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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 multiply powers with the same base?
y = k/x
(a-b)(a²+ab+b²)
x²-y²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

2. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
(a-b)(a+b)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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.
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.

3. What is the point-slope form?
(y-y1)=m(x-x1)
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
Probability A + Probability B
4s (where s = length of a side)

4. In intersecting lines - opposite angles are _____.
Equal
A=?r2
(y-y1)=m(x-x1)
Sum of terms/number of terms

5. What is an 'equilateral' triangle?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Pi*d
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

6. Define 'proportionate' values
1. Given event A: A + notA = 1.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Middle term

7. What is the unfactored version of x²-y² ?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2l+2w
(x+y)(x-y)
2(pi)r

8. What is the surface area of a cylinder?
Not necessarily. This is a trick question - because x could be either positive or negative.
2(pi)r(r+h)
The average - mean - median - or mode.
2(pi)r

9. What is the unfactored version of (x+y)² ?
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 + 2xy + y²
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.
Order does matter for a permutation - but does not matter for a combination.

10. 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.
The set of points which are all the same distance (the radius) from a certain point (the center).
Opens up
(y-y1)=m(x-x1)

11. When a line crosses two parallel lines - ________.
y-y1=m(x-x1)
The four big angles are equal and the four small angles are equal
(x+y)(x-y)
(0 -0)

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

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13. If x² = 144 - does v144 = x?
Pi*r^2
Lwh
Not necessarily. This is a trick question - because x could be either positive or negative.
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.

14. The length of one side of any triangle is ____ than the sum of the other two sides.
Less
1/2bh
2Length + 2width [or (length + width) x 2]
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'.

15. Define the range of a set of numbers.
Equal
1.7
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.
1/2bh

16. 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.
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.
Opens up
1/1

17. Volume of Cone
(x1+x2)/2 - (y1+y2)/2
Probability A + Probability B
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.
1/3pir^2*h

18. What is the area of a solid rectangle?
2(lw+wh+lh)
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.
½(base x height) [or (base x height)÷2]
Sum of terms/number of terms

19. What is the volume of a cylinder?
(pi)r^2(h)
An ange whose vertex is the center of the circle
1/x^a
1/1

20. What is the sum of the inside angles of an n-sided polygon?
Negative
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.
(n-2)180
Middle term

21. What is the unfactored version of (x-y)² ?
2(pi)r
Not necessarily. This is a trick question - because x could be either positive or negative.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
x² -2xy + y²

22. Perimeter of a square
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'.
4s (where s = length of a side)
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.
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.

23. How do you find the nth term of a geometric sequence?
Probability A * Probability B
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.
T1 * r^(n-1)
Probability A + Probability B

24. Area of a triangle
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.
(y2-y1)/(x2-x1)
½(base x height) [or (base x height)÷2]
2l+2w

25. How do you find the sum of a geometric sequence?
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
The four big angles are equal and the four small angles are equal
T1 * r^(n-1)/(r-1)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

26. How do you find the sum of an arithmetic sequence?
(n/2) * (t1+tn)
A+b
The distance from one point on the circle to another point on the circle.
A=?r2

27. What is a '30:60:90' triangle?
x°/360 times (2 pi r) - where x is the degrees in the angle
2(lw+wh+lh)
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
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

28. Area of a square
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.
2(lw+wh+lh)
y = kx
S² - where s = length of a side

29. Rough est. of v2 =
T1 * r^(n-1)/(r-1)
1.4
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.
Sum of terms/number of terms

30. Volume of pyramid
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.
1/3Bh
Bh
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.

31. What is the area of a triangle?
1/2bh
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
Probability A + Probability B
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.

32. Define the mode of a set of numbers.
2lw+2lh+2wh
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
T1 * r^(n-1)/(r-1)
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.

33. Explain the special properties of zero.
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.
The distance from one point on the circle to another point on the circle.
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.

34. When you reverse FOIL - the term that needs to add out is the _____
Middle term
1/2bh
?r²
Lw

35. Area of a trapezoid
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Opens down
Between 0 and 1.

36. Slope
S*v2
1/2bh
(y2-y1)/(x2-x1)
y-y1=m(x-x1)

37. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
An ange whose vertex is the center of the circle
Probability A * Probability B
Arrangements - orders - schedules - or lists.

38. What is the area of a cylinder?
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
(y-y1)=m(x-x1)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2(pi)r(r+h)

39. Area of Rectangle
2x2x2x5x5
(x1+x2)/2 - (y1+y2)/2
Lw
The distance across the circle through the center of the circle.The diameter is twice the radius.

40. In a parabola - if the first term is positive - the parabola ________.
x°/360 times (?r²) - where x is the degrees in the angle
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Opens up
(a+b)²

41. For a bell curve - what three terms might be used to describe the number in the middle?
Lwh
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.
Probability A + Probability B
The average - mean - median - or mode.

42. Quadratic Formula
Bh
Lwh
b±[vb²-4ac]/2a
An ange whose vertex is the center of the circle

43. How do you calculate the percentage of change?
2 pi r
(n degrees/360) * 2(pi)r
Arrangements - orders - schedules - or lists.
Percentage Change = Difference/Original * 100

44. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Negative
(x+y)(x-y)
(pi)r^2
Probability A + Probability B

45. Perimeter of rectangle
The distance from one point on the circle to another point on the circle.
?d OR 2?r
Total distance/total time
2l+2w

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

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47. How do you calculate a diagonal inside a 3-dimensional rectangular box?
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

48. Central Angle
An ange whose vertex is the center of the circle
2lw+2lh+2wh
(x-y)²
S*v2

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

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50. Area of Triangle
The total # of possible outcomes.
?r²
1/2bh
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.