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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. Define the range of a set of numbers.
(x-y)²
x°/360 times (2 pi r) - where x is the degrees in the angle
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.
4s

2. Diameter
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Number of desired outcomes/number of total outcomes
The distance across the circle through the center of the circle.The diameter is twice the radius.
2pi*r

3. What is the distance formula?
1/3Bh
Not necessarily. This is a trick question - because x could be either positive or negative.
(pi)r^2
Sqr( x2 -x1) + (y2- y1)

4. What is the length of an arc?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Negative
x°/360 times (2 pi r) - where x is the degrees in the angle
(n degrees/360) * 2(pi)r

5. 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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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

6. In a coordinate system - what is the origin?
1/2bh
(0 -0)
x²-y²
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'.

7. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Bh
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.
2(pi)r
(x1+x2)/2 - (y1+y2)/2

8. What is an 'equilateral' triangle?
Middle term
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
x² -2xy + y²

9. What is the side ratio 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 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.
4/3pir^3
Not necessarily. This is a trick question - because x could be either positive or negative.

10. Arc
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
Not necessarily. This is a trick question - because x could be either positive or negative.
?r²
Part of a circle connecting two points on the circle.

11. Rough est. of v2 =
An ange whose vertex is the center of the circle
1.4
(a+b)²
y = k/x

12. How do you calculate the surface area of a rectangular box?
1.7
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(x1+x2)/2 - (y1+y2)/2

13. What is the equation of a line?

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14. Rough est. of v3 =
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) * (t1+tn)
y = kx
1.7

15. (a+b)(c+d)
T1 * r^(n-1)
(a+b)(a²-ab+b²)
Ac+ad+bc+bd
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.

16. Perimeter of a rectangle
Opens down
2(pi)r
1/3Bh
2Length + 2width [or (length + width) x 2]

17. In intersecting lines - opposite angles are _____.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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
Equal
T1 * r^(n-1)/(r-1)

18. x^a * x^b = x^__
Percentage Change = Difference/Original * 100
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.
A+b
S² - where s = length of a side

19. What is the factored version of (x+y)(x-y) ?
2(lw+wh+lh)
x²-y²
Middle term
The four big angles are equal and the four small angles are equal

20. Area of Circle
Pi*r^2
A segment connecting the center of a circle to any point on the circle
2pir^2 + 2pir*h
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

21. What is the average?
Sum of terms/number of terms
(x1+x2)/2 - (y1+y2)/2
x² + 2xy + y²
y = kx

22. Quadratic Formula
1/x^a
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
4s (where s = length of a side)
b±[vb²-4ac]/2a

23. What is the 'Third side' rule for triangles?
(pi)r^2
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
Pi*r^2

24. Circumference of a circle using radius
2pi*r
C =?d
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.
2(lw+wh+lh)

25. What is the unfactored version of 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.
½(base x height) [or (base x height)÷2]
(x+y)(x-y)
Last term

26. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Pi*r^2
Total distance/total time
(a+b)²
1. Given event A: A + notA = 1.

27. How do you find the nth term of an arithmetic sequence?
2(lw+wh+lh)
T1 + (n-1)d
A+b
A=bh

28. Explain the special properties of zero.
The distance across the circle through the center of the circle.The diameter is twice the radius.
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.
A+b
2 pi r

29. When you reverse FOIL - the term that needs to multiply out is the _____
y = kx
?d OR 2?r
Last term
(x+y)(x-y)

30. Chord
2pir^2 + 2pir*h
Number of desired outcomes/number of total outcomes
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.
The distance from one point on the circle to another point on the circle.

31. Area of Rectangle
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Lw
y2-y1/x2-x1

32. How do you find the nth term of a geometric sequence?
T1 * r^(n-1)
T1 * r^(n-1)/(r-1)
Opens up
(n degrees/360) * 2(pi)r

33. Lines reflected over the x or y axis have ____ slopes.
(n-2)180
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.
Negative
(pi)r^2

34. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
2x2x2x5x5
(a+b)²
The distance across the circle through the center of the circle.The diameter is twice the radius.

35. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

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36. How do you find the sum of a geometric sequence?
T1 * r^(n-1)/(r-1)
Not necessarily. This is a trick question - because x could be either positive or negative.
(n degrees/360) * (pi)r^2
x°/360 times (2 pi r) - where x is the degrees in the angle

37. If something is certain to happen - how is the probability of this event expressed mathematically?
(n-2)180
An ange whose vertex is the center of the circle
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.
1/1

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

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39. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
(x+y)(x-y)
4/3pir^3
(n/2) * (t1+tn)
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.

40. Area of a trapezoid
2x2x2x5x5
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Less
Pi*d

41. The length of one side of any triangle is ____ than the sum of the other two sides.
Less
y = kx
Part of a circle connecting two points on the circle.
1/2bh

42. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
A=?r2
(a-b)²
1/2bh

43. Define 'proportionate' values
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Lw
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
4s (where s = length of a side)

44. What is the side ratio for a Right Isosceles triangle?
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
4s (where s = length of a side)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(n degrees/360) * 2(pi)r

45. Surface Area of rectangular prism
2lw+2lh+2wh
Sum of the lengths of the sides
C =?d
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

46. Volume of sphere
4/3pir^3
(a+b)(a-b)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1.7

47. What is the point-slope form?
(y-y1)=m(x-x1)
A=bh
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 = k/x

48. What is the area of a triangle?
(n degrees/360) * (pi)r^2
The set of points which are all the same distance (the radius) from a certain point (the center).
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.
1/2bh

49. a²-2ab+b²
2lw+2lh+2wh
(a-b)²
Bh
(n degrees/360) * (pi)r^2

50. How do you find the midpoint?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A segment connecting the center of a circle to any point on the circle
(x1+x2)/2 - (y1+y2)/2
Order does matter for a permutation - but does not matter for a combination.