SAT Practice Math Questions: Linear and Quadratic Functions
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.
- 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)
- If a2 – b2 = 40 and a – b = 10, then a + b =
- A. 4
- B. 10
- C. 14
- D. 30
Answers and explanations
- 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:
A slope of
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
Starting at (–2, –3) and following these directions yields this graph:
- A. When you see a quadratic expression in a problem, see whether it can be factored. a2 – b2 should look familiar to you: it factors out to (a – b) (a + b). Because a2 – b2 = 40 and a – b = 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.