GRE Math 2

Instructions:

• Answer 50 questions in 15 minutes.
• If you are not ready to take this test, you can study here.
• Match each statement with the correct term.
• Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

This is a study tool. The 3 wrong answers for each question are randomly chosen from answers to other questions. So, you might find at times the answers obvious, but you will see it re-enforces your understanding as you take the test each time.

1. What is the area of a solid rectangle?
2pir^2 + 2pir*h
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1.7
2(lw+wh+lh)


2. Circumference of cirlce using diameter
N x M
?d OR 2?r
y-y1=m(x-x1)
Pi*d


3. In a parabola - if the first term is negative - the parabola ________.
T1 * r^(n-1)/(r-1)
Opens up
N x M
Opens down


4. Perimeter (circumference) of a circle
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2 pi r
y = kx


5. a²+2ab+b²
x°/360 times (2 pi r) - where x is the degrees in the angle
1/1
Probability A + Probability B
(a+b)²


6. Area of Square
Equal
S^2
The length of any one side of a triangle must be less than the sum of the other two sides. It must also be greater than the difference between the other two sides. So - 'A' will always be < B+C - and > B-C or C-B.
(a+b)(a-b)


7. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
Sqr( x2 -x1) + (y2- y1)
Pi*r^2
N x M
(pi)r^2


8. Area of Circles
4s (where s = length of a side)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Negative
A=?r2


9. How do you find the nth term of a geometric sequence?
The range is the difference between the biggest and smallest numbers in the set. Example: for the set {2 -6 -13 -3 -15 -4 -9} the smallest number is 2 - largest is 15 - so the range is 15-2=13.
This triangle is a square divided along its diagonal. Interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2lw+2lh+2wh
T1 * r^(n-1)


10. Quadratic Formula
T1 + (n-1)d
b±[vb²-4ac]/2a
x°/360 times (2 pi r) - where x is the degrees in the angle
(x+y)(x-y)


11. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
(a-b)(a²+ab+b²)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A median is the middle value of a set of numbers. For an odd number of values - it'S simply the middle number. For an even number of values - take the average of the center two values.
That they often have not just one answer - but two. For example - solving x² -10x + 24 = 0 factors to (x-4)(x-6)=0 - which means x could equal either 4 or 6. Just accept it.


12. Sector
Sum of terms/number of terms
The part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.
This triangle is a square divided along its diagonal. Interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2pi*r


13. How do you calculate the probability of two events in a row? (Probability of A and B)
(y2-y1)/(x2-x1)
Probability A * Probability B
2l+2w
That - unlike a normal chart - they are constructed to HIDE information or make it HARDER to understand. Be sure to scroll down - read everything - and look carefully for hidden information - asterisks - footnotes - small print - and funny units.


14. Perimeter of a square
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(y-y1)=m(x-x1)
4s (where s = length of a side)


15. What is the area of a circle?
y2-y1/x2-x1
(pi)r^2
T1 * r^(n-1)
Absolute value is a number'S distance away from zero on the number line. It is always positive - regardless of whether the number is positive or negative. It is represented with | |. For example - |-5| = 5 - and |5| = 5.


16. Area of a square
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Pir^2h
S*v2
S² - where s = length of a side


17. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
The part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.
1. Raising a fraction (between 0 and 1) to a power greater than 1 results in a SMALLER number. For example: (1/2)² = 1/4.2. A number raised to the 0 power is 1 - no matter what the number is. For example: 1 -287° = 1.
A segment connecting the center of a circle to any point on the circle


18. What'S the most important thing to remember about charts you'll see on the GRE?
An ange whose vertex is the center of the circle
That - unlike a normal chart - they are constructed to HIDE information or make it HARDER to understand. Be sure to scroll down - read everything - and look carefully for hidden information - asterisks - footnotes - small print - and funny units.
4s (where s = length of a side)
(a-b)(a+b)


19. (a+b)(a-b)=
y = k/x
A²-b²
(a+b)²
x°/360 times (2 pi r) - where x is the degrees in the angle


20. Volume of pyramid
Bh
The distance from one point on the circle to another point on the circle.
Opens down
1/3Bh


21. Slope
Absolute value is a number'S distance away from zero on the number line. It is always positive - regardless of whether the number is positive or negative. It is represented with | |. For example - |-5| = 5 - and |5| = 5.
(y2-y1)/(x2-x1)
The distance across the circle through the center of the circle.The diameter is twice the radius.
y = k/x


22. Define the 'Third side' rule for triangles

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23. Area of Triangle
2(pi)r(r+h)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/2bh
Pir^2h


24. Perimeter of polygon
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Opens up
Sum of the lengths of the sides
Part of a circle connecting two points on the circle.


