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The SAT covers most of the same topics every single test.  There are some topics that occur with greater frequency than others.  If you focus on mastering these question-types, then you can add 100 to 200 points to your score in a short amount of time.

Below is a simple toolkit for seeing these quick increases.  We chose each item in the toolkit by selecting a random sample of College Board SAT tests and determining the question types that appeared most frequently.  The topics that we selected, collectively, account for approximately 25% of all tests, or between 38 and 39 questions.  The breakdown is as follows:

Math: 28-22 questions

Writing and Language: 10-13

Click each link below for a different element of the toolkit.

Math

Writing and Language

Math

Coordinate Geometry

1.       Slope-Intercept Form

Lines in a coordinate plane are defined by the following generic equation:

y = mx + b

·         x and y define points on the line

·         m is the slope

·         b is the y-intercept, where the line intersects with the y axis.

As long as you understand what each part of the equation represents, then you have a powerful tool for manipulating and solving many problems that deal with lines on a coordinate plane.

2.       Slope Formula

You can think of the slope as how steep the line is.  Use the following formula to calculate the slope of a line:

m = (y2 – y1)/(x2 – x1), where (x1, y1) and (x2, y2) are points on a line.

The value of the slope itself offers very important information.  Keep in mind the following scenarios:

·         If the slope is positive, then the line goes on an incline:

·         If the slope is negative, then the line goes on a decline:

·         If the slope is positive, the greater it is, the steeper it is.  The closer the slope is to 0, the more level it becomes.

·         If the slope is negative, the closer it is to 0, the more level it is.  The more negative it becomes, the steeper the line will be on the decline.

·         Horizontal lines have a slope of 0.

·         Vertical lines have an undefined slope, owing to the fact that all the x coordinates are the same, making the denominator 0—constituting an undefined fraction.

·         Lines with the same slopes are parallel.  E.g.: y = 5x + 2; y = 5x -17.  These lines will never touch in space.

·         Lines with slopes that are negative reciprocals are perpendicular.  E.g. y = 2x + 3; y = -½ x – 7.  These lines will intersect at exactly one point in space to form four right angles.

*Tip 1: If a line does not conform to the slope-intercept form, solve for y to get it there!

*Tip 2: Draw a coordinate plane or use your graphing calculator.

Sometimes, coordinate geometry problems can be difficult to visualize.  For the trickier problems, don’t hesitate to make a quick drawing of a coordinate plane, or simply plug in all the information into your graphing calculator.  Visually representing a problem is usually the first step to understanding, and ultimately, solving it.

Practice

1.       A line in the xy plane passes through the point (1,3) and has a slope of -2.  At what point does the line intersect with the y-axis?

A)      (-5,0)

B)      (5,0)

C)      (0,5)

D)      (-2,0)

Try this problem on your own first before you review the explanation.

Explanation to question 1

1.       Find the equation for the line whose slope is perpendicular to y = 4x - 6.

A) y = 4x

B)  y = -4x + 6

C)  y = -1/4x -1

D)      y = x - 4

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