ALGEBRA 1 UNIT 2 REVIEW

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1 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 and exponential functions. Section 2: Topic 3 Topic 5 Topic 6 Topic 7 The 2017 junior class from Nike High School raised funds for a Senior Welcome Party when they get back to school in Fall It costs $3,500 to rent out a place to host the party plus $17 per student for food and drinks. The junior class raised $9,000. a. How many students can attend the end of year party? b. If 275 students attend the Welcome Party, how much money may the class save or owe after the party? c. The current enrollment for this class is 324 students. Is money raised by the junior class enough to make sure all students can attend? Justify your answer. At Celebration Taco Feast they have the exponential burrito, which is an 18-inch double flour tortilla with choice of cheese and meat for $7.45. Each topping for the burrito costs $0.75. If Joshua ordered the exponential burrito and was charged $14.95, how many toppings were in his burrito? Justify your answer by using an algebraic equation to solve this problem step by step. Exercise 3 Phillip has been hired as a sales associate Countryside Sports Company. He has two salary options. He can either receive a fixed salary of $ per week or a salary of $ per week plus a 10% commission of his weekly sales. Determine the dollar amount of sales that he must generate each week in order for the option with commission to be the better choice? Exercise 4 The Hot Summer Fair is coming to town! Admission to the fair costs $12.99 and each ride costs $1.75. You have $35 to spend at the fair including admission. Write and solve an inequality to determine the maximum number of rides you can enjoy at the Hot Summer Fair? Exercise 5 Tony scored 22 and 25 points in the first two games of a basketball tournament. Tony s goal is to make the All-Tournament Team. So far, in all of the tournaments he s been to, all of the players who made the All- Tournament Team scored an average between 27 and 32 points in the tournaments. Determine the range of points Tony should score in his next game to make the All-Tournament Team

2 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 Section 2: Topic 8 Topic 9 Solve the following problems. a. Isaiah planted a seedling in his garden and recorded its height every week. The equation shown can be used to estimate the height, h, of the seedling after w weeks since he planted the seedling. h = 1 2 w Solve the formula for w, the number of weeks since he planted the seedling. b. Under the Brannock device method, shoe size and foot length for women are related by the formula S = 3F 21, where S represents the shoe size and F represents the length of the foot in inches. Solve the formula for F. Elizabeth s tablet has a combined total of 20 game and business apps. Let x represent the number of game apps and y represent the business apps. Which of the following could represent the number of game and business apps on Elizabeth s tablet? Select all that apply and graph this scenario on the coordinate plane provided. x + y = 20 7 game apps and 14 business apps x y = 20 y = x game apps and 12 business apps xy =

3 MAFS.912.A-CED.1.4: Rearrange formulas to highlight a quantity of interest, using the same reasoning as in solving equations. Section 2: Topic 8 Consider the formula for the perimeter of a rectangle, P = 2l + 2w, where l is the length and w is the width. Solve this formula for the width. The formula for the volume of a cone is V = > 1 πra h, where r is the radius of the base and h is the height of the cone. Create a formula to find the height of a cone. Exercise 3 The formula to find the volume of a sphere is V = 2 1 πr1, where r is the radius of the sphere. Create a formula to find the radius of a sphere

4 MAFS.912.A-REI.1.1: 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 they original equation has a solution. Construct a viable argument to justify a solution method. Section 2: Topic 2 Topic 3 For each algebraic equation, select the property or properties that could be used to solve it. Algebraic Equation Addition or Subtraction Property of Equality Multiplication or Division Property of Equality Distributive Property Commutative Property B 2 = 12 o o o o 5x + 4 = 14 o o o o 7x = 36 o o o o x 9 = 1 o o o o 6(5x 1) = 54 o o o o 10 x = 8 o o o o 7 + x = 14 o o o o 2(x 8) + 7x = 50 o o o o - 4 -

