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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. Surface Area of rectangular prism
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'.
2lw+2lh+2wh
Ac+ad+bc+bd
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

2. What is the distance formula?
1.4
The distance from one point on the circle to another point on the circle.
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.
Sqr( x2 -x1) + (y2- y1)

3. Area of a square
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
S² - where s = length of a side
S^2

4. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
T1 * r^(n-1)/(r-1)
A=?r2
(a+b)(a²-ab+b²)

5. a²-2ab+b²
Order does matter for a permutation - but does not matter for a combination.
Probability A + Probability B
4pir^2
(a-b)²

6. Perimeter (circumference) of a circle
2 pi r
(x+y)(x-y)
1.4
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

7. What is the formula for the diagonal of any square?
(x1+x2)/2 - (y1+y2)/2
b±[vb²-4ac]/2a
(n-2)180
S*v2

8. x^a * x^b = x^__
A+b
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
Middle term
1/3pir^2*h

9. What is the probability?
(x+y)(x-y)
y2-y1/x2-x1
Lwh
Number of desired outcomes/number of total outcomes

10. Area of rectangle - square - parallelogram
Not necessarily. This is a trick question - because x could be either positive or negative.
A=?r2
S*v2
A=bh

11. Surface Area of Cylinder
2lw+2lh+2wh
2pir^2 + 2pir*h
1/3Bh
Lw

12. What'S the most important thing to remember about charts you'll see on the GRE?
1
2(pi)r(r+h)
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.
Arrangements - orders - schedules - or lists.

13. Explain the difference between a digit and a number.

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14. What is the average speed?
2(pi)r
S*v2
Total distance/total time
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

15. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.

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16. What is the length of an arc?
(n degrees/360) * 2(pi)r
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.
2(pi)r(r+h)
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.

17. What number goes on the bottom of a probability fraction?
Last term
The total # of possible outcomes.
(a-b)(a+b)
y = kx

18. What is a '30:60:90' triangle?
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
Part of a circle connecting two points on the circle.
1/3pir^2*h
y-y1=m(x-x1)

19. Arc
An ange whose vertex is the center of the circle
Part of a circle connecting two points on the circle.
The four big angles are equal and the four small angles are equal
Pi*d

20. How do you find the sum of a geometric sequence?
Number of desired outcomes/number of total outcomes
(n-2)180
T1 * r^(n-1)/(r-1)
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

21. Perimeter of polygon
Between 0 and 1.
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.
Pi*r^2
Sum of the lengths of the sides

22. How do you calculate a diagonal inside a 3-dimensional rectangular box?
T1 * r^(n-1)/(r-1)
Total distance/total time
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.

23. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
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.
Sqr( x2 -x1) + (y2- y1)
N x M
1/3pir^2*h

24. Area of Parallelogram
(a+b)²
Bh
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A²-b²

25. How do you solve a permutation?
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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x°/360 times (2 pi r) - where x is the degrees in the angle
2lw+2lh+2wh

26. What do combination problems usually ask for?
Groups - teams - or committees.
y2-y1/x2-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
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.

27. What is the area of a solid rectangle?
2(lw+wh+lh)
(a-b)(a²+ab+b²)
Sqr( x2 -x1) + (y2- y1)
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.

28. The length of one side of any triangle is ____ than the sum of the other two sides.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Less
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.

29. Explain the special properties of zero.
Probability A * Probability B
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

30. What is the area of a cylinder?
Arrangements - orders - schedules - or lists.
Order does matter for a permutation - but does not matter for a combination.
x² -2xy + y²
2(pi)r(r+h)

31. In a parabola - if the first term is negative - the parabola ________.
Middle term
y-y1=m(x-x1)
S² - where s = length of a side
Opens down

32. What is the area of a sector?
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.
(n degrees/360) * (pi)r^2
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 average - mean - median - or mode.

33. How do you find the sum of an arithmetic sequence?
Bh
N x M
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
(n/2) * (t1+tn)

34. Lines reflected over the x or y axis have ____ slopes.
(x+y)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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Negative

35. Define the formula for calculating slope.
x² + 2xy + y²
The four big angles are equal and the four small angles are equal
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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

36. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
(x1+x2)/2 - (y1+y2)/2
S² - where s = length of a side
1/2 h (b1 + b2)

37. What is the side ratio for a 30:60:90 triangle?
(0 -0)
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.
2 pi r
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

38. Area of Square
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.
Between 0 and 1.
S^2
The distance across the circle through the center of the circle.The diameter is twice the radius.

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

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40. (a+b)(c+d)
Probability A + Probability B
Ac+ad+bc+bd
Pir^2h
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

41. What is the point-slope form?
2(pi)r(r+h)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(y-y1)=m(x-x1)
4s

42. In a coordinate system - identify the quadrants and describe their location.
4/3pir^3
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Bh
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.

43. What is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A=bh
A=?r2
(x+y)(x-y)

44. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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
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.
Part of a circle connecting two points on the circle.
1/2bh

45. For a bell curve - what three terms might be used to describe the number in the middle?
(pi)r^2(h)
The average - mean - median - or mode.
x°/360 times (2 pi r) - where x is the degrees in the angle
4s

46. Point-Slope form
1/2bh
2pir^2 + 2pir*h
y-y1=m(x-x1)
Pi*r^2

47. Volume of sphere
(a-b)(a+b)
4/3pir^3
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.
Number of desired outcomes/number of total outcomes

48. a² - b² is equal to
Not necessarily. This is a trick question - because x could be either positive or negative.
(x+y)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.
(a+b)(a-b)

49. In a parabola - if the first term is positive - the parabola ________.
Opens up
4/3pir^3
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.
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'.

50. To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(a-b)(a+b)
Probability A + Probability B
A+b