University:
College Entrance Preparation
Course:
ACT Preparation (Mathematics)
Academic year:

2020
Views:

408

Pages:

7
Author:

hacedoras1kxy

Pre-Algebra Semester 1 Review **Name:** **Date:** **Period:** **Chapter 2** Directions: Solve for the variable in each equation. 1. 3/4c = 18 4/3 * 3/4c = 18 * 4/3 c = 24 2. -2.7d = 810 d = -300 3. 2x + 4 = 7 2x = 3 x = 3/2 4. 6 - 3x = 21 -3x = 15 x = -5 5. 4x + 2 = 2x + 8 2x = 6 x = 3 6. 6n - 1 = 4n - 5 2n = -4 n = -2 7. 15(20 + d) = 420 300 + 15d = 420 15d = 120 d = 8 8. 6(x - 3) + 10 = 2(3x - 4) 6x - 18 + 10 = 6x - 8 6x - 8 = 6x - 8 0 = 0 9. Cassidy went to the movies with some of her friends. The tickets cost $6.50 each, and they spent $17.50 on snacks. The total amount paid was $63.00. Write an equation representing the amount spent. Determine how many people went to the movies. y = 6.50(x) + 17.50 63 = 6.50(x) + 17.50 x = 7 10. A personal trainer buys a weight bench for $500 and "w" weights for $24.99 each. The total cost of the purchase is $846.99. How many weights were purchased? 846.99 = 500 + 24.99(w) 346.99 = 24.99(w) w = 13.8 ≈ 13 weights 11. Pizza Shack charges $8 per pizza, Pizza on the Plaza charges $10 per pizza, but does not charge a delivery fee. Write an equation that could be used to find the number of pizzas for which the cost, including delivery, will be the same. Shack: y = 8x + 4 Plaza: y = 10x 8x + 4 = 10x 2x = 4 x = 2 **Directions: Translate each sentence into an equation.** 12. Four less than five times a number is equal to 11. 5x - 4 = 11 13. Fifteen more than half a number is 9. 1/2x + 15 = 9 14. Six less than seven times a number is -26. 7x - 6 = -26 15. -12 is eight more than four times a number. 4x + 8 = -12 **Chapter 3** **Directions: Determine the constant rate of change from the tables provided.** 16. The relationship between the time and the amount of songs played: | Time (minutes) (x) | Number of Songs (y) | |---|---| | 0 | 0 | | 1 | 2 | | 2 | 4 | | 3 | 6 | | 4 | 8 | Constant Rate of Change = Δy/Δx = 2/1 = 2 17. The relationship between a temperature in degrees Fahrenheit and temperature in degrees Celsius: | Degrees Celsius (x) | Degrees Fahrenheit (y) | |---|---| | 0 | 32 | | 5 | 41 | | 10 | 50 | | 15 | 59 | | 20 | 68 | Constant Rate of Change = Δy/Δx = 9/5 18. Which formula represents the rate of change? A) Ax + By = C B) x₁/y₁ * x₂/y₂ C) (y₂ - y₁) / (x₂ - x₁) D) y = mx + b Answer: C) 19. Given the points (5, 3) and (13, 5) on a line, determine the slope of the line. (x₁, y₁) (x₂, y₂) (5, 3) (13, 5) Slope = (y₂ - y₁) / (x₂ - x₁) = (5 - 3) / (13 - 5) = 2/8 = 1/4 20. Determine if the lines with the points (3, -5) and (-3, 5) has a positive or negative slope. (x₁, y₁) (x₂, y₂) (3, -5) (-3, 5) Slope = (y₂ - y₁) / (x₂ - x₁) = (5 - (-5)) / (-3 - 3) = 10/-6 = negative slope