Algebra 1 Midterm Review 2025 PDF

Name: ______________________________________________ Date: ________ Midterm Review Algebra 1 Block: _______ Topic 1: FUNCTIONS 1. Determine which of the following are functions. Explain how you know. A. B. C.) (2,7) D. (3, 7) -7 9 (7,7)...

Name: ______________________________________________ Date: ________ Midterm Review Algebra 1 Block: _______ Topic 1: FUNCTIONS 1. Determine which of the following are functions. Explain how you know. A. B. C.) (2,7) D. (3, 7) -7 9 (7,7) -3 11 (9,7) -1 -8 68 -3 19 -9 -10 2. Evaluate the following expressions given the functions below: xy g(x) = -3x + 1 f(x) = -x + 2 ( ) = ( ) = ( ) A. g(10) = B. f(3) = C. j(-2) = D. h(–2) = E. Find x if g(x) = 16 F. Find x if h(x) = –6 G. Find x if f(x) = 23 y 3. Given this graph of the function f(x), find: 5 A. f(–4) = B. f(0) = C. f(3) = D. f(-5) = - E. x when f(x) = 2 F. x when f(x) = 0 G. f(-2) + f(2) 5 f( x) x 5 -5 4. Use a compound inequality to represent the domain and range of each graph:  A. B. C. Topic 2: LINEAR 5. Graph using slope and y-intercept. a) y = 3x – 2 b) + 2 = 2 slope: slope: y-int.: y-int.: Find the slope and y-intercept for each line. Then, write an equation in function notation. 6. 7. y-intercept: y-intercept: slope: slope: f(x)= f(x)= Topic 3: LITERAL EQUATIONS Solve each equation for the given variable. 8. =(ℎ ) 2for h 9. P = 2(l + w)for l 10. 8x − 4y = −12 for y Topic 4: SYSTEMS OF EQUATIONS 11. 12.. Sketch the graph of the solution to the system of inequalities. 13. 14.  16. 15. Solve the systems by Graphing. 17. = 2 – 3 18. = 4 = −23 + 5 = −2 Solve the systems by Elimination. 19. – – = 6 20. 2 + 5 = 20 6 + 2 = 12 – 4 + 10 =  40 Solve the systems by Substitution. 21. 2 – 3 = −4 22. = 18 + 5 + 3 = 7 2 – 3 = – 13 23. You are selling tickets for RBR’s basketball game. General admission tickets are $5.00 and students receive a $2.00 discount. You sell 350 tickets and collect $1450. How many of each type of ticket did you sell? Variables: Equations: Solution: Topic 5: EXPONENTIAL FUNCTIONS Graph the function and label at least three points on the graph. x 1 ⎛ ⎞ 24. y⎟=⋅ x y = 325. 4 ⎜ 2 ⎝ ⎠ Write an equation to represent each exponential model. 26. 5, 25, 125, 625, …… 27. 28. y = ___ ( )x y = ___ ( )x y = ___ ( )x Answer the following questions. Show your work and the formulas that you used. Circle final answer. 29. You deposited $500 in an account that pays annual compound interest rate of 8%. How much money will be in your account at the end of 9 years? 30. Write an exponential decay model that represents the following situation. You buy a car for $15,000 and its value depreciates 15% each year. Find the value of the car after 5 years. 31. Mr. Smith has an apple orchard. He hires his daughter, Lucy, to pick apples and offers her two payment options: Option A: $1.50 per bushel of apples picked Option B: 1 cent for picking zero bushels (just for showing up), 3 cents for picking one bushels, 9 cents for picking two bushels, and so on, with the amount of money tripling for each additional bushel picked. (A) Write a function to model each option. A(b) = B(b) = (B) If Lucy picks six bushels of apples, which option should she choose? A(6) = B(6) = (C) If Lucy picks 12 bushels of apples, which option should she choose? A(12) = B(12) =  (D) How many bushels of apples does Lucy need to pick to make Option B better for her than Option A? (E) Which model is more realistic? Explain your reasoning? Topic 6: STATISTICS 1. Using the information below, answer the questions regarding the following box plot. The speeds, in miles per hour, of 24 cars on a particular road are recorded and represented on the box and-whiskers diagram shown below. Answer each of the following questions based on this diagram. What is the interquartile range of this data? _________________________ What is the range of this data? ________________________ What percent of this data lies at or below 37mph? What does 37mph represent? ________________________________________________________________ 2. Biologists are modeling the number of flu cases as it spreads around a particular city. The total number of cases, y, was recorded each day, x, after the total first reached 16. The data for the first week is shown in the table below. Use your calculator to find an equation of the line of best fit. Record each equation and the determination of coefficient of determination ( 2). Determine which model fits the data best and explain your answer. Round coefficients to 2 decimal places and 2 values to 4 decimal places. Linear = Exponential = Quadratic = 2 = 2 = 2 = A) Which model best fits the data? Justify your answer. B) Based on your equation, how many cases are there after 12 days? 3. The RBRHS Varsity Basketball team is playing really well. Below are the points they have scored in the past 10 games. {77, 78, 80, 82, 84, 87, 94, 80, 92, 85} a. Draw the normal distribution curve, label all intervals and percentages (round mean and standard deviation to the nearest whole number). b. What percentage of the scores would you expect to be between 79 and 89? c. During their next game, the RBR basketball team scored 68 points. Calculate the z-score. d. The z-score for one of the games is 1.1. What is the expected score for the game? 4. Ms. Lenhard gives a math test and records the grades of her 18 students as follows: {68, 72, 74, 74, 78, 80, 80, 80, 82, 85, 85, 86, 87, 90, 92, 92, 95,  98} Mean = Median = Mode = Q1 = Q3 = IQR = Range = What percent scored between If she curved the test by 3 78 and 90 on the test? points, what would be the new mean? 5. The data below represents the total number of points each hockey team of the NHL Eastern Conference earned this past hockey season. {52, 66, 88, 93, 101, 100, 117}. Calculate the following (round to the nearest hundredth) Mean ( ) = Standard deviation ( ) = Variance ( 2) = 6. The formula for calculating the z score is provided. − = z = z-score = mean = standard deviation A) The Carolina Hurricanes scored 111 B) If the Devils had a z-score of 1.264, points last season. What is their z- score? how many points did they score last season?