5 The following equation is solved for x. 7 x + 2 3x 3 = 6 Use the properties to justify the reason for each step in the chart below. Statements a. F BGA H1B = 6 1 a. Given b. 7 x+2 3x 3 = b. c. 7 x + 2 3x = 18 c. Reasons d. 7x x = 18 d. e. 7x 3x + 14 = 18 e. f. 4x + 14 = 18 f. Equivalent Equation g. 4x = g. h. 4x = 4 h. Equivalent Equation i. 4x 4 = 4 4 h. x = 1 j. Equivalent Equation Exercise 3 Use the box below to solve the following equation for x and justify each step. i. 2x 3 2x 1 = 3 4x Statements Reasons - 5 -

6 MAFS.912.A-REI.2.3: Solve linear equations and inequalities in one variable, including equations with coefficients represented by letters. Section 2: Topic 1 Topic 2 Topic 3 Topic 5 Topic 6 Topic 7 Which of the following equations have the correct solution? Select all that apply. o 4x + 3 = 11; x = 2 o 2(x + 1) x = 40; x = 39 o BHF 4 = 4; x = 29 o 3 = 5x 3; x = 0 o 14 = 1 x + 5; x = 12 3 Consider the equations 5 x 7 = 25 and 5x 7 = 25. a. Are these equations equilavent? Justify your answer. b. Amy argues that you can use the distributive property in 5 x 7 = 25, then use the addition property of equality to isolate the term 5x, and finally use the division property of equality to isolate x. Ethan argues that 5 x 7 = 25 can be solved without using the distributive property. He claims that you can divide both side by 5 to isolate x 7 and add 7 to both sides to isolate x. Who is correct? Explain your answer in the box. A Amy B Ethan C Both D Neither Solve the following equation. Justify each step. Exercise 3 0.7x x = 0.7 x Exercise 4 Solve and describe the difference between the following algebraic statements. 2 x = 15 2 x x >

7 Exercise 5 Find the solution set to each inequality, express the solution in set notation and graph the solution. 6m + 2 < 5m 4 O P x 7 > 27 8(p 6) 4(p 4) 7 5x + 2 < 22 4p 12 or 8 2p <

8 MAFS.912.A-REI.2.4: Solve quadratic equations in one variable. Section 2: Topic 4 Consider the following equations. 3 x 2 x + 3 = 0 2y 4 3y + 9 = 0 Are the pair of solutions for x the same as the pair of solutions for y? Justify your answer. Which equations have the solution set of > A, 3? Select all that apply. 4x 2 x + 3 = 0 x + > x + 3 = 0 A 3x 6 3x 6 = 0 6x- 3 4x + 12 = 0 x > x + 3 = 0 A x > x 3 = 0 A 4x + 2 x + 3 = 0 Exercise 3 Ted and Maggie solved the following equation, 3x 2 Ted x + 5 = 0. Their work is shown below. Maggie 3x 2 x + 5 = 0 3x 2 x + 5 = 0 3x 2 = 0 or x + 5 = 0 3x 2 = 0 or x + 5 = 0 3x = 2 or x = 5 3x = 2 or x = 5 x = 2 3 or x = 5 x = 2 3 Who is correct? Correct the mistake in the incorrect work. or x = 5-8 -

9 MAFS.912.A-REI.4.10: 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). Section 2: Topic 9 Chloe has 40 songs on her phone s playlist. The playlist features songs from her two favorite artists, Beyoncé and Kodak. a. Create an equation using two variables to represent this situation. b. List at least three solutions to the equation that you created. c. Does this equation have infinitely many solutions? Why or why not? d. Create a graph that represents the solution set to your equation. e. Why are there only positive values on this graph? f. Is this function discrete or continuous? - 9 -

10 If there's no snow (or rain) falling from the sky and you re not in a cloud, then the temperature decreases by about 5.4 F for every 1,000 feet up you go in elevation. a. Create an equation using two variables to represent this situation. b. List at least three possible solutions. c. How many solutions are there to this equation? d. Create a visual representation of all the possible solutions on the graph. g. Is this function discrete or continuous?