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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. a² - b² is equal to
1.7
The distance across the circle through the center of the circle.The diameter is twice the radius.
(pi)r^2(h)
(a+b)(a-b)

2. Define the mode of a set of numbers.
Probability A * Probability B
2x2x2x5x5
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'.
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.

3. What is inversely proportional?
1/3Bh
y = k/x
The average - mean - median - or mode.
Less

4. Define the formula for calculating slope.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Pi*d
?r²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

5. a²-2ab+b²
(a-b)²
Less
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.

6. Explain the special properties of zero.
1/1
b±[vb²-4ac]/2a
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.
y = kx

7. If something is certain to happen - how is the probability of this event expressed mathematically?
1.4
1/1
Not necessarily. This is a trick question - because x could be either positive or negative.
x°/360 times (2 pi r) - where x is the degrees in the angle

8. What is the average?
Sum of terms/number of terms
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
½(b1 +b2) x h [or (b1 +b2) x h÷2]

9. Volume of prism
Total distance/total time
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.
Bh
(pi)r^2

10. Define 'proportionate' values
A segment connecting the center of a circle to any point on 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.
(x+y)²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

11. Rough est. of v3 =
Number of desired outcomes/number of total outcomes
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2x2x2x5x5
1.7

12. Area of Square
Pir^2h
Pi*d
2(pi)r(r+h)
S^2

13. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
4s
(x1+x2)/2 - (y1+y2)/2
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.

14. Slope
(y2-y1)/(x2-x1)
Order does matter for a permutation - but does not matter for a combination.
Pi*r^2
x² -2xy + y²

15. What is the factored version of x² + 2xy + y² ?
(x+y)²
The average - mean - median - or mode.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Bh

16. a²+2ab+b²
Not necessarily. This is a trick question - because x could be either positive or negative.
(a+b)²
N x M
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

17. Define the 'Third side' rule for triangles

18. Area of rectangle - square - parallelogram
Pi*d
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.
The four big angles are equal and the four small angles are equal
A=bh

19. x^a * x^b = x^__
A+b
1.7
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.
?r²

20. What is the length of an arc?
Order does matter for a permutation - but does not matter for a combination.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(n degrees/360) * 2(pi)r
N x M

21. What is the average speed?
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(a-b)(a²+ab+b²)
Total distance/total time

22. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
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.
y2-y1/x2-x1
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.

23. x^-a =
1/x^a
2Length + 2width [or (length + width) x 2]
½(base x height) [or (base x height)÷2]
Sum of terms/number of terms

24. What is the probability?
(x1+x2)/2 - (y1+y2)/2
?d OR 2?r
Number of desired outcomes/number of total outcomes
1/3pir^2*h

25. Rough est. of v1 =
(a-b)²
1
2(pi)r
A²-b²

26. If x² = 144 - does v144 = x?
Negative
Not necessarily. This is a trick question - because x could be either positive or negative.
Number of desired outcomes/number of total outcomes
Bh

27. Perimeter of a square
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Pi*r^2
4s (where s = length of a side)

28. How do you calculate the surface area of a rectangular box?
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.
C =?d
Sum of terms/number of terms
Less

29. What is the volume of a solid rectangle?
x°/360 times (2 pi r) - where x is the degrees in the angle
Not necessarily. This is a trick question - because x could be either positive or negative.
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
Lwh

30. Area of a circle
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.
?r²
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

31. In a parabola - if the first term is negative - the parabola ________.
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.
Opens down
Total distance/total time
1.4

32. What is the unfactored version of (x-y)² ?
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.
(x+y)(x-y)
x² -2xy + y²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

33. perimeter of square
4s
2l+2w
Less
A segment connecting the center of a circle to any point on the circle

34. How do you find the nth term of a geometric sequence?
2(pi)r(r+h)
The distance from one point on the circle to another point on the circle.
T1 * r^(n-1)
Percentage Change = Difference/Original * 100

35. When you reverse FOIL - the term that needs to add out is the _____
Middle term
Sqr( x2 -x1) + (y2- y1)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Lwh

36. Radius (Radii)
2pir^2 + 2pir*h
(a-b)(a²+ab+b²)
A segment connecting the center of a circle to any point on the circle
x² -2xy + y²

37. What is the unfactored version of (x+y)² ?
1/3pir^2*h
x² + 2xy + y²
T1 * r^(n-1)/(r-1)
The average - mean - median - or mode.

38. a³+b³
Lwh
1.7
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(a+b)(a²-ab+b²)

39. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
The four big angles are equal and the four small angles are equal
(x+y)²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

40. Lines reflected over the x or y axis have ____ slopes.
Negative
Groups - teams - or committees.
The total # of possible outcomes.
Not necessarily. This is a trick question - because x could be either positive or negative.

41. What is a '30:60:90' triangle?
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.
Percentage Change = Difference/Original * 100
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
y-y1=m(x-x1)

42. What are the side ratios for a 30:60:90 triangle?
2pi*r
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
(0 -0)

43. How do you find the nth term of an arithmetic sequence?
The set of points which are all the same distance (the radius) from a certain point (the center).
Lw
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
T1 + (n-1)d

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

45. Sector
(x1+x2)/2 - (y1+y2)/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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.

46. What is the 'distributive law'?
1. Given event A: A + notA = 1.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]

47. Does order matter for a permutation? How about for a combination?
(pi)r^2(h)
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.
Order does matter for a permutation - but does not matter for a combination.
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.

48. a³-b³
(a-b)(a²+ab+b²)
A segment connecting the center of a circle to any point on the circle
(pi)r^2(h)
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'.

49. Volume of pyramid
An ange whose vertex is the center of the circle
y = k/x
1/3Bh
(n-2)180

50. What is the surface area of a cylinder?
2(pi)r(r+h)
Opens up
(y-y1)=m(x-x1)
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