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GRE Math 2

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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. Surface Area of Sphere
4s
The distance across the circle through the center of the circle.The diameter is twice the radius.
4pir^2
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.

2. (a+b)(c+d)
Ac+ad+bc+bd
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.
Lwh
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

3. How do you find the slope?
4s (where s = length of a side)
Sum of the lengths of the sides
y2-y1/x2-x1
Bh

4. Rough est. of v3 =
y = kx
1.7
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.
2x2x2x5x5

5. a²-b²
x² + 2xy + y²
(a-b)(a+b)
Sum of terms/number of terms
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.

6. Define 'proportionate' values
?r²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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'.
C =?d

7. x^-a =
1/x^a
A segment connecting the center of a circle to any point on the circle
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-b)(a+b)

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

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9. How do you calculate the surface area of a rectangular box?
S² - where s = length of a side
?d OR 2?r
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.
1.4

10. What is the side ratio for a 30:60:90 triangle?
A=?r2
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1.4
A=bh

11. How do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2pi*r
Probability A + Probability B
Order does matter for a permutation - but does not matter for a combination.

12. Circumference Formula
x² -2xy + y²
4pir^2
C =?d
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

13. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
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'.
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.
Groups - teams - or committees.

14. What is the unfactored version of (x+y)² ?
2x2x2x5x5
x² + 2xy + y²
4s
C =?d

15. How do you solve a permutation?
1/1
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.
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
(n/2) * (t1+tn)

16. Diameter
1/2bh
The distance across the circle through the center of the circle.The diameter is twice the radius.
A=?r2
Pir^2h

17. Surface Area of rectangular prism
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.
(pi)r^2(h)
2lw+2lh+2wh
y-y1=m(x-x1)

18. What is inversely proportional?
S^2
y = k/x
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/x^a

19. How do you multiply and divide square roots?
Probability A + Probability B
(a+b)²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2x2x2x5x5

20. length of a 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.
x°/360 times (2 pi r) - where x is the degrees in the angle
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.
Probability A * Probability B

21. What is the 'distributive law'?
(a-b)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.
Last term
Number of desired outcomes/number of total outcomes

22. a² - b² is equal to
(a+b)(a-b)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
Arrangements - orders - schedules - or lists.

23. Area of Circles
2 pi r
The four big angles are equal and the four small angles are equal
A=?r2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

24. What number goes on the bottom of a probability fraction?
(a-b)(a²+ab+b²)
T1 * r^(n-1)/(r-1)
The total # of possible outcomes.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

25. How do you calculate the percentage of change?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
x°/360 times (?r²) - where x is the degrees in the angle
Percentage Change = Difference/Original * 100
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

26. What'S the most important thing to remember about charts you'll see on the GRE?
(0 -0)
Probability A * Probability B
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.
C =?d

27. Chord
1/2bh
1/x^a
1.4
The distance from one point on the circle to another point on the circle.

28. If something is certain to happen - how is the probability of this event expressed mathematically?
1. Given event A: A + notA = 1.
T1 * r^(n-1)/(r-1)
x°/360 times (?r²) - where x is the degrees in the angle
1/1

29. Perimeter of rectangle
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(a-b)(a+b)
Opens down
2l+2w

30. In a parabola - if the first term is positive - the parabola ________.
Opens up
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.
1/1
Total distance/total time

31. What is the area of a solid rectangle?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Negative
2(lw+wh+lh)
2Length + 2width [or (length + width) x 2]

32. What is the factored version of x² + 2xy + y² ?
Opens down
x² -2xy + y²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(x+y)²

33. Lines reflected over the x or y axis have ____ slopes.
y2-y1/x2-x1
1. Given event A: A + notA = 1.
1
Negative

34. What is the volume of a solid rectangle?
Negative
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
A=?r2
Lwh

35. Area of a circle
½(base x height) [or (base x height)÷2]
?r²
Sum of terms/number of terms
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'.

36. Circle
The set of points which are all the same distance (the radius) from a certain point (the center).
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 formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(x1+x2)/2 - (y1+y2)/2

37. Quadratic Formula
b±[vb²-4ac]/2a
4/3pir^3
2pi*r
2l+2w

38. How do you find the nth term of a geometric sequence?
The average - mean - median - or mode.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
T1 * r^(n-1)

39. How do you find the sum of an arithmetic sequence?
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.
(n degrees/360) * (pi)r^2
(n/2) * (t1+tn)
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.

40. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
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'.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Middle term

41. Circumference of a circle
?d OR 2?r
Arrangements - orders - schedules - or lists.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1/3Bh

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

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43. What is the side ratio for a Right Isosceles triangle?
An ange whose vertex is the center of 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.
Ac+ad+bc+bd
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

44. What are the side ratios for a 30:60:90 triangle?
2l+2w
Less
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

45. List two odd behaviors of exponents
(x1+x2)/2 - (y1+y2)/2
Probability A * Probability B
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.
S² - where s = length of a side

46. (a+b)(a-b)=
Opens down
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.
The total # of possible outcomes.
A²-b²

47. What is the area of a sector?
A=bh
(pi)r^2(h)
Arrangements - orders - schedules - or lists.
(n degrees/360) * (pi)r^2

48. x^a * x^b = x^__
4s
Sum of the lengths of the sides
A+b
Opens up

49. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2(lw+wh+lh)
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
½(base x height) [or (base x height)÷2]

50. What is the area of a cylinder?
2(pi)r
S² - where s = length of a side
1/x^a
2(pi)r(r+h)

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GRE Math 2

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