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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. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
2(pi)r
4s
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

2. Sector
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
y2-y1/x2-x1
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.
2x2x2x5x5

3. length of a sector
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
x°/360 times (2 pi r) - where x is the degrees in the angle
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

4. Area of a sector
Not necessarily. This is a trick question - because x could be either positive or negative.
2x2x2x5x5
?r²
x°/360 times (?r²) - where x is the degrees in the angle

5. Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(pi)r^2(h)
1
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

6. What is inversely proportional?
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.
Sum of the lengths of the sides
1.7
y = k/x

7. What do combination problems usually ask for?
The set of points which are all the same distance (the radius) from a certain point (the center).
C =?d
Groups - teams - or committees.
Probability A + Probability B

8. Circumference of cirlce using diameter
A²-b²
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.
T1 * r^(n-1)/(r-1)
Pi*d

9. What is 'absolute value' - and how is it represented?

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

11. Volume of prism
2Length + 2width [or (length + width) x 2]
A=bh
S*v2
Bh

12. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
1/2 h (b1 + b2)
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.
(pi)r^2(h)

13. What is a 'Right isosceles' triangle?
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.
Opens down
Bh
(y2-y1)/(x2-x1)

14. How do you find the sum of a geometric sequence?
T1 * r^(n-1)/(r-1)
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
x² -2xy + y²
An ange whose vertex is the center of the circle

15. Area of rectangle - square - parallelogram
1/1
A=bh
½(base x height) [or (base x height)÷2]
1/2bh

16. Chord
1/2bh
2(lw+wh+lh)
?r²
The distance from one point on the circle to another point on the circle.

17. Area of a triangle
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Arrangements - orders - schedules - or lists.
½(base x height) [or (base x height)÷2]
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.

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

19. What is the surface area of a cylinder?
1/3pir^2*h
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2(pi)r(r+h)
2 pi r

20. What is the unfactored version of (x+y)² ?
x² + 2xy + y²
Less
4pir^2
The total # of possible outcomes.

21. What is the area of a circle?
The total # of possible outcomes.
(pi)r^2
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. 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

22. Rough est. of v3 =
1.7
(pi)r^2(h)
Order does matter for a permutation - but does not matter for a combination.
(a+b)(a²-ab+b²)

23. Slope
Probability A * Probability B
(x1+x2)/2 - (y1+y2)/2
(y2-y1)/(x2-x1)
1/2bh

24. How do you solve a permutation?
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
1.7
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

25. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
(x-y)²
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
1/x^a

26. The probability of an event happening and the probability of an event NOT happening must add up to what number?
(x1+x2)/2 - (y1+y2)/2
1. Given event A: A + notA = 1.
Groups - teams - or committees.
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'.

27. What is the unfactored version of (x-y)² ?
1/3Bh
x² -2xy + y²
Number of desired outcomes/number of total outcomes
Bh

28. How do you calculate the percentage of change?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Percentage Change = Difference/Original * 100
Sqr( x2 -x1) + (y2- y1)
(y2-y1)/(x2-x1)

29. What must be true before a quadratic equation can be solved?

30. (a+b)(c+d)
2pi*r
?d OR 2?r
Ac+ad+bc+bd
Part of a circle connecting two points on the circle.

31. If something is certain to happen - how is the probability of this event expressed mathematically?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
1/1

32. Define the 'Third side' rule for triangles

33. perimeter of square
Arrangements - orders - schedules - or lists.
4s
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 set of points which are all the same distance (the radius) from a certain point (the center).

34. Volume of Cone
2l+2w
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)(a²-ab+b²)
1/3pir^2*h

35. Define the mode of a set of numbers.
Lwh
(y2-y1)/(x2-x1)
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.
y = k/x

36. How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Sqr( x2 -x1) + (y2- y1)
A+b

37. What is the volume of a solid rectangle?
2pir^2 + 2pir*h
½(base x height) [or (base x height)÷2]
y = k/x
Lwh

38. What is the factored version of x² -2xy + y² ?
A+b
(x-y)²
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
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

39. x^a * x^b = x^__
4/3pir^3
1/2bh
A+b
(a+b)(a²-ab+b²)

40. a³+b³
(a+b)(a²-ab+b²)
?r²
T1 * r^(n-1)/(r-1)
x°/360 times (2 pi r) - where x is the degrees in the angle

41. Rough est. of v1 =
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.
2lw+2lh+2wh
1
A digit is a number that makes up other numbers. There are ten digits: 0 -1 -2 -3 -4 -5 -6 -7 -8 -9. Every 'number' is made up of one or more digits. For example - the number 528 is made up of three digits - a 5 - a 2 - and an 8.

42. Define the range of a set of numbers.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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.
?d OR 2?r

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

44. Area of Triangle
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.
1/2bh
(a-b)(a²+ab+b²)
A segment connecting the center of a circle to any point on the circle

45. When a line crosses two parallel lines - ________.
4s
(a+b)(a²-ab+b²)
The four big angles are equal and the four small angles are equal
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.

46. (a+b)(a-b)=
A²-b²
1/3Bh
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.
(y2-y1)/(x2-x1)

47. What is the distance formula?
Lwh
Opens up
2x2x2x5x5
Sqr( x2 -x1) + (y2- y1)

48. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
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.
N x M
1/2bh
b±[vb²-4ac]/2a

49. When you reverse FOIL - the term that needs to multiply out is the _____
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.
Last term
2pir^2 + 2pir*h
Opens up

50. What is the average speed?
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.
?d OR 2?r
Total distance/total time
2x2x2x5x5