SAT Practice Math Questions: Linear and Quadratic Functions

By Geraldine Woods, Ron Woldoff

Although functions seem like a pretty abstract concept, a huge number of real-life situations can be modeled using functions. To do well on the Math section of the SAT, you definitely want to know the most common types of functions: linear and quadratic.

All linear functions have the form y = mx + b or f (x) = mx + b. In graphing terms, m represents the slope of the line being drawn, while b represents its y-intercept.

Quadratic functions, on the other hand, have the form y = ax2 + bx + c or f (x) = ax2 + bx + c. Graphically, they’re represented by a parabola, a shape that resembles the basic rollercoaster hump.

The following practice questions deal with both linear and quadratic functions.

Practice questions

  1. If f (x) is a linear function with a slope of 2, passing through the point (–2, –3), f (x) must also pass through the point
    • A. (1, 2)
    • B. (1, 3)
    • C. (2, 2)
    • D. (2, 3)
  2. If a2b2 = 40 and ab = 10, then a + b =
    • A. 4
    • B. 10
    • C. 14
    • D. 30

Answers and explanations

  1. B. The best way to solve this problem is to draw a graph. To get it right, you have to remember the meaning of slope:

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    A slope of

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    for example, tells you to move 2 spaces up (the rise) and 5 spaces to the right (the run). You don’t have to be a great artist, just count the spaces. The function in this problem has a slope of 2, which is the same as

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    Starting at (–2, –3) and following these directions yields this graph:

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  2. A. When you see a quadratic expression in a problem, see whether it can be factored. a2b2 should look familiar to you: it factors out to (ab) (a + b). Because a2b2 = 40 and ab = 10, (10) (a + b) = 40 so a + b = 4. Notice that you didn’t even have to figure out what a and b are to solve the problem, which happens a lot on the SAT.