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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. Volume of Cylinder
2x2x2x5x5
Pir^2h
Middle term
4s

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

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3. What is the unfactored version of x²-y² ?
(x+y)(x-y)
(x-y)²
(n-2)180
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.

4. What do permutation problems often ask for?
2lw+2lh+2wh
4/3pir^3
½(base x height) [or (base x height)÷2]
Arrangements - orders - schedules - or lists.

5. What is the factored version of (x+y)(x-y) ?
4s
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-b)(a²+ab+b²)
x²-y²

6. Area of rectangle - square - parallelogram
(0 -0)
A=bh
(a-b)(a²+ab+b²)
(a-b)(a+b)

7. What is the area of a solid rectangle?
(x-y)²
2(lw+wh+lh)
2lw+2lh+2wh
x² -2xy + y²

8. If x² = 144 - does v144 = x?
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.

9. Area of a square
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2(lw+wh+lh)
S² - where s = length of a side
(a+b)(a²-ab+b²)

10. When you reverse FOIL - the term that needs to multiply out is the _____
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.
Middle term
A=?r2
Last term

11. If something is possible but not certain - what is the numeric range of probability of it happening?
T1 + (n-1)d
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Between 0 and 1.
(n-2)180

12. Quadratic Formula
(y-y1)=m(x-x1)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
b±[vb²-4ac]/2a

13. Point-Slope form
Order does matter for a permutation - but does not matter for a combination.
y-y1=m(x-x1)
(x1+x2)/2 - (y1+y2)/2
½(base x height) [or (base x height)÷2]

14. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
4s (where s = length of a side)
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'.
Lw

15. Central Angle
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(b1 +b2) x h [or (b1 +b2) x h÷2]
An ange whose vertex is the center of the circle
2Length + 2width [or (length + width) x 2]

16. a²-b²
Sqr( x2 -x1) + (y2- y1)
(a-b)(a+b)
y2-y1/x2-x1
?r²

17. a³-b³
(a-b)(a²+ab+b²)
1/x^a
(n-2)180
2lw+2lh+2wh

18. Arc
2lw+2lh+2wh
Part of a circle connecting two points on the circle.
x°/360 times (?r²) - where x is the degrees in the angle
The four big angles are equal and the four small angles are equal

19. Surface Area of rectangular prism
Opens up
(n degrees/360) * 2(pi)r
2lw+2lh+2wh
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.

20. How do you multiply and divide square roots?
1/2bh
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
4s (where s = length of a side)
A²-b²

21. What is the factored version of x² -2xy + y² ?
(x-y)²
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(r+h)
(x+y)²

22. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
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 - and greater than the difference between the other two sides.
A=bh

23. How do you calculate the percentage of change?
1/2bh
Percentage Change = Difference/Original * 100
Bh
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

24. What is the formula for the diagonal of any square?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
S*v2
Middle term
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

25. Circumference Formula
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
C =?d
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(a+b)(a²-ab+b²)

26. Area of Square
4s (where s = length of a side)
Ac+ad+bc+bd
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
S^2

27. What is directly proportional?
y = kx
½(base x height) [or (base x height)÷2]
4/3pir^3
Ac+ad+bc+bd

28. Sector
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.
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.
Percentage Change = Difference/Original * 100
2pi*r

29. x^a * x^b = x^__
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
y-y1=m(x-x1)
A+b
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.

30. Perimeter (circumference) of a circle
2 pi r
Opens up
T1 * r^(n-1)/(r-1)
Middle term

31. In intersecting lines - opposite angles are _____.
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.
Equal
(y-y1)=m(x-x1)
Arrangements - orders - schedules - or lists.

32. Surface Area of Sphere
4pir^2
Pir^2h
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A=?r2

33. How do you find the nth term of a geometric sequence?
A=?r2
T1 * r^(n-1)
Pir^2h
Groups - teams - or committees.

34. In a coordinate system - identify the quadrants and describe their location.
y2-y1/x2-x1
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(a-b)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.

35. How do you multiply powers with the same base?
S^2
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
2(pi)r

36. 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.
Negative
2(pi)r
(n-2)180

37. Area of Rectangle
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.
Lw
½(base x height) [or (base x height)÷2]
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

38. What is the distance formula?
Bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Sqr( x2 -x1) + (y2- y1)

39. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
(pi)r^2(h)
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.
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

40. Radius (Radii)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(n degrees/360) * (pi)r^2
Probability A * Probability B
A segment connecting the center of a circle to any point on the circle

41. What is the volume of a solid rectangle?
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.
Bh
Opens up
Lwh

42. What do combination problems usually ask for?
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.
A²-b²
x°/360 times (2 pi r) - where x is the degrees in the angle
Groups - teams - or committees.

43. Volume of sphere
4/3pir^3
1. Given event A: A + notA = 1.
2pi*r
(a-b)(a²+ab+b²)

44. In a parabola - if the first term is negative - the parabola ________.
2(pi)r(r+h)
Opens down
(n degrees/360) * 2(pi)r
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

45. a² - b² is equal to
(a+b)(a-b)
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.
2pir^2 + 2pir*h

46. How do you calculate the probability of two events in a row? (Probability of A and B)
Groups - teams - or committees.
Probability A * Probability B
Between 0 and 1.
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.

47. Define the 'Third side' rule for triangles

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48. What number goes on the bottom of a probability fraction?
1/1
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=?r2
The total # of possible outcomes.

49. a³+b³
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
(n/2) * (t1+tn)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(a+b)(a²-ab+b²)

50. What is a 'Right isosceles' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Percentage Change = Difference/Original * 100
4s (where s = length of a side)
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.