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SAT Math: Geometry

Circles

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Knowsys Method

Read the problem carefully.  This problem deals with sectors, which are sections of a circle.  If you think of a circle as a pie, then sectors are slices of that pie.  

Identify the bottom line.  degrees in 1/6 of a circle - degrees in 1/9 of circle = ?

Assess your options.  If a sector makes up 1/6 a circle, then that sector must contain 1/6 of the 360 degrees in the circle.  Use that logic to figure out how many degrees are contained in each sector mentioned in the problem, then subtract the smaller number of degrees from the larger number to find the difference. 

Attack the problem.

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Loop back.  Verify that you solved for the bottom line.

The correct answer is C.
This is a medium level problem.  

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

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SAT Math: Geometry

Coordinate Geometry

In the xy-coordinate plane, line m is parallel to the x axis, and it passes through the point (4, -7).  Which of the following is an equation for line m?

A. x = -4
B. y = 4
C. y = -7
D. y + 7 = x - 4
E.  y – 7 = x + 4

Knowsys Method

Read the problem carefully.  Take careful note that the line in the question is parallel to the x axis.  

Identify the bottom line.  equation for line m = ?

Assess your options.  We must solve this problem by plugging the line into the point-slope formula.  The point slope formula is:

Screen Shot 2014-01-03 at 4.28.28 PM.jpg

Attack the problem.  We need to use the point-slope formula, but to do so, we must determine the slope (m) and the y-intercept (b).  It makes it a little easier to explain this problem if we draw out the line on the coordinate grid, but you do not have to do this step.  

Screen Shot 2014-01-03 at 4.23.46 PM.jpg

As the illustration shows, line m is parallel to the x axis, which makes it is a completely horizontal line.  A horizontal line has a slope of 0.  Think about it: if the y value never changes, then the change in y is zero, and no matter what the change in x, 0 divided by anything is 0.  Since you know that the y value never changes, you also know the y-intercept will be (0,-7).  Plug these values into the point-slope formula.

y = mx + b
y = (0)x -7
y = -7

Loop back.  Verify that you solved for the bottom line.

The correct answer is C.
This is a medium level problem.

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

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Screen Shot 2014-01-03 at 4.28.28 PM.jpg

SAT Math: Geometry

Polygons

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If all angles in the polygon above are congruent, then a =
A.  20
B.  35
C.  60
D.  72
E.  120

Knowsys Method. 

Read the problem carefully.  The problem states that all angles in the polygon are congruent, which means that you can apply rules for regular polygons. 

Identify the bottom line.  a = ?

Assess your options.  There are two ways to find the total number of degrees in a regular polygon.  You can:

1) use the polygon rule:
     180 (n – 2 )
     n is the number of vertices

2) divide the polygon into triangles and multiply the number of triangles by 180 degrees  

We will demonstrate both methods below.  

Attack the problem.  Either use the polygon rule or divide the polygon into triangles to find the total number of degrees in the polygon.  

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Now, divide the total number of degrees in this polygon by the number of vertices to find the measure of each individual angle. 

Screen Shot 2013-12-18 at 11.29.37 AM.jpg

The interior angle and a are supplementary, so subtract 120 from 180 to get the value of a. 

180 – 120 = 60  

Loop back.  Did you find the value of a?  Yes.  a = 60, which is answer choice C.

The correct answer is C.

This is a medium level problem. 

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

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SAT Math: Geometry

Triangles

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In the figure above, what is the sum, in terms of a, of angles b, c, d, and e?

A.  a
B.  2a
C.  180 – a
D.  180 – 2a
E.   360 – a

Knowsys Method

Read the problem carefully.  Notice that the image is drawn to scale because it does not indicate otherwise.  

Identify the bottom line.  b + c + d + e = ?

Assess your options.  If you find yourself stumped on a triangle problem on the SAT, run through the facts and rules you know about triangles and determine whether any of this knowledge applies to the problem at hand.  This problem is categorized as a “hard” level problem, but knowing one simple fact about triangles makes this problem easy to solve.  

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FACT: The exterior angle d equals the sum of the opposite interior angles a and b.

So, d = a + b.  

Attack the problem.
Angle a is an exterior angle to both triangles in the image.  That means:

a = b + c

AND

a = d + e

Therefore:

b + c + d + e = 2a

Loop back.  You found the solution to the bottom line.  

The correct answer is B.

This is a hard level problem.

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

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SAT Math: Geometry

Lines and Angles

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Knowsys Method

 

Read the question carefully.  Make note that the figure is not drawn to scale, so the sizes of the angles in the picture do not reflect their true measurements.

Identify the bottom line.  a = ?

Assess your options.  Visualize the point in the center as the center of a circle.  The number of degrees around the center point is 360, just like the number of degrees around the center of a circle.  That means that all of these angle measurements should add together to equal 360 degrees.  If you set that up as an equation, then you can solve for a.

Attack the problem.  Set up your equation and find the value of a.
2a + 4a + 5a + 7a = 360
                       18a = 360
                       ÷18    ÷18
                           a = 20

Loop back. Did you find the value of a?  Yes.  All that is left is to select the letter of the correct answer.

The correct answer is (C).
This is a medium level question.

 

Want some help reviewing the math concepts you need to master?  Try out the Knowsys Pre-Algebra Flashcards, the Knowsys Algebra I Flashcards, and the Knowsys SAT & ACT Math Practice book.  

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