**1.** Write the expression for three times the sum of twice a number and one minus 6.

**Answer:**3(2x+1) – 6

**Explanation:**The expression is three times the sum of twice a number and 1, which is 3(2x+1). Then, 6 is subtracted from this expression.

**2.** Which of the following inequalities is equivalent to 3 – (1/2)x ≥ 2?

**Answer:**x ≤ 2

**Explanation:**To simplify this inequality, subtract 3 from both sides to get:

Then, multiply both sides by -2 (remembering this flips the direction of the inequality) to get x ≤ 2.

**3.** 6 is 30% of what number?

**Answer:**20

**Explanation:**30% is 3/10. The number itself must be 10/3 of 6, or (10/3) × 6 = 20.

**4.** Solve the following equation:

**Answer:**0.0523

**Explanation:**Multiplying by 10^(-3) means moving the decimal point three places to the left, putting in zeroes as necessary.

**5.** A closet is filled with red, blue, and green shirts. If 1/3 of the shirts are green and 2/5 are red, what fraction of the shirts are blue?

**Answer:**4/15

**Explanation:**The total fraction taken up by green and red shirts will be:

The remaining fraction is:

**6.** On Monday, Robert mopped the floor in 4 hours. On Tuesday, he did it in 3 hours. If on Monday, his average rate of mopping was *p* sq. ft. per hour, what was his average rate on Tuesday?

**Answer:**(4/3)

*p*sq. ft. per hour

**Explanation:**Robert accomplished his task on Tuesday in 3/4 the time compared to Monday. He must have worked 4/3 as fast.

**7.** A rectangle has a length that is 5 feet longer than three times its width. If the perimeter is 90 feet, what is the length in feet?

**Answer:**35

**Explanation:**Denote the width as

*w*and the length as

*l*. Then, l=3w+5. The perimeter is 2w+2l = 90. Substituting the first expression for l into the second equation yields 2(3w+5)+2w = 90, or 8w = 80, so w = 10. Putting this into the first equation, it yields:

**8.** A company invests $50,000 in a building where they can produce saws. If the cost of producing one saw is $40, then which function expresses the amount of money the company pays? The variable *y* is the money paid and x is the number of saws produced.

**Answer:**y = 40x+50,000

**Explanation:**For manufacturing costs, there is a linear relationship between the cost to the company and the number produced, with a

*y*-intercept given by the base cost of acquiring the means of production, and a slope given by the cost to produce one unit. In this case, that base cost is $50,000, while the cost per unit is $40. So, y = 40x+50,000.

**9.** How do you solve V = lwh for *h*?

**Answer:**h = V/lw

**Explanation:**The formula can be manipulated by dividing both sides by the length,

*l*, and the width,

*w*. The length and width will cancel on the right, leaving height by itself.

**10.** The square and circle have the same center. The circle has a radius of *r*. What is the area of the shaded region?

**Answer:**(4 – π)r^2

**Explanation:**The area of the shaded region is the area of the square, minus the area of the circle. The area of the circle will be πr^2. The side of the square will be 2r, so the area of the square will be 4r^2. Therefore, the difference is: