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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 the equation of a line?

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2. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
T1 * r^(n-1)
(y2-y1)/(x2-x1)
(a-b)(a+b)

3. Point-Slope form
y-y1=m(x-x1)
?r²
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
1/2bh

4. 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.
Sum of terms/number of terms
Number of desired outcomes/number of total outcomes
2(pi)r

5. 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.
(n-2)180
The four big angles are equal and the four small angles are equal
Probability A * Probability B

6. Volume of Cylinder
1/3pir^2*h
(a-b)(a²+ab+b²)
The distance from one point on the circle to another point on the circle.
Pir^2h

7. Perimeter of a square
(a-b)(a²+ab+b²)
Last term
4s (where s = length of a side)
y2-y1/x2-x1

8. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Negative
A+b
S*v2

9. What is the 'Third side' rule for triangles?
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'.
1/3pir^2*h
Equal
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.

10. Define the 'Third side' rule for triangles

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11. What is the area of a circle?
Total distance/total time
A²-b²
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.
(pi)r^2

12. (a+b)(a-b)=
A²-b²
A+b
2Length + 2width [or (length + width) x 2]
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.

13. Perimeter of polygon
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.
2lw+2lh+2wh
Sum of the lengths of the sides
A=?r2

14. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
(a+b)²
(x+y)²
Lwh
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.

15. What are the side ratios for a 30:60:90 triangle?
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.
Sum of terms/number of terms
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2Length + 2width [or (length + width) x 2]

16. The probability of an event happening and the probability of an event NOT happening must add up to what number?
T1 * r^(n-1)/(r-1)
1. Given event A: A + notA = 1.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

17. How do you calculate the probability of two events in a row? (Probability of A and B)
?d OR 2?r
Probability A * Probability B
Opens down
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

18. What do combination problems usually ask for?
Groups - teams - or committees.
(pi)r^2
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
y = kx

19. Circumference of cirlce using diameter
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
2lw+2lh+2wh
Pi*d
S^2

20. Quadratic Formula
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.
y = kx
Bh
b±[vb²-4ac]/2a

21. What is the unfactored version of x²-y² ?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1/3Bh
?r²
(x+y)(x-y)

22. Volume of Cone
A segment connecting the center of a circle to any point on 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.
Pir^2h
1/3pir^2*h

23. Sector
(a+b)(a²-ab+b²)
2pi*r
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.
Groups - teams - or committees.

24. Area of Trapezoid
1/2 h (b1 + b2)
2pi*r
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2 pi r

25. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
(x+y)(x-y)
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.
T1 * r^(n-1)/(r-1)
N x M

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

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27. Rough est. of v2 =
2pir^2 + 2pir*h
The distance from one point on the circle to another point on the circle.
1.4
1/2bh

28. What is an 'equilateral' 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
T1 * r^(n-1)/(r-1)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
x² + 2xy + y²

29. Surface Area of Sphere
S*v2
2(pi)r(r+h)
1. Given event A: A + notA = 1.
4pir^2

30. Circle
4pir^2
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
A segment connecting the center of a circle to any point on the circle
The set of points which are all the same distance (the radius) from a certain point (the center).

31. How do you find the sum of a geometric sequence?
2pir^2 + 2pir*h
T1 * r^(n-1)/(r-1)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The four big angles are equal and the four small angles are equal

32. What is the volume of a cylinder?
(pi)r^2(h)
1/1
S*v2
(x+y)²

33. In intersecting lines - opposite angles are _____.
A segment connecting the center of a circle to any point on the circle
S*v2
Equal
(n-2)180

34. What is the surface area of a cylinder?
2pir^2 + 2pir*h
Ac+ad+bc+bd
2(pi)r(r+h)
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

35. Circumference of a circle using radius
2pi*r
?r²
Between 0 and 1.
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.

36. Lines reflected over the x or y axis have ____ slopes.
Negative
(n-2)180
1.4
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

37. Area of a sector
(x-y)²
2l+2w
x°/360 times (?r²) - where x is the degrees in the angle
(a-b)²

38. What is the area of a triangle?
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
1/3Bh
T1 + (n-1)d
1/2bh

39. 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
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.
1/2 h (b1 + b2)
Sum of the lengths of the sides

40. What'S the most important thing to remember about charts you'll see on the GRE?
The four big angles are equal and the four small angles are equal
Number of desired outcomes/number of total outcomes
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.
x²-y²

41. x^a * x^b = x^__
x² + 2xy + y²
1/2bh
A+b
Last term

42. Area of rectangle - square - parallelogram
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
A=bh

43. Chord
The distance from one point on the circle to another point on the circle.
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.
Part of a circle connecting two points on the circle.
Arrangements - orders - schedules - or lists.

44. If something is certain to happen - how is the probability of this event expressed mathematically?
(0 -0)
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.
1/1
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

45. Surface Area of rectangular prism
?d OR 2?r
2lw+2lh+2wh
The average - mean - median - or mode.
Equal

46. What is the area of a sector?
y2-y1/x2-x1
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(n degrees/360) * (pi)r^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.

47. What is the sum of the inside angles of an n-sided polygon?
Pi*d
(a+b)²
The average - mean - median - or mode.
(n-2)180

48. 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.
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.
S*v2
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

49. Explain the special properties of zero.
2(pi)r(r+h)
2 pi r
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.
4pir^2

50. Area of Triangle
2(lw+wh+lh)
1/2bh
½(base x height) [or (base x height)÷2]
2Length + 2width [or (length + width) x 2]