PSAT Math Grid-Ins Practice Test 2: Math Techniques

1. Mathew and Moriah purchased a tandem bicycle for $540. If the amount Moriah paid was $30 less than twice the amount Mathew paid, how much, in dollars, did Moriah pay?

(Disregard the dollar sign when gridding in your answer.)

2. Kimberly is an apiologist studying the sugar content of different sugar-water solutions to determine which is preferred by her hive of honeybees. After trying Solution 1, which has a sugar content of 25%, and Solution 2, which has a sugar content of 10%, she decides to make a new solution. She mixes 50 ounces of Solution 1 with some quantity of Solution 2 to make Solution 3, which has a sugar content of 15%. How many ounces of Solution 2 did Kimberly use to make Solution 3?

3. 15% of the members of the incoming freshmen class at a certain university are left-handed, and the remaining members are right-handed. 65% of the same incoming freshmen class are female, and the rest are male. If of the left-handed students are male, then what percent of the female class is right-handed, to the nearest tenth of a percent? (Disregard the percent sign when gridding your answers. For example, if the answer is 43.2%, grid in 43.2.)

4. Estimated Numbers of Cell Phone Users by Type (in millions)

If a cell phone user is selected at random in 2008, what is the probability that user is a contracted user?

5. Marcia can type 18 pages per hour, and David can type 14 pages per hour. If they work together, how many minutes will it take them to type 24 pages?

6. If f(x) = x² - x + 4, a is non-negative, and f(a) = 10, what is the value of a?

7.

In the above graph, parabola f(x) is represented by the equation f(x) = x² - 4 and line g(x) is represented by the equation g(x)= -x -4. Line g(x) intersects parabola f(x) at point (0, -4).

For x = 12, how much greater is the value of f(x) than g(x)?

8.

In the above graph, parabola f(x) is represented by the equation f(x) = x² - 4 and line g(x) is represented by the equation g(x)= -x -4. Line g(x) intersects parabola f(x) at point (0, -4).

A new line, h(x), is added to the graph. The line h(x) is perpendicular to line g(x), intersecting with line g(x) at the point (-12, 0). What is the x-coordinate of the point where line h(x) will intersect parabola f(x) in Quadrant 1?