Algebra Two EOC

The online scientific calculator that is supposed to be what you will have access to. Please practice with this calculator:

Some resources

Khan Academy youtube video goes over questions…explains solutions of some sample questions that are similar to questions on the eoc test:

website where I got the practice problems on the following pages…go to this website to find answers/solutions. Also, this website has videos for each standard. This packet is EXTRA CREDIT!

Algebra and Modeling 36%

What You Need To Know...

MAFS.912.A-APR.1.1 - Add, Subtract, and multiply polynomials.

  1. The benchmark will be assessed using Drag and Drop Response, Hot Spot Response, Equation Response, Multiple Choice Response, Open Response or Manipulate Text.
  2. Items may require students to prove polynomial identities and use them to describe numerical.
    Ex. x2 – y2 or x3 – y3, etc.
  3. Items will include adding, subtracting, and multiplying polynomials with rational coefficients and no more than 5 terms.
  4. Items may require students to generate Pythagorean triples.

Example One

Example Two

MAFS.912.A-APR.4.6 – Rewrite and recognize rational expressions in different forms.

  1. The benchmark will be assessed using Drag and Drop Response, Equation Response, Graphic Response, Multiple Choice Response, Multi-select Response or Open Response.
  2. Items may require students to know and apply the Remainder Theorem for determining factors and/or zeroes. For a polynomial p(x) and a number a, the remainder on division by x – a is p(a), so p(a) = 0 if and only if (x – a) is a factor of p(x).
  3. Items may require students to rewrite expressions by inspection or by long division.

Example One

Example Two

Use the Fundamental Theorem of Algebra and Descartes' Rule of Signs to find the number of possible positive, negative, and complex zeros for the following function:

Example Three

MAFS.912.A-CED.1.1 – create equations and inequalities in one variable and use them to solve problems.

  1. The benchmark will be assessed using Drag and Drop Response, Equation Response, Hot Spot Response, Multiple Choice Response or Open Response.
  2. Items may include equations from linear and quadratic functions and simple rational, absolute and exponential functions.
  3. Items may require students to rearrange formulas to highlight a particular variable.
  4. Items may require students to recognize equivalent expressions.

Example One

Ronald can deliver papers in his neighborhood 8 hours faster than his little brother Jimmy can. If they work together, they can complete the job in 3 hours. Solve for how long it would take for Jimmy to complete this job on his own. Using complete sentences, explain each step of your work.

Example Two

MAFS.912.A-CED.1.2 – create equations in two or more variables to represent relationships between quantities.

  1. The benchmark will be assessed using Equation Response, Graphic Response, Hot Spot Response, Multiple Choice Response or Multi-select Response.
  2. Items may include systems of linear equations or a system including a linear and a quadratic equation in two variables. Students may need to solve algebraically and graphically.
  3. Items may require students to represent constraints and to interpret solutions as viable and non-viable.
  4. Systems are limited to a system of 2 x 2 linear equations with rational coefficients; a system of 3 x 3 linear equations with rational coefficients; or a system of two equations with a linear equation with rational coefficients and a quadratic of the form.
  5. Students may be required to graph a circle whose center is (0, 0).

Example One

Example Two

Isaac is getting his own cell phone plan and wants to make the best decision. He decides to compare cell phone plans. MobileONE has an unlimited talk plan for a flat fee of $80 per month. Talk-A-Lot charges $0.15 per minute with a monthly fee of $25. By-The-Minute has no monthly fee, but it is $0.50 per minute.

Explain to Isaac how he can graph these cell phone plans and, describe what key features of the graphs he should consider when making a decision about what plan to choose.

Example Three

Line j passes through points (8, 4) and (6, 10). Line k is perpendicular to j. What is the slope of line k?

MAFS.912.A-REI.1.1 – construct a viable argument in solving a simple equation.

  1. The benchmark will be assessed using Drag and Drop Response, Equation Response, Movable Text Response, Multiple Choice Response, Selectable Text Response, or Open Response.
  1. Students may be required to complete an algebraic proof or construct a viable argument.

