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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 area of a cylinder?
A=bh
Not necessarily. This is a trick question - because x could be either positive or negative.
2(pi)r(r+h)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

2. What is a 'Right isosceles' triangle?
2 pi r
Probability A + Probability B
1/2 h (b1 + b2)
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.

3. Point-Slope form
The distance across the circle through the center of the circle.The diameter is twice the radius.
y-y1=m(x-x1)
Probability A + Probability B
Lwh

4. Area of Rectangle
Lw
x²-y²
(x+y)²
Bh

5. How do you find the nth term of an arithmetic sequence?
Sum of terms/number of terms
(x-y)²
A²-b²
T1 + (n-1)d

6. Define the 'Third side' rule for triangles

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7. Radius (Radii)
Sum of the lengths of the sides
A segment connecting the center of a circle to any point on the 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.
1/3pir^2*h

8. What is the area of a sector?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
y2-y1/x2-x1
x²-y²
(n degrees/360) * (pi)r^2

9. Area of a square
b±[vb²-4ac]/2a
S² - where s = length of a side
A=bh
(pi)r^2(h)

10. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
C =?d
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
?d OR 2?r

11. Area of Triangle
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.
2(lw+wh+lh)
1/2bh
Sqr( x2 -x1) + (y2- y1)

12. Area of a triangle
Last term
T1 + (n-1)d
Probability A * Probability B
½(base x height) [or (base x height)÷2]

13. What is the distance formula?
4s
(y2-y1)/(x2-x1)
Percentage Change = Difference/Original * 100
Sqr( x2 -x1) + (y2- y1)

14. Area of Circles
(n/2) * (t1+tn)
A=?r2
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
4s

15. Volume of Cylinder
An ange whose vertex is the center of the circle
Pir^2h
2l+2w
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

16. a²-b²
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.
Equal
(a+b)²
(a-b)(a+b)

17. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
T1 + (n-1)d
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

18. How do you solve a permutation?
1
1. Given event A: A + notA = 1.
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
A²-b²

19. If something is certain to happen - how is the probability of this event expressed mathematically?
The four big angles are equal and the four small angles are equal
Pir^2h
1/1
1/x^a

20. For a bell curve - what three terms might be used to describe the number in the middle?
2(pi)r(r+h)
Between 0 and 1.
The average - mean - median - or mode.
Opens down

21. What do combination problems usually ask for?
(pi)r^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
Groups - teams - or committees.
(n degrees/360) * 2(pi)r

22. Area of Circle
y-y1=m(x-x1)
Pi*r^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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

23. What is the side ratio for a Right Isosceles triangle?
Pi*d
(pi)r^2
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The average - mean - median - or mode.

24. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
Negative
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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

25. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
2l+2w
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.
Between 0 and 1.
S² - where s = length of a side

26. What is the average speed?
1/1
(y-y1)=m(x-x1)
Total distance/total time
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

27. Arc
y = kx
Part of a circle connecting two points on the circle.
1/2bh
1/1

28. What is the prime factorization of 200?
T1 + (n-1)d
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
A segment connecting the center of a circle to any point on the circle
2x2x2x5x5

29. Area of Square
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.
Pi*d
(n degrees/360) * 2(pi)r
S^2

30. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
A=bh
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
Probability A + Probability B

31. Perimeter of a square
4s (where s = length of a side)
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'.
1/1
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.

32. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
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.
2lw+2lh+2wh
(x+y)(x-y)

33. Define the mode of a set of numbers.
The distance from one point on the circle to another point on the circle.
Opens up
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.
(x-y)²

34. What is the factored version of (x+y)(x-y) ?
A segment connecting the center of a circle to any point on the circle
(pi)r^2(h)
x²-y²
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.

35. Circumference Formula
C =?d
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.
1
x°/360 times (?r²) - where x is the degrees in the angle

36. What is the volume of a cylinder?
Sum of the lengths of the sides
(n/2) * (t1+tn)
x²-y²
(pi)r^2(h)

37. Surface Area of Cylinder
(a-b)(a²+ab+b²)
A=?r2
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
2pir^2 + 2pir*h

38. Circumference of a circle using radius
The average - mean - median - or mode.
4s
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2pi*r

39. What is the surface area of a cylinder?
T1 * r^(n-1)
Groups - teams - or committees.
Lwh
2(pi)r(r+h)

40. How do you find the sum of a geometric sequence?
2l+2w
Middle term
T1 * r^(n-1)/(r-1)
2x2x2x5x5

41. 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.
x°/360 times (2 pi r) - where x is the degrees in the angle
(a+b)(a²-ab+b²)
2(pi)r

42. What is the length of an arc?
(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.
(n degrees/360) * 2(pi)r
(n degrees/360) * (pi)r^2

43. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
2(pi)r
N x M
Equal
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

44. (a+b)(a-b)=
A²-b²
The average - mean - median - or mode.
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
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.

45. In a parabola - if the first term is negative - the parabola ________.
y = k/x
Last term
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.
Opens down

46. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Lwh
(n-2)180
Pir^2h

47. When you reverse FOIL - the term that needs to multiply out is the _____
(0 -0)
Last term
The distance from one point on the circle to another point on the circle.
1.7

48. Diameter
(a+b)²
The distance across the circle through the center of the circle.The diameter is twice the radius.
Groups - teams - or committees.
The total # of possible outcomes.

49. Lines reflected over the x or y axis have ____ slopes.
The distance across the circle through the center of the circle.The diameter is twice the radius.
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.
Negative
y = kx

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

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