SAT Math: Exponential Functions

One of the function types that you may see on the New SAT is the exponential function, which students are normally introduced to in Algebra II. These functions, which can be used to model population growth, to compute compound interest, and for other applications in science, have equations in the form:

f(x) = a·b^x

In this equation, a and b are constants and the variable, x, appears as an exponent.

The number a is the initial value (when x = 0). For a population growth problem, it would represent the initial population of whatever group you are looking at. For a compound interest problem, the a represents the amount of the deposit or the loan.

SAT Math: A Challenging Quadratic Function Problem

As you prepare for the SAT, you’ll definitely want to review quadratic functions. You’ll need to know how to solve quadratic equations, as well as understand the properties of the graphs of these functions.

Here’s a challenging problem involving a quadratic function. Give it a try and then scroll down for the solution.

f(x) = a(x + b)(x – 8)

The equation above represents a quadratic function where a and b are constants. If the function is graphed in the xy-plane, its vertex is at the point (2, -54). What is the value of a + b?

(A)  4
(B)  5.5
(C)  6
(D)  7.5

SAT Math: A Challenging Functions Problem

As my students and I have prepared for the new SAT, one of the things we’ve noticed is that the more challenging Math problems aren’t just computational or problems where you can throw something into your calculator to get the answer. They are more theoretical — you have to really know the math in order to come up with the correct answer.

Let’s consider a challenging problem involving functions.

A function is defined by the equation below.

f(x) = a(x – 2)(x – 10)

If the minimum value of the function is -8, what is the value of a?

A)  -2
B)  1/4
C)  1/2
D)  2

ACT Math: Even and Odd Functions

The ACT Math section always contains a few trigonometry questions that go beyond the basic SOH-CAH-TOA problems that you learned in geometry.  Sometimes these problems have to do with the properties of functions, and one of the concepts you might be tested on is whether a function is even or odd.

So what does it mean for a function to be even or odd?

SAT Math: Functions That Intersect Geometric Figures

This post addresses another of the types of problems that appear near the end of an SAT Math section among the harder questions. This type of problem requires you to integrate what you know about functions with your knowledge of geometry. Most of these problems are multi-step and require you to think ahead about what you need to know in order to solve the problem and how you can figure those things out.

Let’s consider a problem:

Triangle ABC is isosceles and has a perimeter of 32.  The vertices of its base are (-6,0) and (6, 0). The parabola has its vertex at (0, -2) and it intersects the triangle at the midpoints of segments AB and AC. If the parabola has an equation in the form f(x) = ax² + k, what is the value of a? (A)  -1/3
(B)  1/3
(C)  2/3
(D)  3/4
(E)  4/3