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
Evidence-based Reading: 6-7 questions
Click each link below for a different element of the toolkit.
Writing and Language
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.
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?
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