Example One

Which polynomial identity will prove that 25 - 4 = 21 ?

  1. Difference of Cubes
  2. Square of a Binomial
  3. Difference of Squares
  4. Sum of Cubes

Example Two

MAFS.912.A-REI.4.11 – Explain why the solution of y = f(x) and y = g(x) is the solutions of the equation f(x) = g(x).

  1. The benchmark will be assessed using Equation Response, Multiple Choice Response, Multi-select Response, Table Response, Simulation Response or Open Response.
  2. Items may require students to find solutions by using a graph, a table of values, or by successive approximations to a given place value.
  3. Items are restricted to exponential with a rational exponent, polynomial of degree greater than 2, rational, absolute value, and logarithmic.
  4. Items may require the student to know the role of the x-coordinate and the y-coordinate in the intersection of f(x) = g(x).

Example One


Determine the x-coordinate of P. Write your answer with rational exponents.

Example Two

MAFS.912.A-SSE.2.3 – Choose and produce an equivalent form of an expression and understand the properties the quantity represents.

  1. The benchmark will be assessed using Drag and Drop Response, Equation Response, Multiple Choice Response, Multi-select Response, or Open Response.
  2. Items may require students to factor a quadratic expression to find zeroes; complete the square in a quadratic expression to find the max. or min. value of the function; or to use the properties of exponents to transform expressions for exponential functions.
  3. Items may require students to interpret the parts of an expression.
  4. Items may include factoring, difference of two squares, sum and difference of cubes, or polynomials with the highest degree of 3.

Example One

Your friend, Sara, missed school yesterday. Your teacher went over how to solve a function by factoring. Explain to Sara how to solve the two functions below by factoring.

Example Two

What is the 4th term when the function below is arranged in descending order?

Example Three

Your teacher just called on you to explain how to find the vertex in the equation below. How will you respond?

MAFS.912.N-CN.3.7 – Solve quadratic equations with real coefficients that have complex solutions.

  1. The benchmark will be assessed using Drag and Drop Response, Equation Response, Multiple Choice Response or Multi-select Response.
  2. Items may require students to solve quadratics in one variable by completing the square, inspection, factoring, taking square roots and quadratic formula.
  3. Students will be required to recognize when the quadratic formula gives complex solutions and write them a ± bi for real numbers a and b.
  4. Students may be required to rewrite a quadratic equation in vertex form.
  5. Students must be able to recall the quadratic formula from memory.

Example One

Example Two

Example Three

Functions & Modeling- 36%

MAFS.912.F-BF.1.2 – Write arithmetic and geometric sequences both recursively and with an explicit formula.

  1. The benchmark will be assessed using Equation Response, Movable Test Response, Multiple Choice Response, Table Response or Open Response.
  2. Items may require students to derive the formula for the sum of a finite geometric series (ex. mortgage payments).
  3. Items may require students to write an arithmetic or geometric explicit function from a given recursive formula and vice versa.
  4. Items may require students to compose or write functions with given information.

Example One

The function ƒ(x) = 0.16x represents the number of U.S. dollars equivalent to x Chinese yuan. The function g(x) = 13.60x represents the number of Mexican pesos equivalent to x U.S. dollars. You can use g(ƒ(x)) to find the number of Mexican pesos equivalent to x Chinese yuan. What is the value, in Mexican pesos, of an item that costs 15 Chinese yuan?

Example Two

A bank offers a savings account that accrues simple interest annually based on an initial deposit of $500. If S(t) represents the money in the account at the end of t years and S(5) = 575, write a function that could be used to determine the amount of money in the account over time. Show your work or explain your reasoning.

Example Three

Another bank offers a savings account that accrues compound interest annually at a rate of 3%. The bank in the previous problem offered $15 per year in interest.

What is the initial amount needed in this account so that it will have the same amount of money at the end of 10 years as the account in the previous problems at the end of 10 years? Show your work or explain your reasoning.

