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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
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.
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 ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
4/3pir^3

2. 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.
(x+y)(x-y)
1
Less

3. What is a 'Right isosceles' triangle?
1.4
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. Given event A: A + notA = 1.
Middle term

4. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
A=bh
S*v2
Ac+ad+bc+bd

5. Circumference of a circle using radius
Equal
2pi*r
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Bh

6. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
A=bh
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.
Part of a circle connecting two points on the circle.
Pi*r^2

7. a³-b³
1/x^a
(a-b)(a²+ab+b²)
2(lw+wh+lh)
A+b

8. Central Angle
Lw
Lwh
x² + 2xy + y²
An ange whose vertex is the center of the circle

9. a²-2ab+b²
Order does matter for a permutation - but does not matter for a combination.
Pi*d
2Length + 2width [or (length + width) x 2]
(a-b)²

10. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
(y-y1)=m(x-x1)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/2bh
N x M

11. What is the area of a circle?
A=?r2
N x M
A=bh
(pi)r^2

12. Perimeter of a rectangle
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.
2Length + 2width [or (length + width) x 2]
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
1/1

13. Area of Triangle
Groups - teams - or committees.
y2-y1/x2-x1
1/2bh
½(base x height) [or (base x height)÷2]

14. What is an 'equilateral' triangle?
1
1/x^a
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
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

15. a²+2ab+b²
(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.
Total distance/total time
(a+b)²

16. What is the unfactored version of x²-y² ?
(x+y)(x-y)
Pir^2h
A=?r2
Bh

17. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Between 0 and 1.
1. Given event A: A + notA = 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'.
(a-b)(a+b)

18. What is directly proportional?
A segment connecting the center of a circle to any point on the circle
1
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.
y = kx

19. What is the unfactored version of (x-y)² ?
x² -2xy + y²
S^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.
Probability A * Probability B

20. Perimeter of rectangle
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2l+2w
An ange whose vertex is the center of the circle
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.

21. Define the mode of a set of numbers.
1/x^a
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(a-b)(a+b)

22. What is the surface area of a cylinder?
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.
Less
S² - where s = length of a side
2(pi)r(r+h)

23. Area of a sector
4/3pir^3
x°/360 times (?r²) - where x is the degrees in the angle
2pi*r
1/2bh

24. To divide powers with the same base...
A²-b²
2x2x2x5x5
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
4pir^2

25. a² - b² is equal to
The set of points which are all the same distance (the radius) from a certain point (the center).
(n/2) * (t1+tn)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a+b)(a-b)

26. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
1.7
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Probability A + Probability B
x²-y²

27. What is the 'Third side' rule for triangles?
2 pi r
(x1+x2)/2 - (y1+y2)/2
2(lw+wh+lh)
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.

28. 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
y2-y1/x2-x1
2(pi)r
Bh

29. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Middle term
Lw
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

30. x^a * x^b = x^__
1.7
1. Given event A: A + notA = 1.
(y2-y1)/(x2-x1)
A+b

31. What are the side ratios for a 30:60:90 triangle?
Opens up
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Probability A * Probability B
The four big angles are equal and the four small angles are equal

32. What'S the most important thing to remember about charts you'll see on the GRE?
(a+b)(a²-ab+b²)
N x M
Sum of terms/number of terms
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.

33. What number goes on the bottom of a probability fraction?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a-b)²
The total # of possible outcomes.
(x-y)²

34. Chord
The distance from one point on the circle to another point on the circle.
(n degrees/360) * 2(pi)r
Between 0 and 1.
Bh

35. What is the average?
(n-2)180
Sum of terms/number of terms
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(x+y)²

36. Surface Area of Cylinder
2pir^2 + 2pir*h
Number of desired outcomes/number of total outcomes
Not necessarily. This is a trick question - because x could be either positive or negative.
Pi*d

37. Slope
(pi)r^2(h)
(y2-y1)/(x2-x1)
Total distance/total time
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.

38. How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2 pi r
Part of a circle connecting two points on the circle.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

39. When you reverse FOIL - the term that needs to add out is the _____
Between 0 and 1.
1.4
Middle term
(x1+x2)/2 - (y1+y2)/2

40. a³+b³
Arrangements - orders - schedules - or lists.
(n degrees/360) * (pi)r^2
1.4
(a+b)(a²-ab+b²)

41. 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.
4s
x² -2xy + y²
Sqr( x2 -x1) + (y2- y1)

42. Surface Area of rectangular prism
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.
2lw+2lh+2wh
A segment connecting the center of a circle to any point on the circle
1/2 h (b1 + b2)

43. For a bell curve - what three terms might be used to describe the number in the middle?
S² - where s = length of a side
The average - mean - median - or mode.
Pir^2h
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.

44. Define the 'Third side' rule for triangles

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45. What is the 'distributive law'?
1/2 h (b1 + b2)
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.
y = kx
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.

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

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47. In a parabola - if the first term is negative - the parabola ________.
Bh
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Opens down
The distance across the circle through the center of the circle.The diameter is twice the radius.

48. What do permutation problems often ask for?
Opens up
Arrangements - orders - schedules - or lists.
A+b
b±[vb²-4ac]/2a

49. Area of a triangle
(n degrees/360) * 2(pi)r
b±[vb²-4ac]/2a
Part of a circle connecting two points on the circle.
½(base x height) [or (base x height)÷2]

50. Area of Circle
The four big angles are equal and the four small angles are equal
1/1
A=bh
Pi*r^2