Regular Algebra 1 Fall Final Exam Review

Transcription

1 Regular Algebra 1 Fall Final Exam Review Name: 1. A home store is having a 10%- off sale on all in-stock bathroom floor tile. What is the relationship between the sale price of the tile and the original price? Identify the independent and dependent values. Independent: Dependent: 2. A balloon is inflated with helium. As helium is added to the balloon, the volume increases until it finally busts. Identify the independent and dependent variables. Independent : Dependent: 3. Brian decides to start a lawn mowing business. He calculates the charge for each lawn using the function f(t) = 4t + 5.5, where t is the number of hours spent mowing the lawn. He always works for at least one full hours. What does the slope represent: What does the y-intercept represent: 4. Determine whether each table represents a linear function or a non-linear function. x y x y x y What is the domain and the range of the function? Domain: Range: Is it a function?: Why or why not? 6. Simplify the expression 5x 2 + 8x 2 2( 4x + 6x 2 ). What is the Leading Coefficient? What is the x-coefficient? What is the constant?

2 7. Find the slope of the line that contains the points (4, 8) and ( 2, 4). Slope Now write the equation of the line that passes through the points in And in Point-Slope Form Slope-Intercept Form 8. Write the linear regression for the data, and identify & interpret the correlation coefficient: Predict the number of passengers in A county fair charges a gate admission of $8.00 per person. It costs $1.50 for a person to ride on of the fair rides. Write and solve an inequality to determine the amount of rides you can take for this situation if you come to the fair with $18.00 to spend. Inequality: Solve: 10. Write the equation that has a y-intercept of (0, 1) and a slope of -4 in slope-intercept form. Then graph. Equation:

3 11. Generate a graph, table, mapping diagram, and set notation using the ordered pairs for the function using the given x values: {-1, 0, 2} y = 2x 2 1 Input (x) Output (y) Ordered Pair (x, y) Domain: Range: 12. When x = 44, y = If y varies directly with x, what is y when x equals 1? 13. For the function of f(x) = 75x , what is the value of f(x) when x = 2? 14. What is the parent function of all linear functions. Parent Function: Graph the parent function: 15. Angelo runs 7 miles per week and increases his distance by 1 mile each week. Write an equation to represent this situation. Graph the equation of the situation. Equation : Graph: After how many weeks, will Angelo be running 12 miles per week?

4 16. Recall scatterplots, sketch a graph of a positive, negative, and no correlation. 17. Dan began his stamp collection with just 5 stamps in the first year. Every year thereafter, his collection grew 5 times as large as the year before. How many stamps were in Dan's collection after 4 years? 18. The Elmwood Public Library has 85 Spanish books in its collection. Each month, the librarian plans to order 8 new Spanish books. How many Spanish books will the library have after 15 months? 19. A bicycle rental costs $10 plus $1.50 per hour. Write an equation that represents the cost as a function of the number of hours. Identify the slope and the y-intercept and describe their meanings. Equation: Slope: and its meaning: y-intercept: and its meaning: 20. The admission fee at an amusement park is $12, and each ride costs $3.50. The park also offers an all-day pass with unlimited rides for $33. For what numbers of rides is it cheaper to buy an all-day pass?

5 21. Convert the following functions in to slope-intercept form, identify the slope, and y-intercept. Function and work Slope-intercept form m b A. 3x 8y 2 1 y x 4 B. 2 C. y 1 3( x 2) 22. Write the equation in slope-intercept form for the line that passes through (4, 6) and is perpendicular to the line described by y = x Solve and graph the following compound inequality: d 2 < 5 and d Solve and graph the following inequality: 2(c 3) > Use intercepts to graph the following equation. 2x 4y = 16

6 26. Find the indicated term of the arithmetic sequence using the formula of an arithmetic sequence: a n = a 1 + d(n 1) 31 st term: 12, 7, 2, -3, 27. Give two solutions of the linear inequality and two non-solutions. Two solutions: and Two non-solutions: and 28. Write the linear inequality for the graph above: Linear inequality: 29. Solve the system of linear equations by graphing (use your graphing calculator!): y = 2x + 9 { y = 1 Solution: x What is the solution of the system graphed here: