Algebra 1 Major Content Review
Topic / Standards1 / A-SSE.1
Interpret expressions that represent a quantity in terms of its context.★
- Interpret parts of an expression, such as terms, factors, and coefficients.
- Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as (x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as
(x2 – y2)(x2 + y2).
2 / A-APR.1
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.
3 / A-CED.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 and exponential functions.
A-CED.2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
4 / A-CED.3
Represent 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.
A-CED.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.
5 / A-REI.1
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.
A-REI.3
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
6 / A-REI.4
Solve quadratic equations in one variable.
- Use the method of completing the square to transform any quadratic equation in x into an equation of the form (x – p)2 = q that has the same solutions.
- Solve quadratic equations by inspection (e.g., for x2 = 49), 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.
7 / A-REI.10
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).
A-REI.11
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.★
A-REI.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.
8 / F-IF.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).
F-IF.2
Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.
F-IF.3
Recognize that sequences are functions, sometimes defined recursively, whose domain is a subset of the integers. For example, the Fibonacci sequence is defined recursively by f(0) = f(1) = 1, f(n+1) = f(n) + f(n-1) for n ≥ 1.
9 / F-IF.4
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.★
F-IF5
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.★
F-IF.6
Calculate and interpret the average rate of change of a function (presented symbolically or as a table) over a specified interval. Estimate the rate of change from a graph.★
10 / F-IF.7ab
Graph functions expressed symbolically and show key features of the graph, by hand in simple cases and using technology for more complicated cases.★
- Graph linear and quadratic functions and show intercepts, maxima, and minima.
- Graph square root, cube root, and piecewise-defined functions, including step functions and absolute value functions.
Write a function defined by an expression in different but equivalent forms to reveal and explain different properties of the function.
- 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.
11 / F-LE.1
Distinguish between situations that can be modeled with linear functions and with exponential functions.
- Prove that linear functions grow by equal differences over equal intervals, and that exponential functions grow by equal factors over equal intervals.
- Recognize situations in which one quantity changes at a constant rate per unit interval relative to another.
- Recognize situations in which a quantity grows or decays by a constant percent rate per unit interval relative to another.
12 / F-LE.2
Construct linear and exponential functions, including arithmetic and geometric sequences, given a graph, a description of a relationship, or two input-output pairs (include reading these from a table).
F-LE.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.
F-LE.5
Interpret the parameters in a linear or exponential function in terms of a context.
13 / F-BF.1a
Write a function that describes a relationship between two quantities.★
- Determine an explicit expression, a recursive process, or steps for calculation from a context.
Identify the effect on the graph of replacing f(x) by f(x) + k, kf(x), f(kx), and f(x + k) for specific values of k (both positive and negative); find the value of k given the graphs. Experiment with cases and illustrate an explanation of the effects on the graph using technology.
14 / S-ID.7
Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.
S-ID.8
Compute (using technology) and interpret the correlation coefficient of a linear fit.
S-ID.9
Distinguish between correlation and causation.
Name ______Algebra 1 Review #1
A-SSE.1
Interpret expressions that represent a quantity in terms of its context.★
- Interpret parts of an expression, such as terms, factors, and coefficients.
- Interpret complicated expressions by viewing one or more of their parts as a single entity. For example, interpret P(1+r)n as the product of P and a factor not depending on P.
A-SSE.2
Use the structure of an expression to identify ways to rewrite it. For example, see x4 – y4 as
(x2)2 – (y2)2, thus recognizing it as a difference of squares that can be factored as (x2 – y2)(x2 + y2).
1. The owner of a small computer repair business has one employee, who is paid an hourly rate of $22. The owner estimates his weekly profit using the function. In this function, represents the number of
(1) computers repaired per week
(2) hours worked per week
(3) customers served per week
(4) days worked per week
2. When factored completely, the expression is equivalent to
(1)
(2)
(3)
(4)
3. Which expression is equivalent to ?
(1)
(2)
(3)
(4)
4. The elephant population in northwestern Namibia and Etosha National Park can be predicted by the expression, where b is the number of years since 1995.Combined estimates for Etosha National Park and the Northwestern Population are shown on the table below.