Example Four

Example Five


Example Six

MAFS.912.F-BF.2.3 – Identify the effect on the graph (transformations) of replacing f(x) by f(x) + k, f(kx)and f(x + k) for given values of k.

  1. The benchmark will be assessed using Drag and Drop Response, Equation Response, Graphic Response, or Multiple Choice Response.
  2. Items may require students to find the value of k when given a graph of the function and its transformation.
  3. Items may require students to explain how a graph is affected by a value of k.
  4. Functions can be linear, quadratic or exponential with integral exponents.

Example One

Example Two


Describe the transformation that maps the graph of f(x) to f(x + 5). Justify your answer algebraically or by using key features of the graphs.

MAFS.912.F-BF.2.4 – Find inverse functions.

  1. The benchmark will be assessed using Equation Response, Graphic Response, or Multiple Choice Response.
  2. Items may require students to find an inverse of an equation; verify that one function is the inverse of another; or look at a table of a function to determine values of the function’s inverse.
  3. Functions may include linear functions, quadratics , radical functions and rational functions.

Example One

Example Two

MAFS.912.F-IF.3.8 – Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.

  1. The benchmark will be assessed using Drag and Drop Response, Equation Response, Graphic Response, Hot Spot Response, Multi-select Response, Multiple Choice Response or Open Response.
  2. Items may require students to factor or complete the square in a quadratic function to show zeroes, extreme values, and symmetry of the graph.
  3. Items may require students to use the properties of exponents to interpret expressions for exponential functions.
  4. Items may require students to identify zeroes, asymptotes, end behavior, and characteristics of trig functions (period, midline, amplitude and phase shift).
  5. Functions may also include square root, cube root, piecewise-defined functions, step functions, and absolute value functions.

Example One

Example Two

Example Three

MAFS.912.F-LE.1.4 – Rewrite exponential models as a logarithm with a base of 2, 10, or e.

  1. The benchmark will be assessed using Equation Response or Multi-select Response.
  2. Items may require students to evaluate the logarithm or to use the change of base formula.
  3. Items may require students to leave the answer as a logarithm or to find the value using a calculator.

Example One

Example Two

Based on a model, the solution to the equation below gives the number of years it will take for the population of country A to reach 50 million. What is the solution to the equation expressed as a logarithm?

MAFS.912.F-TF.1.2 – Explain how the unit circle in the coordinate plane enables the extension of trigonometric functions to all real numbers using radian measures of angles traversed counterclockwise around the unit circle.

  1. The benchmark will be assessed using Equation Response, Graphic Response, Hot Spot Response, Movable Text Response, Selectable Text Response or Open Response.
  2. Items may require students to: find arc length or sector area based on radian measures; convert radian measure to degree measure and vice versa; or prove the Pythagorean identity.
  3. Trig ratios are limited to sine or cosine.

Example One

Example Two

MAFS.912.F-TF.2.5 – Choose trigonometric functions to model periodic phenomena with specified amplitude, frequency, and midline.

  1. The benchmark will be assessed using Equation Response, Graphic Response, Multi-select Response, or Multiple Choice Response.
  2. Students may be asked to complete a function that models a real-world context by providing missing values.
  3. Items are limited to sine and cosine functions.
  4. Items may require the student to choose and interpret units.

Example One

Example Two

Find the value of the amplitude, period, and midline for the above sin function.Round your numeric values to the nearest whole number.

MAFS.912.G-GPE.1.2 – Derive the equation of a parabola given a focus and directrix.

  1. The benchmark will be assessed using Equation Response.
  1. Items will require students to write the equation of a parabola when given the focus and directrix. The directrix will be parallel to a coordinate axis.

Example One

Example Two


Statistics, Probability,

& the Numbering System - 28%

MAFS.912.N-CN.1.2 – Use the relation i 2= -1 and the commutative, associative, and distributive properties to add, subtract, and multiply complex numbers.

