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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 equation of a line?

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2. Circumference of a circle using radius
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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. Volume of Cylinder
Pir^2h
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.
(0 -0)
Percentage Change = Difference/Original * 100

4. Circumference of a circle
T1 * r^(n-1)/(r-1)
The distance across the circle through the center of the circle.The diameter is twice the radius.
(n-2)180
?d OR 2?r

5. Define the 'Third side' rule for triangles

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6. a³+b³
2(lw+wh+lh)
(x1+x2)/2 - (y1+y2)/2
1.7
(a+b)(a²-ab+b²)

7. To divide powers with the same base...
A segment connecting the center of a circle to any point on the circle
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2Length + 2width [or (length + width) x 2]
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.

8. What is a 'Right isosceles' triangle?
A=?r2
Lw
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.
Equal

9. How do you multiply powers with the same base?
1/x^a
4pir^2
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

10. When a line crosses two parallel lines - ________.
4/3pir^3
The four big angles are equal and the four small angles are equal
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
b±[vb²-4ac]/2a

11. Perimeter of polygon
Sum of the lengths of the sides
1/1
S² - where s = length of a side
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.

12. What is inversely proportional?
x²-y²
Opens down
y = k/x
The average - mean - median - or mode.

13. What must be true before a quadratic equation can be solved?

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14. Arc
y-y1=m(x-x1)
Part of a circle connecting two points on the circle.
1/2 h (b1 + b2)
Opens down

15. a²-2ab+b²
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.
(a-b)²
2l+2w
Lwh

16. Volume of prism
S^2
(0 -0)
Bh
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'.

17. The length of one side of any triangle is ____ than the sum of the other two sides.
Less
y = kx
y = k/x
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. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
Between 0 and 1.
T1 * r^(n-1)
(a+b)(a-b)

19. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Probability A + Probability 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.
2(pi)r
1/3Bh

20. What is the unfactored version of (x+y)² ?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The total # of possible outcomes.
x² + 2xy + y²
(x-y)²

21. Rough est. of v1 =
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.
(a-b)(a²+ab+b²)
1/2bh
1

22. Perimeter of a square
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
A+b
2x2x2x5x5
4s (where s = length of a side)

23. Area of Trapezoid
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
1/2 h (b1 + b2)
1/x^a
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

24. What do permutation problems often ask for?
2x2x2x5x5
Arrangements - orders - schedules - or lists.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Bh

25. What is the area of a circle?
N x M
(a+b)(a²-ab+b²)
(x-y)²
(pi)r^2

26. Volume of Cone
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Bh
Last term
1/3pir^2*h

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

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28. Perimeter of rectangle
Last term
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
2l+2w
2Length + 2width [or (length + width) x 2]

29. Lines reflected over the x or y axis have ____ slopes.
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.
Negative
Part of a circle connecting two points on the circle.
Lwh

30. How do you calculate a diagonal inside a 3-dimensional rectangular box?
Negative
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
x°/360 times (2 pi r) - where x is the degrees in the angle
2l+2w

31. What is an 'equilateral' triangle?
The four big angles are equal and the four small angles are equal
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

32. What do combination problems usually ask for?
Groups - teams - or committees.
2Length + 2width [or (length + width) x 2]
(a+b)²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

33. When you reverse FOIL - the term that needs to add out is the _____
Pi*r^2
Middle term
y = k/x
½(b1 +b2) x h [or (b1 +b2) x h÷2]

34. List two odd behaviors of exponents
A²-b²
4s
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.
2pir^2 + 2pir*h

35. What is the 'Third side' rule for triangles?
y-y1=m(x-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
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+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.

36. How do you solve a permutation?
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 ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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
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.

37. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
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.
2pir^2 + 2pir*h

38. 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.
(a+b)²
Part of a circle connecting two points on the circle.
The set of points which are all the same distance (the radius) from a certain point (the center).

39. What is the average?
Sum of terms/number of terms
2pir^2 + 2pir*h
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(a-b)(a+b)

40. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Sqr( x2 -x1) + (y2- y1)
Middle term
2lw+2lh+2wh
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.

41. In a parabola - if the first term is positive - the parabola ________.
Opens up
(x1+x2)/2 - (y1+y2)/2
1/3pir^2*h
Order does matter for a permutation - but does not matter for a combination.

42. Volume of sphere
2Length + 2width [or (length + width) x 2]
S² - where s = length of a side
4/3pir^3
T1 * r^(n-1)/(r-1)

43. What is the factored version of (x+y)(x-y) ?
Ac+ad+bc+bd
½(b1 +b2) x h [or (b1 +b2) x h÷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.
x²-y²

44. What is the distance formula?
(y2-y1)/(x2-x1)
(a+b)(a-b)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Sqr( x2 -x1) + (y2- y1)

45. How do you find the sum of a geometric sequence?
2x2x2x5x5
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
½(b1 +b2) x h [or (b1 +b2) x h÷2]
T1 * r^(n-1)/(r-1)

46. How do you find the slope?
2x2x2x5x5
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.
y2-y1/x2-x1
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

47. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
Negative
Pi*r^2
(a-b)(a+b)

48. What is the side ratio for a 30:60:90 triangle?
Opens down
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(x+y)(x-y)
1

49. Area of Circle
N x M
(x+y)(x-y)
Pi*r^2
T1 + (n-1)d

50. What is the average speed?
2Length + 2width [or (length + width) x 2]
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
Total distance/total time