25. In a coordinate system - identify the quadrants and describe their location.
2(pi)r
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
y2-y1/x2-x1
Number of desired outcomes/number of total outcomes


26. Circumference of a circle
A=bh
y = mx + b -- where: x -y are the coordinates of any point on the line (allows you to locate) m is the slope of the line b is the intercept (where the line crosses the y-axis) - Sometimes on the GRE - 'a' is substituted for 'm' - as in 'y = ax + b'.
2l+2w
?d OR 2?r


27. Explain the special properties of zero.
(x1+x2)/2 - (y1+y2)/2
Sum of terms/number of terms
Zero is even. It is an integer. It is neither positive nor negative. Zero multiplied by any other number = zero. You cannot divide by zero.
Probability A * Probability B


28. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

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29. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
1.7
An isoceles right angle. Remember that interior angles are 90:45:45 degrees. The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A²-b²
1. Given event A: A + notA = 1.


30. Area of Rectangle
Lw
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
The four big angles are equal and the four small angles are equal
?r²


31. Area of Circle
Pi*r^2
The distance across the circle through the center of the circle.The diameter is twice the radius.
(n degrees/360) * (pi)r^2
1/2 h (b1 + b2)


32. What is the sum of the inside angles of an n-sided polygon?
(n-2)180
This is an equilateral triangle that has been divided along its height. Interior angles are 30:60:90 degrees. Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse. This allows you to deduce any side - given
Pir^2h
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


33. Central Angle
An ange whose vertex is the center of the circle
Sum of the lengths of the sides
A²-b²
2l+2w


34. What is the length of an arc?
Bh
(n degrees/360) * 2(pi)r
x°/360 times (2 pi r) - where x is the degrees in the angle
x²-y²


35. a²-2ab+b²
2(pi)r(r+h)
(a-b)²
(a+b)(a-b)
Middle term


36. Explain the difference between a digit and a number.

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37. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

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38. How do you find the midpoint?
The part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.
(a+b)(a-b)
A+b
(x1+x2)/2 - (y1+y2)/2


39. Arc
The four big angles are equal and the four small angles are equal
(0 -0)
Part of a circle connecting two points on the circle.
?r²


40. Area of a sector
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
1/2bh
The total # of possible outcomes.
x°/360 times (?r²) - where x is the degrees in the angle


41. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
1/2bh
x°/360 times (?r²) - where x is the degrees in the angle
1. Factored: x² - y² Unfactored: (x+y)(x-y) 2. Factored: (x+y)² Unfactored: x² + 2xy + y² 3. Factored: (x-y)² Unfactored: x² - 2xy + y²
1


42. What is the side ratio for a 30:60:90 triangle?
b±[vb²-4ac]/2a
1/3pir^2*h
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
y = k/x


43. Volume of sphere
4/3pir^3
The mode is the number in a set that occurs most frequently. Example: for the set {3 -6 -3 -8 -9 -3 -11} the number 3 appears most frequently so it is the mode.
2Length + 2width [or (length + width) x 2]
1/2bh


44. What is the equation of a line?

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45. Area of a trapezoid
Not necessarily. This is a trick question - because x could be either positive or negative.
Total distance/total time
½(b1 +b2) x h [or (b1 +b2) x h÷2]
A+b


46. (a+b)(c+d)
A(b+c) = ab + ac a(b-c) = ab - ac For example - 12(66) + 12(24) is the same as 12(66+24) - or 12(90) = 1 -080.
1/2bh
Bh
Ac+ad+bc+bd


47. What is directly proportional?
y = kx
1/3Bh
The equation must be set equal to zero. If during the test one appears that'S not - before you can solve it you must first manipulate it so it is equal to zero.
(x+y)²


48. When you reverse FOIL - the term that needs to add out is the _____
Calculate and add the areas of all of 6 its sides.Example: for a rectangle with dimensions 2 x 3 x 4 - there will be 2 sides each - for each combination of these dimensions. That is - 2 each of 2x3 - 2 each of 3x4 - and 2 each of 4x2.
Pir^2h
y = k/x
Middle term


49. Area of Parallelogram
Lw
Bh
2lw+2lh+2wh
1/2 h (b1 + b2)


50. What is the surface area of a cylinder?
T1 * r^(n-1)
1/2bh
Bh
2(pi)r(r+h)