Name Algebra 1 Midterm Review Period. = 10 4x e) x ) Solve for y: a) 6x 3y = 12 b) 4y 8x = 16

Transcription

1 Name Algebra 1 Date Midterm Review Period 1) Solve each equation: a) x 2x + 2 = 3 b) = 13 c) 64 = 9x +1 d) x 7 2 = 10 4x e) x = 3x 2) Solve for y: a) 6x 3y = 12 b) 4y 8x = 16 3) Solve and graph each inequality: a) 3x + 6 < 15 b) 8 4x ) Solve each absolute value equation: a) 4x + 4 = 12 b) x 5 = 3 c) 2x = 9

2 5) Find the slope of the line passing through each pair of points: a) (5, 2) & (7, 12) b) ( 1, 4) & (5, 5) c) (9, 4) & (9, 8) 6) Write an equation in slope-intercept form of the line with slope = 3 and y-intercept = 5 7) Write an equation in slope-intercept form of the line passing through the points (9, 2) & (3, 4) 8) Find the x- and y-intercepts of each line: a) 3x + 2y = 12 b) y = 3x 8 9) Are the lines y = 4 3 x + 5 and 4x + 3y = 1 parallel, perpendicular or neither? 10) Joe is starting a new job in His salary is $35,600. At the beginning of the next year he will receive a raise of $1,560. Assume he will receive the same raise every year. a) Write an equation for finding Joe s salary after b) Find Joe s salary in 2017.

3 11) How does the graph of y = 4x 2 differ from that of y = 4x? 12) Solve the system: y = x + 5 y = 2x 4 13) You bowled 5 games over the weekend. You remember recording scores of 116, 105, 109 and 113, but you cannot remember your 5 th score. You know your overall average was a 109. What did you score in the 5 th game? 14) Describe how you can tell if two lines are parallel, perpendicular or neither without graphing them. 15) Describe how you can tell if a system of equations has one solution, no solutions or infinite solutions. 16) The ratio of the number of right-handed students to left-handed students at N.P.H.S. is 9:1. There are 360 right-handed students in school. How many lefthanded students are there?

4 17) Which of the following ordered pairs is a solution of 4y 2x + 5? A) ( 1, 1) B) (0, 0) C) ( 1, 1) D) ( 2, 0) 18) The equation 4w + 10j = 120 is used to determine the number of water bottles w and the number of juice bottles j that can be bought for $120. If you purchase 6 bottles of juice, how many bottles of water can you buy? A) 10 B) 15 C) 20 D) 25 19) Which inequality does the graph below represent? A) x < 20 B) x 20 C) x > 20 D) x 20 20) Find the solution to the inequality 9 2x +1 < 5 21) Which point is in the solution set for the inequality 4x y > 1? A) ( 1, 2) B) (0, 1) C) (0, 2) D) (2, 0)

5 22) In a sample of 100 randomly selected students, 65 students choose comedy as their favorite type of movie. Based on this data, how many of the 2480 students in school would NOT choose comedy as their favorite type of movie? 23) Which of the following ordered pairs is a solution of 2y 6x + 10? A) ( 1, 1) B) (0, 0) C) ( 1, 1) D) ( 2, 1) 24) Which of the following is the graph of the solution to the inequality 2x + 5 > 9? 25) Find the solutions to the absolute value equation 2x = 6? 26) An auto repair shop charges $75 per hour for labor plus an additional $89 for parts. If the shop worked for 2 hours, which equation represents the total repair cost C? A) C = 75(2) 89 B) C = 89(2) + 75 C) C = D) C = 75(2) + 89

6 27) Find the slope of the line pictured below: 28) Write the equation of the line pictured below: 29) What is the slope of the line through the points (3, 2) and (5, 8)? 30) Which function does the table represent? A) y = 2x B) y = 5x C) y = x + 6 D) y = x ) What is the x-intercept of the equation y = 5x + 3? 32) What is the y-intercept of the equation 10 = 2x + 5y?

7 33) What is the solution of the system of equations shown below? 34) How many solutions does the system of equations shown below have? 35) What is the solution of the system 36) Which inequality does the graph below represent? A) y > 2x + 4 B) y > 2x + 2 C) y < 2x + 4 D) y > 2x + 4

8 37) Which inequality does the graph below represent? A) y > 5x 1 B) y 5x 1 C) y < 5x 1 D) y 5x 1 38) A rental car agency charges $19 per day plus 12 cents per mile to rent a car. Another agency charges $22 per day plus 9 cents per mile to rent the same car. How many miles will have to be driven for the cost of a car from the two agencies to equal each other? 39) Simplify: a) 36a11 bc 4 9a 4 b 2 c 0 b) (4x 2 y 6 ) 2 (2x 3 y 4 z) 3 40) Write in scientific notation. 41) Write 456,290,000 in scientific notation. 42) A jumbo jet carries 325 passengers, 40 in first class, and the remainder in coach. If the average first class ticket is $695 and the average coach ticket is $341, how much will the airline gross if the plane is full?

9 Free-Response 1) Ballroom Rental Party Hours Used # of People Cost Attending First party 8 hours 100 $6,136 Second party 4 hours 75 $4,318 You want to rent a ballroom for two different parties from the same dining hall. The dining hall charges 2 fees: 1) an hourly fee and 2) a fee for each person attending the party. According to this table, how much does the dining hall charge per hour? And how much does the dining hall charge per person? Explain your answers for full credit. 2) Katie purchased a new cell phone for $199. It costs her $72 per month for service (Yes, unlimited texting and data are included). a) Write an equation modeling the total cost of the cell phone, C, as a function of time, t. b) How much will the phone cost for an entire year? c) Katie has paid a total of $703 so far for her phone. How long has she owned the phone?

10 3) The Math Club sold 2200 tickets for the Math Olympics Competition. Admission prices were $8 for adults and $4 for students. The total amount collected was $12,400. How many adults and students attended the competition? 4) Graph the system of linear inequalities. Shade the final solution to the system. y - 4 x 1 3x 2y > 10 5) A line passes through the points (-18, 5) and (2, -3). a) Write the equation of the line in point-slope form. b) Convert your equation into slope-intercept form. c) Convert your equation into standard form.