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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 circumference of a circle?
T1 * r^(n-1)/(r-1)
(a+b)²
2(pi)r
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.

2. How do you find the midpoint?
2 pi r
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(x1+x2)/2 - (y1+y2)/2
1/3Bh

3. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
y-y1=m(x-x1)
4/3pir^3
(n degrees/360) * (pi)r^2

4. What is the 'Third side' rule for triangles?
x°/360 times (?r²) - where x is the degrees in the angle
Arrangements - orders - schedules - or lists.
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.
C =?d

5. Rough est. of v1 =
1
T1 * r^(n-1)/(r-1)
Last term
Order does matter for a permutation - but does not matter for a combination.

6. Central Angle
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.
Opens down
(x1+x2)/2 - (y1+y2)/2
An ange whose vertex is the center of the circle

7. perimeter of square
4s
An ange whose vertex is the center of the circle
2Length + 2width [or (length + width) x 2]
(a+b)²

8. Volume of Cylinder
A=?r2
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Pir^2h
x°/360 times (?r²) - where x is the degrees in the angle

9. Area of Parallelogram
Bh
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. 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.
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.

10. Area of Trapezoid
A=?r2
1/2 h (b1 + b2)
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 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.

11. How do you calculate the percentage of change?
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
Percentage Change = Difference/Original * 100
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

12. What do combination problems usually ask for?
Groups - teams - or committees.
(a+b)²
1/3pir^2*h
½(b1 +b2) x h [or (b1 +b2) x h÷2]

13. Area of a triangle
C =?d
The set of points which are all the same distance (the radius) from a certain point (the center).
½(base x height) [or (base x height)÷2]
Probability A * Probability B

14. Circle
y2-y1/x2-x1
The set of points which are all the same distance (the radius) from a certain point (the center).
(a-b)(a+b)
x°/360 times (?r²) - where x is the degrees in the angle

15. Area of a trapezoid
2(pi)r
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(n/2) * (t1+tn)
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. Lines reflected over the x or y axis have ____ slopes.
Negative
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'.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

17. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
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.
(a-b)(a²+ab+b²)
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.

18. Circumference of a circle using radius
Part of a circle connecting two points on the circle.
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.
x² + 2xy + y²
2pi*r

19. a² - b² is equal to
T1 + (n-1)d
(a+b)(a-b)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

20. What is the factored version of (x+y)(x-y) ?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x²-y²
(a-b)²
x°/360 times (2 pi r) - where x is the degrees in the angle

21. length of a sector
(x1+x2)/2 - (y1+y2)/2
x°/360 times (2 pi r) - where x is the degrees in the angle
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.
x²-y²

22. What is the distance formula?
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
Sqr( x2 -x1) + (y2- y1)
Lw
Less

23. What is the unfactored version of (x-y)² ?
x² -2xy + 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'.
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.
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.

24. What is the factored version of x² + 2xy + y² ?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
(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.

25. What is the volume of a solid rectangle?
S^2
(pi)r^2(h)
Lwh
C =?d

26. Point-Slope form
y-y1=m(x-x1)
2x2x2x5x5
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Pi*d

27. What is the formula for the diagonal of any square?
1/2 h (b1 + b2)
The total # of possible outcomes.
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.
S*v2

28. Circumference of a circle
1/2bh
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.
?d OR 2?r
T1 + (n-1)d

29. How do you calculate the surface area of a rectangular box?
Pir^2h
4s
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
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.

30. Define a factorial of a number - and how it is written.
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.
Part of a circle connecting two points on the circle.
(n/2) * (t1+tn)
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'.

31. How do you multiply powers with the same base?
(a-b)(a²+ab+b²)
The distance from one point on the circle to another point on the circle.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.

32. What is inversely proportional?
y = k/x
2l+2w
(pi)r^2(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.

33. a²-b²
1. Given event A: A + notA = 1.
(a-b)(a+b)
S*v2
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

34. Perimeter of a rectangle
Sum of the lengths of the sides
x² -2xy + y²
Equal
2Length + 2width [or (length + width) x 2]

35. Quadratic Formula
Negative
b±[vb²-4ac]/2a
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

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

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37. What is the side ratio for a Right Isosceles triangle?
1/x^a
(a-b)(a²+ab+b²)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
?d OR 2?r

38. Volume of prism
(x1+x2)/2 - (y1+y2)/2
Bh
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.
Order does matter for a permutation - but does not matter for a combination.

39. Circumference of cirlce using diameter
(a+b)²
The total # of possible outcomes.
(n/2) * (t1+tn)
Pi*d

40. Surface Area of Sphere
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Probability A * Probability 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
4pir^2

41. In a parabola - if the first term is positive - the parabola ________.
(y2-y1)/(x2-x1)
(y-y1)=m(x-x1)
Opens up
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

42. The length of one side of any triangle is ____ than the sum of the other two sides.
(n degrees/360) * 2(pi)r
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.
b±[vb²-4ac]/2a
Less

43. Area of a circle
Sqr( x2 -x1) + (y2- y1)
?r²
Sum of terms/number of terms
S^2

44. a²-2ab+b²
(a-b)²
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
4s (where s = length of a side)
Total distance/total time

45. What'S the most important thing to remember about charts you'll see on the GRE?
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
The four big angles are equal and the four small angles are equal
(x-y)²

46. What is the 'distributive law'?
T1 + (n-1)d
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.
Between 0 and 1.
Part of a circle connecting two points on the circle.

47. Perimeter of polygon
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
C =?d
Sum of the lengths of the sides
2(pi)r(r+h)

48. What do permutation problems often ask for?
y-y1=m(x-x1)
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
The distance from one point on the circle to another point on the circle.
Arrangements - orders - schedules - or lists.

49. Explain the special properties of zero.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
2Length + 2width [or (length + width) x 2]
x°/360 times (2 pi r) - where x is the degrees in the angle

50. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
(x1+x2)/2 - (y1+y2)/2
(n degrees/360) * (pi)r^2