# 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*) = *x*^{2} - *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*) = *x*^{2} - 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*) = *x*^{2} - 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?

### Test Information

- 8 questions
- 12 minutes
- See All test questions

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