. (Old Standard 6: MA.912.A.6.2)
Which answer choice is equivalent to the expression below?
- C.
- D.
Simplify:
34B. 34C.
35. (Old Standard 6: MA.912.A.6.2)
What is the value of x in the equation shown below?
(8x)[(2x)]−2 = 8
A. C.
B. 1D. 4
36A. (Old Standard 6: MA.912.A.6.2)
Simplify the expression below.
Perform the following operations and simplify, or... just simplify!
36B.
36C.
36D.
36E.
36F.
36G.
36H. for
36I.
36J.
MAFS.912.F-IF.1.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.Also assesses MAFS.912.F-IF.1.1 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. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).
Also assesses MAFS.912.F-IF.2.5 Relate the domain of a function to its graph and, where applicable, to the quantitative relationship it describes. For example, if the function h(n) gives the number of person-hours it takes to assemble n engines in a factory, then the positive integers would be an appropriate domain for the function.
Write a function for the situations in 37A and37B. Is the graph continuous or discrete?
37A.A movie store sells DVDs for $11 each. What is the cost, C, of n DVDs?
a. / C = 11n; continuous / c. / C = 11 + n; continuousb. / C = 11 + n; discrete / d. / C = 11n; discrete
37B.A produce stand sells roasted peanuts for $1.90 per pound. What is the cost, C, of p pounds of peanuts?
a. / C = 1.90p; continuous / c. / C = 1.90 + p; continuousb. / C = 1.90p; discrete / d. / C = 1.90 + p; discrete
38. Neil plans to paint sweatshirts. The paint costs $14.75. The sweatshirts cost $7.50 each.
Write a function C( x) , for cost of x sweatshirts. Determine the cost of four sweatshirts.
39. Elizabeth plans to decorate T-shirts to sell at a fair. The decorations cost a total of $52.50 and the T-shirts cost $6.50 each. Which function expresses the cost, C( x) , of the project in terms of the number of T-shirts decorated, x?
A. = 6.50x
B. = 6.50x + 52.50
C. = 52.50x + 6.50
D. = 6.50 + 52.50
40. (Old Standard 2: MA.912.A.2.3)
Given the function f(x) = 2x + 2, what is the value of x if f(x) = 6?
41. Find the range of for the domain {–1, 3, 7, 9}.
42. Let . Find and.
43. (Old Standard 2: MA.912.A.2.4)
What is the range of the following relation?
{(5, 0), (6, −1), (1, 4), (0, 5), (2, 3)}
44. Does the input-output table represent a function? If it does represent a function, list the domain and range. If it does not represent a function, explain why.
For items 45A and 45B, state the domain and range. Determine whether the relation is a function.
45A45B
MAFS.912.A-CED.1.1 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational, absolute, and exponential functions.Also assesses MAFS.912.A-REI.2.3 Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
Also assesses MAFS.912.A-CED.1.4 Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. For example, rearrange Ohm’s law, V = IR, to highlight resistance, R.
46. Julie is required to pay a 2% state income tax on all income over $3,000. In addition to the 2% tax, she must pay an extra 2.5% state income tax on all income over $20,000. Julie earned more than $20,000 last year and paid $992.50 in state income taxes. What was her total income for the year?
A. $22,056B. $25,056C. $34,500D. $39,700
47A New York City taxi charges $3 per ride plus as additional $0.50 per mile. Which function below shows how to calculate the total cost of a taxi ride that is x miles long?
A. =$3x +$0.50
B. =$3x – $0.50
C. = $0.50x + $3
D. = $0.50x – $3
48A.The ages of three friends are consecutively one year apart. Together, their ages total 48 years. Which equation can be used to find the age of each friend (where ?represents the age of the youngest friend)?
A. 3a = 48
B. a(a + 1)(a + 2) = 48
C. a + (a − 1) + (a − 2) = 48
D. a + (a + 1) + (a + 2) = 48
48B.What are the ages of the friends?
A. 16, 17, 18
B. 15, 16, 17
C. 14, 15, 16
D. 17, 18, 19
49. (Old Standard 3: MA.912.A.3.1)
What is the value of x in the equation below?
4(x + 3) = 9x + 16 + 3x
50. Solve. Do not use decimals!! NOT MULTIPLE CHOICE
A. 10x + (2 + 8x) = 4 -5 (3-9x)
B 4x -6x = 9(x+4) – 2
C.
D.
51. A ball is kicked from ground level into the air. Its height y, in feet, after x seconds can be represented by the equation . What is the total elapsed time, in seconds, from the time the ball is kicked until it reaches ground level again?
52.(Old Standard 3: MA.912.A.3.3)
What is the equation below correctly solved for b?
4ab = 6bc − 5b + a
1. Solve the following equation for v. Show all of your work.
The next two problems are multiple choice.
56. (Old Standard 3: MA.912.A.3.4)
Which graph represents the solution set for the compound inequality shown below?
6x + 4 ≥ 34or −1 > 5
A.
B.
C.
D.
57. (Old Standard 3: MA.912.A.3.4)
What is the solution for the inequality shown below?
