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GRE Math 2

Subjects : gre, math

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 'absolute value' - and how is it represented?

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2. How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
y = kx
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.
Not necessarily. This is a trick question - because x could be either positive or negative.

3. If something is certain to happen - how is the probability of this event expressed mathematically?
Sum of the lengths of the sides
2x2x2x5x5
A+b
1/1

4. What are the side ratios for a 30:60:90 triangle?
Last term
Between 0 and 1.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A=bh

5. What is the length of an arc?
1.4
The set of points which are all the same distance (the radius) from a certain point (the center).
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(n degrees/360) * 2(pi)r

6. a³-b³
2(pi)r
(a-b)(a²+ab+b²)
An ange whose vertex is the center of the circle
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

7. What is the 'Third side' rule for triangles?
Sqr( x2 -x1) + (y2- y1)
Middle term
The set of points which are all the same distance (the radius) from a certain point (the center).
The length of any one side of a triangle must be less than the sum of the other two sides - and greater than the difference between the other two sides.

8. Volume of Cone
C =?d
A²-b²
y2-y1/x2-x1
1/3pir^2*h

9. What is the factored version of (x+y)(x-y) ?
1/2 h (b1 + b2)
2pir^2 + 2pir*h
x²-y²
Opens down

10. What number goes on the bottom of a probability fraction?
A=bh
Sum of the lengths of the sides
1/2 h (b1 + b2)
The total # of possible outcomes.

11. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.

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12. a²-2ab+b²
(a+b)²
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(a-b)²
T1 * r^(n-1)/(r-1)

13. How do you find the sum of a geometric sequence?
C =?d
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
T1 * r^(n-1)/(r-1)
Order does matter for a permutation - but does not matter for a combination.

14. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
y2-y1/x2-x1
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.
1/x^a
The length of any one side of a triangle must be less than the sum of the other two sides - and greater than the difference between the other two sides.

15. Slope
2l+2w
C =?d
(n-2)180
(y2-y1)/(x2-x1)

16. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
x°/360 times (2 pi r) - where x is the degrees in the angle
Sqr( x2 -x1) + (y2- y1)
Opens down

17. Define a factorial of a number - and how it is written.
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
The factorial of a number is that number times every positive whole number smaller than that number - down to 1. Example: 6! means the factorial of 6 - which = 65432*1 = 720.
N x M
4s

18. Area of a triangle
T1 * r^(n-1)
½(base x height) [or (base x height)÷2]
2lw+2lh+2wh
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

19. Surface Area of Cylinder
2pir^2 + 2pir*h
2lw+2lh+2wh
2Length + 2width [or (length + width) x 2]
Opens up

20. Circumference of cirlce using diameter
Pi*d
1. Figure out how many slots you have (i.e. there are 3 winning positions in a race - 1st - 2nd - and 3rd) 2. Write down the number of possible options for each slot (i.e. 5 runners in the race - so 5 options for the 1st slot - 4 options for the 2nd
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x°/360 times (2 pi r) - where x is the degrees in the angle

21. What is the side ratio for a Right Isosceles triangle?
y = kx
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Sum of the lengths of the sides
Order does matter for a permutation - but does not matter for a combination.

22. What'S the most important thing to remember about charts you'll see on the GRE?
T1 * r^(n-1)
2pi*r
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.
A²-b²

23. What is the area of a triangle?
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.
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'.
1/2bh
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

24. What is the prime factorization of 200?
y2-y1/x2-x1
A segment connecting the center of a circle to any point on the circle
2x2x2x5x5
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

25. What is the surface area of a cylinder?
2(pi)r(r+h)
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

26. What is the unfactored version of (x-y)² ?
Percentage Change = Difference/Original * 100
x² -2xy + y²
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
1.4

27. Area of Circles
A=?r2
x²-y²
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
Probability A * Probability B

28. What is the factored version of x² -2xy + y² ?
(x-y)²
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Opens up
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.

29. Sector
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.
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.
(0 -0)
y2-y1/x2-x1

30. How do you multiply and divide square roots?
y-y1=m(x-x1)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Ac+ad+bc+bd
?r²

31. How do you find the midpoint?
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'.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
(x1+x2)/2 - (y1+y2)/2

32. If something is possible but not certain - what is the numeric range of probability of it happening?
Pi*d
Between 0 and 1.
Probability A * Probability B
Sum of terms/number of terms

33. Area of a trapezoid
N x M
Between 0 and 1.
(a+b)(a-b)
½(b1 +b2) x h [or (b1 +b2) x h÷2]

34. (a+b)(a-b)=
2(pi)r
A²-b²
2Length + 2width [or (length + width) x 2]
(a-b)(a²+ab+b²)

35. For a bell curve - what three terms might be used to describe the number in the middle?
The distance across the circle through the center of the circle.The diameter is twice the radius.
Not necessarily. This is a trick question - because x could be either positive or negative.
The average - mean - median - or mode.
1/2bh

36. What is the sum of the inside angles of an n-sided polygon?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Pi*d
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'.
(n-2)180

37. Perimeter of rectangle
2l+2w
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
1/2 h (b1 + b2)

38. What is the unfactored version of (x+y)² ?
x² + 2xy + y²
T1 * r^(n-1)
(a-b)(a²+ab+b²)
Pi*d

39. What is the area of a cylinder?
Percentage Change = Difference/Original * 100
(0 -0)
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.
2(pi)r(r+h)

40. Volume of pyramid
T1 + (n-1)d
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.
1/3Bh
Number of desired outcomes/number of total outcomes

41. Define the range of a set of numbers.
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.
Multiply all elements of both sides of the equation by 2 (the denominator of the fraction). This will produce 10x + 3 = 14x. Solve from there: 3 = 4x - x = 3/4.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Middle term

42. What is the equation of a line?

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43. If x² = 144 - does v144 = x?
A=?r2
T1 + (n-1)d
Not necessarily. This is a trick question - because x could be either positive or negative.
The factorial of a number is that number times every positive whole number smaller than that number - down to 1. Example: 6! means the factorial of 6 - which = 65432*1 = 720.

44. Volume of prism
(n degrees/360) * (pi)r^2
Bh
A=bh
?d OR 2?r

45. Define the formula for calculating slope.
T1 + (n-1)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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
T1 * r^(n-1)/(r-1)

46. length of a sector
x² + 2xy + y²
Opens up
4pir^2
x°/360 times (2 pi r) - where x is the degrees in the angle

47. 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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48. Volume of sphere
4/3pir^3
N x M
Probability A + Probability B
(y2-y1)/(x2-x1)

49. Define 'proportionate' values
1/3Bh
(x+y)(x-y)
The length of any one side of a triangle must be less than the sum of the other two sides - and greater than the difference between the other two sides.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

50. Area of Circle
1/2 h (b1 + b2)
1/3Bh
Ac+ad+bc+bd
Pi*r^2