Practice Test B

  1. Solve the equation 2x−2=5x+34.

    1. {174}

    2. {−18}

    3. {152}

    4. {−12}

  2. Solve the equation z2=2z+35.

    1. {472}

    2. {−472}

    3. {23}

    4. {−703}

  3. Solve the equation 1t−2−12=−2t4t−1.

    1. {49}

    2. {12}

    3. {23}

    4. {− 2}

  4. The length of a rectangle is 4 centimeters greater than the width, and the area is 77 square centimeters. Find the dimensions of the rectangle.

    1. 11 centimeters by 15 centimeters

    2. 5 centimeters by 9 centimeters

    3. 7 centimeters by 11 centimeters

    4. 9 centimeters by 13 centimeters

  5. Solve the equation x2+12=−7x.

    1. {3, 4}

    2. {−4, −3}

    3. {−3, 3, 4}

    4. {4, 3}

  6. If Rena invests $7500 at 7% per year, how much additional money must she invest at 12% to ensure that the interest she receives each year is 10% of the total investment?

    1. $11,250

    2. $12,375

    3. $18,000

    4. $21,000

  7. A frame of uniform width borders a painting that is 20 inches long and 13 inches high. Assuming that the area of the framed picture is 368 square inches, find the width of the border.

    1. 3.5 in.

    2. 3 in.

    3. 4 in.

    4. 1.5 in.

  8. Solve −6x−2=(3x+1)2.

    1. ∅

    2. {−13}

    3. {13, 1}

    4. {−1, −13}

  9. Determine the constant that should be added to the binomial

    x2+16x

    so that it becomes a perfect-square trinomial. Then write and factor the trinomial.

    1. 112; x2+16x+112=(x+16)2

    2. 1144; x2+16x+1144=(x+112)2

    3. 136; x2+16x+136=(x+16)2

    4. 144; x2+16x+144=(x+12)2

  10. Solve 7x2+10x+2=0.

    1. {−5−117, −5+117}

    2. {−5−397, −5+397}

    3. {−5−1114, −5+1114}

    4. {−10−117, −10+117}

  11. A box with a square base and no top is made from a square piece of cardboard by cutting 3-inch squares from each corner and folding up the sides. What length of side must the original cardboard square have if the volume of the box is 675 cubic inches?

    1. 18 inches

    2. 21 inches

    3. 15 inches

    4. 14 inches

  12. Solve x2+14x+38=0.

    1. {7−38, 7+38}

    2. {14+38}

    3. {7+11}

    4. {−7−11, −7+11}

  13. Solve the polynomial equation

    5x4−45x2=0

    by factoring and then using the zero-product property.

    1. {−3, 0, 3}

    2. {−3, 3}

    3. {0}

    4. {−35, 0, 35}

  14. Solve the equation

    x−2048−32x=0

    by making an appropriate substitution.

    1. {4096}

    2. {3072}

    3. {8192}

    4. {2048}

  15. Solve the absolute value equation

    |12x+2|=|34x−2|.
     

    1. {12, 16}

    2. ∅

    3. {10}

    4. {0, 16}

In Problems 16 and 17, solve the inequality. Express the solution set in interval notation.

  1. x6−13≤x3+1

    1. (−∞, −8)

    2. (−∞, −8)

    3. (−8, ∞)

    4. [−8, ∞)

  2. −13≤−3x+2<−4

    1. [−5, −2)

    2. (2, 5]

    3. (−5, −2]

    4. [2, 5)

  3. Solve the inequality

    8+|1−x2|≥10

    by first rewriting it as an equivalent inequality without absolute value bars. Express the solution set in interval notation.

    1. (−∞, −6]∪[2, ∞)

    2. [−2, 6]

    3. (−∞, −2]∪[6, ∞)

    4. [−6, 2]

  4. Solve the linear inequality 23x−2<53x.

    1. (−2, ∞)

    2. (∞, 2)

    3. (−∞, −2)

    4. {−2}

    5. (2, ∞)

  5. Solve the inequality 0≤7x−1≤13.

    1. [17, 2]

    2. (−1, 2]

    3. 17

    4. [−1, 2]

    5. (∞, 17]

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