−3 < 2x + 11 < 7
Solve:
58A. 3(5x – 10) < 30x
58B. 12x – 10 > 10x – 20
58C. x – 4x < 5x + 16
59. (Old Standard 3: MA.912.A.3.4)
Which graph represents the solution set for the inequality shown below?
5x + 7 ≤ 23x − 2
A.
B.
C.
D.
60. (Old Standard 3: MA.912.A.3.5)
The math club needs to raise at least $563 for the national competition this summer. They decide to sell slices of pie on March 14, Pi Day, to earn the amount needed. If they sell each slice of pie for $3 and make 75% profit on each slice, what is the minimum number of slices they need to sell to earn enough money for the national competition?
61. The width of a rectangle is 33 centimeters. The perimeter is at least 776 centimeters. Write and solve an inequality to find the possible lengths of the rectangle.
a.
b. 355
c. ≤
d.
MAFS.912.A-CED.1.2 Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.Also assesses MAFS.912.A-REI.3.5 Prove that, given a system of two equations in two variables, replacing one equation by the sum of that equation and a multiple of the other produces a system with the same solutions.
Also assesses MAFS.912.A-REI.3. Solve systems of linear equations exactly and approximately (e.g., with graphs), focusing on pairs of linear equations in two variables.
Also assesses MAFS.912.A-REI.4.12 Graph the solutions to a linear inequality in two variables as a half-plane (excluding the boundary in the case of a strict inequality), and graph the solution set to a system of linear inequalities in two variables as the intersection of the corresponding half-planes.
62. Monique owns a catering business. Last weekend, she catered two events in which all attendees were served
either a chicken or a steak dinner. The table below shows some pricing information about these two events
Before-Tax Prices for Monique’s Catered Events
Day of event / Number of chickenDinners served / Number of steak
Dinners served / Total before-tax
Price of dinners
Saturday / 27 / 17 / $809.50
Sunday / 46 / 34 / $1,495,00
The following system of equations can be used to determine the before-tax prices of c dollars for each chicken dinner and s dollars of each steak dinner Monique served.
27c + 17s = 809.50
46c + 34s = 1,495.00
What is the before-tax price of a chicken dinner?
63. (Old Standard 3: MA.912.A.3.14 )
In the 1600s, a blacksmith could make a living by hand-forging horseshoes and nails. A diligent blacksmith could make one horseshoe in 12 minutes and a nail in 1 minute. In the 1600s, it would take the blacksmith 210 minutes to complete a particular job. With advances in technology, the blacksmith was able to make a horseshoe in 9 minutes and a nail in 40 seconds, and could complete the same job in 155 minutes. In the equations below, h represents the number of horseshoes in the job, and n represents the number of nails in the job.
12h + n = 210
9h + = 155
How many nails were in the job the blacksmith completed?
64. The solution to the system
A. all real numbers B. C. D. (2, 2)
65A. Graph y < 4? – 1
65B. Graph
MAFS.912.A-CED.1.3Represent constraints by equations or inequalities and by systems of equations and/or inequalities, and interpret solutions as viable or nonviable options in a modeling context. For example, represent inequalities describing nutritional and cost constraints on combinations of different foods.
66. Standard 3: MA.912.A.3.11
The table below shows how old Marsha and Tony were in several different years. If T represents Tony's age and M represents Marsha's age, what equation could be used to correctly predict Tony's age when Marsha is M years old?
Year / Marsha / Tony2000 / 6 / 10
2002 / 8 / 12
2004 / 10 / 14
2006 / 12 / 16
67. The table below shows how many cars were washed and how much money was collected for a fundraiser over a certain amount of time one afternoon. C represents cars washed and m represents the money collected, what equation could be used to correctly predict the amount of money collected (m) after c amount of cars are washed?
Time / Cars washed / Money collected12:00 / 0 / 0
2:00 / 16 / $104.00
4:30 / 36 / $234.00
Write a system of two linear equations. Then solve the system. What are the reasonable domain and range?
68A. There are only 35 tickets to be sold for the dance. The number of tickets sold to seniors must be four times the number of tickets sold to juniors.
Equations ______Solution ______Domain______Range______
______
68B. A diamond today costs ten dollars more than twice what it cost last year. The sum of the costs (last year and this year) is $2500. What is the cost of last year's diamond? What are the reasonable domain and range?
Equations ______Solution ______Domain______Range______
______
69A. Is it possible to prepare a lunch that contains four servings of Food A and three servings of Food B and still satisfy the constraints on cost, amount of sugar, and amount of protein? Explain.
69B.Let a represent the number of servings of food A and let b represent the number of servings of food B. Write a set of inequalities that model the constraints on cost, amount of sugar, and amount of protein.
MAFS.912.A-REI.4.11 Understand that the graph of an equation in two variables is the set of all its solutions plotted in the coordinate plane, often forming a curve (which could be a line).Also assesses MAFS.912.A-REI.4.10 Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately (e.g., using technology to graph the functions, make tables of values, or find successive approximations). Include cases where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.
70. Which system has the graph shown?