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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 factored version of x² -2xy + y² ?
y = kx
(x-y)²
Equal
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

2. How do you calculate the surface area of a rectangular box?
2Length + 2width [or (length + width) x 2]
2l+2w
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.
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.

3. Circle
1.7
A+b
The set of points which are all the same distance (the radius) from a certain point (the center).
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.

4. What number goes on the bottom of a probability fraction?
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
The total # of possible outcomes.
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.

5. How do you multiply powers with the same base?
Probability A + Probability B
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Lw
(x-y)²

6. What is inversely proportional?
y = k/x
Equal
y-y1=m(x-x1)
(a-b)(a²+ab+b²)

7. Area of Trapezoid
y = k/x
1/2 h (b1 + b2)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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

8. Volume of sphere
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
4/3pir^3
2pi*r

9. Surface Area of Sphere
S² - where s = length of a side
S^2
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

10. Diameter
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
x²-y²
?d OR 2?r
The distance across the circle through the center of the circle.The diameter is twice the radius.

11. What'S the most important thing to remember about charts you'll see on the GRE?
(pi)r^2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1.7
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.

12. What is the point-slope form?
Pi*d
(y-y1)=m(x-x1)
(n degrees/360) * 2(pi)r
Probability A * Probability B

13. Perimeter (circumference) of a circle
2 pi r
2pir^2 + 2pir*h
Not necessarily. This is a trick question - because x could be either positive or negative.
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.

14. Area of a square
S² - where s = length of a side
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.
Less
The distance from one point on the circle to another point on the circle.

15. What is the probability?
(y2-y1)/(x2-x1)
Opens down
1/3pir^2*h
Number of desired outcomes/number of total outcomes

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

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17. How do you multiply and divide square roots?
(n-2)180
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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(lw+wh+lh)

18. What is the distance formula?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Sqr( x2 -x1) + (y2- y1)
(a-b)(a²+ab+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.

19. Define the formula for calculating slope.
1/3Bh
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2 pi r
N x M

20. Area of a circle
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
?r²
(x1+x2)/2 - (y1+y2)/2
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

21. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
(a+b)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.
S^2
Ac+ad+bc+bd

22. Area of a triangle
2(pi)r(r+h)
½(base x height) [or (base x height)÷2]
1/3pir^2*h
1. Given event A: A + notA = 1.

23. 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.
Pi*d
C =?d
2Length + 2width [or (length + width) x 2]

24. a²-b²
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.
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)
2(pi)r(r+h)

25. What is the volume of a solid rectangle?
(n-2)180
x² -2xy + y²
Lwh
T1 * r^(n-1)/(r-1)

26. What is the prime factorization of 200?
?r²
2x2x2x5x5
A=?r2
Opens up

27. Central Angle
1/2bh
An ange whose vertex is the center of the circle
2(lw+wh+lh)
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.

28. What is the average speed?
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.
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'.
Total distance/total time
½(base x height) [or (base x height)÷2]

29. If x² = 144 - does v144 = x?
(a-b)(a+b)
2 pi r
Not necessarily. This is a trick question - because x could be either positive or negative.
A+b

30. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
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.
2lw+2lh+2wh
Probability A + Probability B
(x-y)²

31. Sector
(x+y)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.
Lwh
(a+b)(a²-ab+b²)

32. Define the mode of a set of numbers.
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.
2(pi)r
2 pi r
y2-y1/x2-x1

33. Perimeter of a rectangle
S² - where s = length of a side
x°/360 times (2 pi r) - where x is the degrees in the angle
2Length + 2width [or (length + width) x 2]
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

34. Circumference of a circle
The average - mean - median - or mode.
S² - where s = length of a side
?d OR 2?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.

35. a²+2ab+b²
(a+b)²
Pir^2h
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
(a-b)(a²+ab+b²)

36. What is the area of a cylinder?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
b±[vb²-4ac]/2a
1/3Bh
2(pi)r(r+h)

37. Volume of pyramid
A+b
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.
Number of desired outcomes/number of total outcomes
1/3Bh

38. What is an 'equilateral' triangle?
2x2x2x5x5
(x+y)²
The distance across the circle through the center of the circle.The diameter is twice the radius.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

39. Area of rectangle - square - parallelogram
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Opens down
(y2-y1)/(x2-x1)
A=bh

40. Area of a trapezoid
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Lw
1/3pir^2*h

41. (a+b)(c+d)
Ac+ad+bc+bd
2(pi)r(r+h)
Order does matter for a permutation - but does not matter for a combination.
A segment connecting the center of a circle to any point on the circle

42. What is the 'distributive law'?
1/2bh
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(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.
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.

43. a²-2ab+b²
(a-b)²
Part of a circle connecting two points on the circle.
1/x^a
2pir^2 + 2pir*h

44. How do you calculate the percentage of change?
(n degrees/360) * (pi)r^2
Percentage Change = Difference/Original * 100
N x M
1/2 h (b1 + b2)

45. Perimeter of a square
(a-b)(a²+ab+b²)
(n/2) * (t1+tn)
(pi)r^2(h)
4s (where s = length of a side)

46. x^a * x^b = x^__
Bh
A+b
Sum of terms/number of terms
(a-b)(a²+ab+b²)

47. Explain the special properties of zero.
Probability A + Probability B
x²-y²
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.
An ange whose vertex is the center of the circle

48. Define 'proportionate' values
Groups - teams - or committees.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
T1 * r^(n-1)/(r-1)
y2-y1/x2-x1

49. How do you find the sum of an arithmetic sequence?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(a-b)(a²+ab+b²)
(n/2) * (t1+tn)

50. What is the unfactored version of (x-y)² ?
T1 * r^(n-1)
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
x² -2xy + y²
Opens down