The pretest in this section covers skills that are used in this book. Doing it at the start of a course will help you identify areas in algebra where reviewing early on will help you succeed.
1. What is the equation of the line in Figure P.1?
2. What is the value of a in Figure P.2?
3. Find a1 and a2 from Figure P.3.
4. Match each of the four lines in Figure P.4 with one of the slopes 0, 1, 2, −1, −2.
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?
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 W2/3W3/2.
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 + Dq = 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 ax = 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?
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?
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?
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