What does the 2,629 represent?
(1) the predicted increase in the number of elephants in the region each year
(2) the predicted number of elephants in the region in 1995
(3) the year when the elephant population is predicted to stop increasing
(4) the percentage of the elephant population is predicted to increase each year
5. A ball was thrown upward into the air. The height, in feet, of the ball above the ground t seconds after being thrown can be determined by the expression. What is the meaning of the 3 in the expression? Select the correct answer.
(1) the ball takes 3 seconds to reach its maximum height
(2) the ball takes 3 seconds to reach the ground
(3) the ball was thrown from a height of 3 feet
(4) the ball reaches a maximum height of 3 feet
6. The “Bulbs on the Bay” Holiday drive-through attraction charges $12 per car plus $1 for every individual, (p), in the car. Which choice represents the total cost (c) per car?
(1) c = p + 12
(2) c = 12(p + 1)
(3) c = 12p + 1
(4) c = 1•(12p)
7. Express the total weight, (p), of a filled animal watering pail, if the pail weighs 12 pounds and the water weighs 8.3 pounds per gallon?Let gallons =g.
(1) p= (8.3)(12)
(2) p= 8.3g+ 12
(3) p= 8.3g– 12
(4) p= 12g+ 8.3
8. Assumebrepresents the number of boys andgrepresents the number of girls in a classroom. We know that there is at least one boy and one girl, and there are more girls than boys. Whichexpression would have a larger value?
(1)
(2)
(3) There is not enough information.
(4) Both expressions are equal.
9. Factor the expression completely.
Name ______Algebra 1 Review #2
A-APR.1
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.
1. Fred is given a rectangular piece of paper. If the length of Fred’s piece of paper is represented by and the width is represented by , then the paper has a total area represented by
(1) (3)
(2) (4)
2. Subtract from . Express the result as a trinomial.
3. A company produces units of a product per month, where represents the total cost and represents the total revenue for the month. The functions are modeled by and . The profit is the difference between revenue and cost where . What is the total profit , for the month?
(1)
(2)
(3)
(4)
4. Express the product of and in standard form.
5. If and , then equals
(1) (3)
(2) (4)
6. Which expression is equivalent to ?
(1)
(2)
(3)
(4)
7. Which expression is equivalent to the expression shown?
(1)
(2)
(3)
(4)
8. Simplify each expression.
A. (a2 – 3a) + (3a2 + 4a)B. (2x3y2)(-4x4y)
C. –2(x + 5) – 7(x –2)D. (c + 2)(c2 – 2c + 5)
9. Express the area of the rectangle as a trinomial:
Name ______Algebra 1 Review #3
A-CED.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 and exponential functions.
A-CED.2
Create equations in two or more variables to represent relationships between quantities; graph equations on coordinate axes with labels and scales.
1. In 2013, the United States Postal Service charged $0.46 to mail a letter weighing up to 1 oz. and $0.20 per ounce for each additional ounce. Which function would determine the cost, in dollars,, of mailing a letter weighing z ounces where z is an integer greater than 1?
(1)
(2)
(3)
(4)
2. A cell phone company charges $60.00 a month for up to 1 gigabyteof data. The cost of additional data is $0.05 per megabyte. If drepresents the number of additional megabytes used and crepresents the total charges at the end of the month, which linearequation can be used to determine a user’s monthly bill?
(1) (3)
(2) (4)
3. John has four more nickels than dimes in his pocket, for a total of$1.25. Which equation could be used to determine the number ofdimes, x, in his pocket?
(1)
(2)
(3)
(4)
4. Sam and Jeremy have ages that are consecutive odd integers.The product of their ages is 783. Which equation could be used tofind Jeremy’s age, j, if he is the younger man?
(1) (3)
(2) (4)
5. Which graph shows a line where each value of y is three more thanhalf of x?
6. During the 2010 season, football player McGee’s earnings, m, were0.005 million dollars more than those of his teammate Fitzpatrick’searnings, f. The two players earned a total of 3.95 million dollars.Which system of equations could be used to determine the amounteach player earned, in millions of dollars?