  1. The benchmark will be assessed using Equation Response or Multi-select Response.
  2. Items may require students to add, subtract, and multiply complex numbers.
  3. Items will require the student to use the relation i 2= -1 to convert imaginary numbers with an even power to a real number.

Example One

Example Two

Example Three

Example Four

MAFS.912.N-RN.1.2 –Rewrite expressions involving radicals and rational exponents using the properties of exponents.

  1. The benchmark will be assessed using Drag and Drop Response, Equation Response, Movable Text Response, Multiple choice Response, Multi-select Response, Open Response, or selectable Text Response.
  2. Items may require students to rewrite an expression with a rational exponent to a radical expression or to rewrite an expression with a radical expression to a rational exponent.

Example One

Example Two

Example Three

Example Four

MAFS.912.S-CP.1.1 – Describe events as subsets of a set of outcomes as unions, intersections, or complements of other events.

  1. The benchmark will be assessed using Drag and Drop Response, Equation Response, Hot Spot Response, Multiple choice Response or Multi-select Response.
  2. Items may require students to determine events that are subsets of a sample space.
  3. Within items unions, intersections, and complements can be described verbally or with notation.
  4. Sample spaces can be written as a set, a list, in a table, or in a Venn diagram.

Example One

Example Two

MAFS.912.S-CP.1.5 – Recognize and explain the concepts of conditional probability and independence in situations.

  1. The benchmark will be assessed using Drag and Drop Response, Equation Response, Multiple choice Response, Multi-select Response, Open Response or Table Response.
  2. Items may require students to construct and interpret two-way frequency tables of data and use the table as a sample space to decide if events are independent and to approximate conditional probabilities.
  3. Students should understand that two events A and B are independent if the probability of A and B occurring together is the product of their probabilities.
  4. Students should understand the conditional probability of A given B as P(A and B)/P(B).

Example One

Example Two

MAFS.912.S-CP.2.7 – Apply the Addition Rule, P(A or B) = P(A) + P(B) – P(A and B).

  1. The benchmark will be assessed using Equation Response, Multiple choice Response or Open Response.
  2. Items may require students to find probabilities using the Addition Rule and to interpret the answer within the real-world context.
  3. Items may require students to find the unknown value when given three of the values with the Addition Rule.

Example One

Example Two

MAFS.912.S-IC.1.1 – Understand statistics as a process for making inferences about population parameters based on a random sample from that population.

  1. The benchmark will be assessed using Equation Response, Multiple choice Response or Open Response.
  2. Items may require students to use observed results from a random sample to make an inference about the population.
  3. Items may also require students to choose and interpret units.

Example One

What conclusion about the difference between the distributions of the heart rates for these two groups can be draw? Justify your answer.

Example Two


What conclusion about the difference between the distributions of the hear rates for the two groups can be drawn? Justify your answer.

If the target heart rate range for adult males aged between 40 and 45 after 20 minutes of exercise is around 175 beats per minute, what recommendation would you make in terms of which machine to use? Justify your answer.

Based upon these data, what conclusion about exercise machines in general can be made?

MAFS.912.S-IC.2.3 – Recognize the purposes of and differences among sample surveys, experiments, and observational studies and explain how randomization relates to each..

  1. The benchmark will be assessed using Equation Response, Multiple choice Response, Open Response or Simulation Response.
  2. Items may require students to use data from a sample survey to estimate a population mean of proportion; develop a margin of error through the use of simulation models for random sampling.
  3. Items may require students to use data from a randomized experiment to compare two treatments.
  4. Items may require students to choose and interpret units.

Example One

For a statistics project, a group of students decide to collect data in order to approximate the percent of people in the town who are left-handed. They ask every third student entering the school cafeteria whether he or she is left-handed or right-handed. What type of method did this group use? Explain which population the group can draw a conclusion about based on their method. Suggest a better method that would allow the students to draw a conclusion about all the residents in their town.