Tutor profile: Richard S.

How do you solve difficult SAT mathematics multiple-choice questions with a lot of variables?

Some problems you can substitute small, simple numbers for the variables to make sense of complicated problems and find the correct response. Other times, you may be able to substitute the given answer choices into the original question to find the correct response.

How can you graph a logarithmic equation without a calculator?

First, determine the base of the logarithmic function. Then, create a table of values of the exponential function associated with that base. Reversing the x- and y- values of this exponential function will give you the coordinates of the base logarithmic function, since this base logarithmic function is the inverse of the base exponential function. Finally, apply any transformations (translations or dilations) that are being made to that base logarithmic function.

What is the best way to memorize the trigonometric values on the Unit Circle?

For the non-quadrant angles, think of each quadrant as consisting of three different triangles: one 45-45-90 triangle with a hypotenuse of 1 and two 30-60-90 triangles with a hypotenuse of 1. Memorizing the ratios between the sides of these triangles will make memorizing the trigonometric values on the Unit Circle easily as you can label all of the coordinates in quadrant I at 30, 45, and 60 degrees, and then just change the signs for the trigonometric values in Quadrants II, III, and IV.