Intermediate Algebra/Chapter1Test

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Chapter 1 Test[edit]

Solve the following problems as indicated:

1. Evaluate ab^2+a(b-c)-bc^2 if a = 3, b = -5, and c = 2.

2. A bike wheel has a circumference of 50 inches. What is the length of its diameter to the nearest hundreth? Use \begin{matrix}C & = &\pi\!d\quad\end{matrix} and \pi\begin{matrix}\approx & 3.14\end{matrix}.

3. Classify each of the following as natural numbers(N), integers(Z), rationals(Q), or irrationals(I). When possible, list all classifications for that number:

  a. \sqrt{49}
  b. -3.84
  c. 6 - (-3)
  d.  \frac{2 \times 5}{4} + \frac{3}{2} 

4. State the property illustrated in each of the following statements:

  a. 2(x + 3) = 2x + 2(3)
  b. 5y - 4 = -4 + 5y
  c. 3m + (2 + m) = (3m + 2) + m
  d. a(1/a) = 1

5. Simplify the following expressions:

  a. 3y(4 + 6x) - 2(y - 6).
  b. 2(a - 5) + 3a
  c. 5[c + 3(2c - 1)]

6. Melvin buys several books stamps, each stamp costs $0.39 and each book contains one dozen stamps (the cost of one book is equal to the price per stamp times the total number of stamps in it.) He pays a total of $24.80 ($1.40 sales tax is included in the final price). How many books of stamps did Melvin buy?

7. Solve |3y - 4| + 5 = 10.

8. Solve the following inequalities:

  a. 2y - 4 > 3
  b. -7x < 35 + 3x
  c. \frac{32}{-x - 2}\ > 4

9. All students at Central High School need a minimum of 40 credits to pass each year. Jack takes seven courses in one year, one of which is worth four credits. What must the minimum credit value of each of the other six courses be if Jack plans to pass this year?