Problems for a Pretest

1. What is the equation of the line in Figure P.1?

Figure P.1

2. What is the value of a in Figure P.2?

Figure P.2

3. Find a₁ and a₂ from Figure P.3.

Figure P.3

4. Match each of the four lines in Figure P.4 with one of the slopes 0, 1, 2, −1, −2.

Figure P.4

5. Solve for P₀:

6. Solve for r:

7. If f(t) = 4t + (t + 3)², find f(0).

8. If f(x) = 4x + 28, solve f(x) = 0.

9. Which of the following is equivalent to 16 − x² + 6x?

(a) 7 + (3 − x)²

(b) 16 − (x − 3)²

(c) 25 − (x − 3)²

(d) 52 − (x − 6)²

(e) 25 − (x + 3)²

(f) None of the above

10. What are the coordinates of the point Q in Figure P.5?

11. What are the coordinates of the point P in Figure P.5?

Figure P.5

12. Find |−10| + |10|.

13. Which of the following is equivalent to ?

(a)

(b)

(c) E + T

(d)

(e)

14. Which of the following is equivalent to ?

(a)

(b)

(c)

(d)

(e)

15. Which of the following is equivalent to x⁻¹y + y⁻¹x?

(a)

(b)

(c)

(d)

(e)

16. If , what is a?

17. Simplify (x²x⁵)⁴.

18. Simplify W^2/3W^3/2.

19. Expand and collect like terms: .

20. Solve 3p + 4 = 9 for p.

21. Solve 2x + a = 5(1 − x) for x.

22. Solve − 3 = 9 for w.

23. Solve for n.

24. Solve Cq + D_q = A for q.

25. With m = 2, x₀ = 3, y₀ = 10, solve y − y₀ = m(x − x₀) for x.

26. Find the value of x when y = 0 if −2x + 9y − 9 = 0.

27. Find the value of s when t = s + 1 if 3s − 8t = 7.

28. Factor 12x² − 6a²x.

29. Factor C²a³b − Cab³.

30. Which of the following is the factored form of x² + 2x − 15?

(a) (x + 1)² − 16

(b) (x − 3)(x + 5)

(c) x(x + 2) − 15

(d) (x + 2)(x − 15)

(e) None of the above

31. What are the zeroes of (x − 2)(x + 1)(2x − 5)?

32. What is the y-intercept of y = (x–2)(x + 1)(2x–5)?

33. If W² − 2W − 8 = 4(W − 2), find all possible values of W.

34. If s = d² + d + 1 and d = g + 1 express s in terms of g.

35. If θ = x² − 1 express (θ + 1)² in terms of x.

36. If b = −2z express b² − 2b in terms of z.

37. The graph of the equation a^x = y passes through the point (−3, ). What is a?

38. If s = 2 and t = 0 is a solution to as⁵ = s⁷ + t, what is a?

39. Using Table P.1, what value of w gives q = 7?

40. Using Table P.2, what is the temperature at 6 pm?

41. For some constant k, let M = kN. If M = 0.84 when N = 12, what is M when N = 6?

42. What is the area of the shaded rectangle in Figure P.6?

Figure P.6

43. What is the area of the shaded triangle in Figure P.6?

44. A price increases by a factor of 1.042. By what percent has the price increased?

45. A car, initially valued at $21,000 is now worth 32% less. What is the car's current value?

46. An item priced at $45 is on sale for 25% off. The customer pays the sale price plus 8% sales tax. How much does the customer pay?

Problems on Trigonometry (Optional)

1. What is the vertical intercept of y = cos x?

2. What are the zeroes of y = sin x between x = 0 and x = 2π (inclusive)?

3. How many degrees is 3π radians?

4. What are the coordinates of the highest point on the sine graph in Figure P.7?

Figure P.7