Algebra and Trigonometry Practice Problem Solutions

Algebra and Trigonometry Problem Set

1. y = -6x³ + 4x² - x + 2
2. Vertical shrink by 1/2, horizontal translation 2 to the left, vertical translation 1 down
3. 4x⁴ - 11x³ + 7x² + 5x - 3
4. $713,476.20
5. Brian is designing a handrail for a staircase and needs to determine the length: 12
6. A meteorologist predicts a 42% chance of rain on Saturday and a 54% chance of rain on Sunday: 27%
7. a_n = 3n - 11
8. (-2, 6) lies on the terminal side of an angle θ in standard position: Sinθ = 3√10 is False, True, True
9. y = log(x - 2)
10. Find the sum of the series: 12
11. The table shows enrollment by gender as an undergraduate or graduate student: 515/2463 = 0.209

Zeros of Functions

12. Find the zeros of the function shown below:
f(x) = x² + 3x - 10: x = 2 and -5

Statistical Distributions

13. Normal Distribution, Skewed Left, Skewed Right (See where the peak of the graph is)

Rational Expressions

14. x = 2 (multiply x-1 on both sides, x(x-1) + x = 3x - 2)

15. Katle and Leo are discussing the following rational expression: x ≠ 4

16. Unknown

Function Analysis

17. Determine if each statement is true or false:

• The y-intercept of g(x) is 3: True
• The maximum of g(x) is greater than the maximum of f(x): True
• The axis of symmetry of f(x) is x = -1: False
• The value of x when f(x) is at its maximum is less than the value of x when g(x) is at its maximum: True

18. Graph starts at: (2, -1), (2, 3), (-2, -1)

Probability and Statistics

19. You flip a coin and roll a six-sided die:

• The number of outcomes in the sample space is 8: False
• The probability that the coin shows heads and the die shows an even number is 1/4: True
• The probability that the coin shows tails and the die shows a number less than 3 is 1/6: True
• The probability that the coin shows heads and the die is not 2 is 5/6: False

Algebraic Data Analysis

20. Mrs. Mendez teaches 180 algebra students:

Quadratic and Trigonometric Forms

21. y = x² + 8x + 15 = y-intercept, y = (x-4)(x+2) = zeros, y = 4(x+2)² - 1 = vertex

22. y = 4cos(2x) - 3

23. Amplitude: 3, Period: π, Midline: y = 1

24. 5π/4

25.