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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. To divide powers with the same base...
1/x^a
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Between 0 and 1.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

2. x^a * x^b = x^__
A+b
2(lw+wh+lh)
?r²
(x+y)(x-y)

3. a³-b³
(a-b)(a²+ab+b²)
Last term
Ac+ad+bc+bd
b±[vb²-4ac]/2a

4. How do you calculate the percentage of change?
Sqr( x2 -x1) + (y2- y1)
Percentage Change = Difference/Original * 100
(x+y)²
The distance across the circle through the center of the circle.The diameter is twice the radius.

5. What is the length of an arc?
(n degrees/360) * 2(pi)r
1.4
Sqr( x2 -x1) + (y2- y1)
A²-b²

6. What is the unfactored version of (x-y)² ?
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.
x² + 2xy + y²
y-y1=m(x-x1)
x² -2xy + y²

7. What is the distance formula?
Groups - teams - or committees.
Last term
Sqr( x2 -x1) + (y2- y1)
Bh

8. Surface Area of Sphere
1/2bh
(a-b)(a+b)
4pir^2
Order does matter for a permutation - but does not matter for a combination.

9. 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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10. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
Multiply each numerator by the other fraction'S denominator. Example: 3/7 and 7/12. Multiply 312 = 36 - and 77 = 49. If you completed the full calculation - you'd also cross-multiply the denominators - but you don'T have to in order to compare values
2(lw+wh+lh)
A segment connecting the center of a circle to any point on the circle

11. What is a '30:60:90' triangle?
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
Last term
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
Pi*r^2

12. Circumference of a circle
?d OR 2?r
1/2bh
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Opens up

13. What is the average speed?
1/x^a
Total distance/total time
Pir^2h
1.7

14. a³+b³
(a+b)(a²-ab+b²)
(a+b)(a-b)
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'.
Pi*r^2

15. What is inversely proportional?
Total distance/total time
y = k/x
Opens up
(pi)r^2

16. Define the mode of a set of numbers.
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.
2(lw+wh+lh)
(n/2) * (t1+tn)
1/2 h (b1 + b2)

17. Perimeter (circumference) of a circle
x² -2xy + y²
2 pi r
y = kx
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

18. Circumference of cirlce using diameter
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
Pi*d
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.

19. perimeter of square
4s
x²-y²
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'.
(a-b)(a+b)

20. What is the area of a sector?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(n degrees/360) * (pi)r^2
(a+b)²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

21. a²-2ab+b²
(a-b)²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
The four big angles are equal and the four small angles are equal
(0 -0)

22. Surface Area of Cylinder
1/2bh
(n degrees/360) * (pi)r^2
S*v2
2pir^2 + 2pir*h

23. Circle
(n/2) * (t1+tn)
A=bh
(y-y1)=m(x-x1)
The set of points which are all the same distance (the radius) from a certain point (the center).

24. Point-Slope form
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.
2(pi)r(r+h)
(a-b)(a²+ab+b²)
y-y1=m(x-x1)

25. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the angle
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
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.

26. If something is certain to happen - how is the probability of this event expressed mathematically?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
S^2
Lw
1/1

27. For a bell curve - what three terms might be used to describe the number in the middle?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2(lw+wh+lh)
The average - mean - median - or mode.
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.

28. What is the unfactored version of x²-y² ?
Middle term
Opens up
1.7
(x+y)(x-y)

29. Circumference of a circle using radius
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
Pir^2h
2pi*r

30. Volume of prism
Bh
A+b
Sqr( x2 -x1) + (y2- y1)
4pir^2

31. What is the volume of a solid rectangle?
y = k/x
(a+b)(a-b)
4pir^2
Lwh

32. Perimeter of a rectangle
Part of a circle connecting two points on the circle.
Pi*r^2
Total distance/total time
2Length + 2width [or (length + width) x 2]

33. What are the side ratios for a 30:60:90 triangle?
(n degrees/360) * (pi)r^2
4s (where s = length of a side)
An ange whose vertex is the center of the circle
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

34. Radius (Radii)
Negative
The average - mean - median - or mode.
A segment connecting the center of a circle to any point on the circle
2(pi)r

35. Define the range of a set of numbers.
T1 * r^(n-1)/(r-1)
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.
Part of a circle connecting two points on the circle.
C =?d

36. List two odd behaviors of exponents
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.
C =?d
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-b)(a²+ab+b²)

37. a²-b²
(a-b)(a+b)
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
Probability A + Probability B
Bh

38. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
N x M
C =?d
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.
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.

39. What is the 'Third side' rule for triangles?
2l+2w
Between 0 and 1.
T1 + (n-1)d
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.

40. How do you find the sum of a geometric sequence?
T1 * r^(n-1)/(r-1)
(x1+x2)/2 - (y1+y2)/2
4s
Ac+ad+bc+bd

41. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
A+b
(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.
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.

42. Area of a square
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.
The four big angles are equal and the four small angles are equal
4pir^2
S² - where s = length of a side

43. In a coordinate system - what is the origin?
(0 -0)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Middle term
The distance across the circle through the center of the circle.The diameter is twice the radius.

44. When you reverse FOIL - the term that needs to add out is the _____
1/2bh
Middle term
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.
2(lw+wh+lh)

45. In a parabola - if the first term is positive - the parabola ________.
The average - mean - median - or mode.
Opens up
C =?d
1/1

46. Define the formula for calculating slope.
(a+b)(a-b)
1/1
Ac+ad+bc+bd
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

47. Volume of Cylinder
Percentage Change = Difference/Original * 100
Pir^2h
Groups - teams - or committees.
(a+b)(a-b)

48. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
Bh
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
1/3Bh

49. In intersecting lines - opposite angles are _____.
Last term
2lw+2lh+2wh
Opens down
Equal

50. Perimeter of a square
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
x² + 2xy + y²
4s (where s = length of a side)
4/3pir^3

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GRE Math 2

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