7. A checking account is set up with an initial balance of$4800, and$400 is removed from the account each month for rent (no other transactions occur on the account).Write an equation whose solution is the number of months,m, it takes for the account balance to reach$2000.
8. A gardener is planting two types of trees:
Type A is three feet tall and grows at a rate of 15 inches per year.
Type B is four feet tall and grows at a rate of 10 inches per year.
Algebraically determine exactly how many years it will take for these trees to be the same height.
9. Jacob and Zachary go to the movie theater and purchase refreshments for their friends. Jacob spends a total of $18.25 on two bags of popcorn and three drinks. Zachary spends a total of $27.50 for four bags of popcorn and two drinks. Write a system of equations that can be used to find the price of one bag of popcorn and the price of one drink. Using these equations, determine and state the price of a bag of popcorn and the price of a drink, to the nearest cent.
10. New Clarendon Park is undergoing renovations to its gardens. One garden that was originally a square is being adjusted so that one side is doubled in length, while the other side is decreased by three meters. The new rectangular garden will have an area that is 25% more than the original square garden. Write an equation that could be used to determine the length of a side of the original square garden. Explain how your equation models the situation. Determine the area, in square meters, of the new rectangular garden.
Name ______Algebra 1 Review #4
A-CED.3
Represent 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.
A-CED.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.
1. Connor wants to attend the town carnival. The price of admission to the carnival is $4.50, and each ride costs an additional 79 cents. If he can spend at most $16.00 at the carnival, which inequality can be used to solve for r, the number of rides Connor can go on, and what is the maximum number of rides he can go on?
(1) / ; 3 rides(2) / ; 4 rides
(3) / ; 14 rides
(4) / ; 15 rides
2. The equation for the volume of a cylinder is. The positive value of r, in terms of h and V, is
(1)
(2)
(3)
(4)
3. The formula for the volume of a cone is . The radius, , of the cone may be expressed as
(1) (3) 3
(2) (4)
4. The formula for the area of a trapezoid is . Express in terms of A, h, and .
The area of a trapezoid is 60 square feet, its height is 6 ft., and one base is 12 ft. Find thenumber of feet in the other base.
5. A school is building a rectangular soccer field that has an area of 6000 square yards. The soccerfield must be 40 yards longer than its width. Determine algebraically the dimensions of thesoccer field, in yards.
6. Edith babysits for x hours a week after school at a job that pays $4 an hour. She has accepted ajob that pays $8 an hour as a library assistant working y hours a week. She will work both jobs.She is able to work no more than 15 hours a week, due to school commitments. Edith wants toearn at least $80 a week, working a combination of both jobs.Write a system of inequalities that can be used torepresent the situation.
Graph these inequalities on the set of axes below.
Determine and state one combination of hours that will allow Edith to earn at least $80 per weekwhile working no more than 15 hours.
7. An animal shelter spends $2.35 per day to care for each cat and $5.50 per day to care for eachdog. Pat noticed that the shelter spent $89.50 caring for cats and dogs on Wednesday.
Write an equation to represent the possible numbers of cats and dogs that could have been at theshelter on Wednesday.
Pat said that there might have been 8 cats and 14 dogs at the shelter on Wednesday. Are Pat’snumbers possible? Use your equation to justify your answer.
Later, Pat found a record showing that there were a total of 22 cats and dogs at the shelter on
Wednesday. How many cats were at the shelter on Wednesday?
Name ______Algebra 1 Review #5
A-REI.1
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.
A-REI.3
Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters.
1. When solving the equation, Emily wroteasher first step. Which property justifiesEmily’s first step?
(1) addition property of equality
(2) commutative property of addition
(3) multiplication property of equality
(4) distributive property of multiplication over addition
2. What is the value of x in the equation ?
(1) / 4(2) / 6
(3) / 8
(4) / 11
3. The inequality is equivalent to
(1)
(2)
(3)
(4)
4. Which value of x satisfies the equation ?
(1) 8.89(3) 19.25
(2) 8.25(4) 44.92
5. Solve: .
(1) (3)
(2) (4)
6. Solve the inequality below to determine and state the smallest possible value for x in the solution set.
7. Given, determine the largest integer value of a when .