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# SAT Math: What It Is and How to Prepare (page 2)

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Updated on Jul 10, 2009

Computation: A student’s test scores are 70, 90, 65, 85, and 75. What score must she get on the next test to raise her average to 80?

a) 73      b) 85         c) 90         d) 92.5      e) 95

The correct answer is e. An average is defined as the sum of the parts, divided by the number of parts. We can therefore write the equation: 80 = (70+90+65+85+75+x)/6. Simplifying further, we get: 80 = (385+x)/6. Solving for x, we get 480 = 385+x, or x=95.

Algebra: If x+y = 7 and x-y = 10, then 2x =

a) 70        b) 17       c) 3          d) -3         e) -17

The correct answer is b. This is an example that shows how the test makers offer chances to be clever. Most people approach this problem by using substitution to isolate and solve for x. But the skillful student saves time by seeing that she only needs to add the two equations, because the y-terms cancel each other.

x+y = 7
+ x-y = 10
2x = 17

Probability/Statistics: Two marbles are drawn at random without replacement from a jar containing 8 red marbles and 6 red marbles. What is the probability of drawing two red marbles?

This is a student response question. Please fill in the answer grid below:

 4 / 1 3

The probability of an event can be written by the following fraction:

(The Number of Desired Outcomes)/ (The Number of Possible Outcomes)

In this problem, there are 14 marbles total. The probability of drawing the first red marble is 8/14. Once it is gone, the probability of drawing the second red marble is 7/13. Because we need both to happen, we multiply the two fractions to get 56/182, which reduces to 4/13.

Functions: Find the point at which the function f(x) = 3x-4 intersects the line y = 5.

a) (5, 3)         b) (0, 5)       c) (-3, 5)       d) (3,5)          e) (0, 4/3)

The correct answer is d. Students with graphing calculators might solve this problem by setting f1 = 3x-4, and f2 = 5. By studying the graph, they could find the point of intersection. But it’s also easy to solve with old-fashioned methods. In the Cartesian coordinate system, points are listed as (x,y.) So if our point is on the line y=5, the point must be (x, 5). Then, we must find the value of x which makes 3x-4 = 5. Solving, we get 3x=9, or x=3. Therefore, the correct point is (3,5).