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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. a³-b³
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(a-b)(a²+ab+b²)
2l+2w
2 pi r

2. The length of one side of any triangle is ____ than the sum of the other two sides.
2l+2w
Less
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
An ange whose vertex is the center of the circle

3. Perimeter of a square
x² -2xy + y²
4s (where s = length of a side)
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.
T1 * r^(n-1)/(r-1)

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.
(n-2)180
2Length + 2width [or (length + width) x 2]
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.

5. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.

6. To divide powers with the same base...
2l+2w
2 pi r
Part of a circle connecting two points on the circle.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

7. How do you find the nth term of a geometric 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.
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
1/2 h (b1 + b2)
T1 * r^(n-1)

8. In a parabola - if the first term is negative - the parabola ________.
Opens down
Order does matter for a permutation - but does not matter for a combination.
Sum of the lengths of the sides
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

9. In a parabola - if the first term is positive - the parabola ________.
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.
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
Opens up

10. Volume of Cylinder
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.
Pir^2h
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.
1.7

11. When you reverse FOIL - the term that needs to add out is the _____
1.7
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
Middle term

12. What is the distance formula?
1/1
b±[vb²-4ac]/2a
Sqr( x2 -x1) + (y2- y1)
(a-b)²

13. What is the prime factorization of 200?
2x2x2x5x5
(a+b)²
Arrangements - orders - schedules - or lists.
1. Given event A: A + notA = 1.

14. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
Sum of terms/number of terms
The four big angles are equal and the four small angles are equal
x² -2xy + y²

15. Arc
2lw+2lh+2wh
Part of a circle connecting two points on the circle.
An ange whose vertex is the center of the circle
4s (where s = length of a side)

16. 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.
1/1
1/3pir^2*h
The distance from one point on the circle to another point on the circle.

17. How do you calculate the surface area of a rectangular box?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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.
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]

18. What is the factored version of x² + 2xy + y² ?
(pi)r^2
Lwh
(x+y)²
Pi*r^2

19. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
Not necessarily. This is a trick question - because x could be either positive or negative.
A=bh
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.

20. What is the area of a cylinder?
Sum of terms/number of terms
(y-y1)=m(x-x1)
2(pi)r(r+h)
1. Given event A: A + notA = 1.

21. Rough est. of v2 =
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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'.
y = k/x
1.4

22. What number goes on the bottom of a probability fraction?
y = k/x
1/3Bh
The total # of possible outcomes.
2(pi)r(r+h)

23. What is the factored version of (x+y)(x-y) ?
(pi)r^2
Ac+ad+bc+bd
Lwh
x²-y²

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.
(pi)r^2
½(base x height) [or (base x height)÷2]
2x2x2x5x5

25. x^a * x^b = x^__
2(lw+wh+lh)
(y2-y1)/(x2-x1)
(x-y)²
A+b

26. Area of a circle
y2-y1/x2-x1
?r²
Less
T1 + (n-1)d

27. What is the factored version of x² -2xy + y² ?
(pi)r^2
Bh
1/3pir^2*h
(x-y)²

28. What is the sum of the inside angles of an n-sided polygon?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(n-2)180
N x M
½(b1 +b2) x h [or (b1 +b2) x h÷2]

29. Area of rectangle - square - parallelogram
A=bh
(x+y)(x-y)
4s
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

30. (a+b)(c+d)
The four big angles are equal and the four small angles are equal
y = k/x
Groups - teams - or committees.
Ac+ad+bc+bd

31. Slope
(a-b)²
(y2-y1)/(x2-x1)
Opens down
1/1

32. Perimeter (circumference) of a circle
Pir^2h
2 pi r
Not necessarily. This is a trick question - because x could be either positive or negative.
Opens down

33. How do you find the sum of a geometric sequence?
S² - where s = length of a side
T1 * r^(n-1)/(r-1)
2x2x2x5x5
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

34. How do you solve a permutation?
(x-y)²
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
Bh
Pi*r^2

35. What are the side ratios for a 30:60:90 triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
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.
Sum of terms/number of terms

36. Lines reflected over the x or y axis have ____ slopes.
Negative
Sqr( x2 -x1) + (y2- y1)
b±[vb²-4ac]/2a
The total # of possible outcomes.

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

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38. Surface Area of Cylinder
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
A+b
2pir^2 + 2pir*h
1/2bh

39. How do you calculate a diagonal inside a 3-dimensional rectangular box?
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.
(x+y)²
Last term
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

40. What'S the most important thing to remember about charts you'll see on the GRE?
1/2bh
The set of points which are all the same distance (the radius) from a certain point (the center).
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.
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.

41. Define the range of a set of numbers.
?d OR 2?r
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.
C =?d

42. a³+b³
A=bh
The distance from one point on the circle to another point on the circle.
(a+b)(a²-ab+b²)
4pir^2

43. How do you find the sum of an arithmetic sequence?
2l+2w
4s (where s = length of a side)
(n/2) * (t1+tn)
Equal

44. For a bell curve - what three terms might be used to describe the number in the middle?
4s
Equal
Negative
The average - mean - median - or mode.

45. Circumference of a circle using radius
Last term
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2pi*r
A²-b²

46. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
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.
Groups - teams - or committees.

47. Area of a square
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.
1/1
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

48. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
Between 0 and 1.
Less
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

49. a²-2ab+b²
(a-b)²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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'.
Between 0 and 1.

50. How do you multiply and divide square roots?
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.
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.
Pir^2h