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GRE Math 2

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. In a parabola - if the first term is positive - the parabola ________.
Opens up
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.
The set of points which are all the same distance (the radius) from a certain point (the center).
(n degrees/360) * (pi)r^2

2. What is directly proportional?
2pi*r
y = kx
y-y1=m(x-x1)
Probability A * Probability B

3. Rough est. of v2 =
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
1.4
A²-b²
(n degrees/360) * (pi)r^2

4. How do you calculate a diagonal inside a 3-dimensional rectangular box?
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2Length + 2width [or (length + width) x 2]
Last term

5. What is the equation of a line?

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6. Area of rectangle - square - parallelogram
A=bh
Middle term
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(a-b)²

7. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
x°/360 times (?r²) - where x is the degrees in the angle
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
2 pi r
Probability A * Probability B

8. Surface Area of Cylinder
y-y1=m(x-x1)
(x+y)(x-y)
2pir^2 + 2pir*h
(a+b)(a²-ab+b²)

9. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
Bh
4s (where s = length of a side)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

10. How do you solve a permutation?
1.7
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
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
S² - where s = length of a side

11. The probability of an event happening and the probability of an event NOT happening must add up to what number?
T1 + (n-1)d
1. Given event A: A + notA = 1.
4s (where s = length of a side)
The distance from one point on the circle to another point on the circle.

12. Area of a sector
1. Given event A: A + notA = 1.
Bh
½(b1 +b2) x h [or (b1 +b2) x h÷2]
x°/360 times (?r²) - where x is the degrees in the angle

13. What is the distance formula?
(a+b)(a-b)
y = k/x
Sqr( x2 -x1) + (y2- y1)
4s

14. Area of a triangle
Sum of the lengths of the sides
4s (where s = length of a side)
T1 + (n-1)d
½(base x height) [or (base x height)÷2]

15. The length of one side of any triangle is ____ than the sum of the other two sides.
C =?d
Less
½(base x height) [or (base x height)÷2]
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.

16. a³-b³
Pi*d
2(pi)r
Pi*r^2
(a-b)(a²+ab+b²)

17. What is the area of a solid rectangle?
2(lw+wh+lh)
(a+b)(a²-ab+b²)
Negative
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

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

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19. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
Number of desired outcomes/number of total outcomes
(y-y1)=m(x-x1)
A segment connecting the center of a circle to any point on the circle

20. What is the unfactored version of (x-y)² ?
y = k/x
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.
x² -2xy + y²
1.4

21. What is an 'equilateral' triangle?
(a-b)(a²+ab+b²)
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
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.

22. Area of Triangle
y-y1=m(x-x1)
1/2bh
The distance across the circle through the center of the circle.The diameter is twice the radius.
2(pi)r

23. Circumference of cirlce using diameter
Last term
Between 0 and 1.
(a+b)(a-b)
Pi*d

24. Explain the special properties of zero.
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
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.
2l+2w
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.

25. What is the circumference of a circle?
y = kx
Ac+ad+bc+bd
Lwh
2(pi)r

26. In a coordinate system - what is the origin?
C =?d
Sum of the lengths of the sides
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(0 -0)

27. When a line crosses two parallel lines - ________.
(x-y)²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(x1+x2)/2 - (y1+y2)/2
The four big angles are equal and the four small angles are equal

28. 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.
The set of points which are all the same distance (the radius) from a certain point (the center).
Pi*d
(pi)r^2

29. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
?d OR 2?r
2x2x2x5x5

30. What is the factored version of (x+y)(x-y) ?
Between 0 and 1.
Percentage Change = Difference/Original * 100
Ac+ad+bc+bd
x²-y²

31. What do combination problems usually ask for?
Groups - teams - or committees.
Pir^2h
C =?d
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. Arc
?r²
1/3Bh
Part of a circle connecting two points on the circle.
(x1+x2)/2 - (y1+y2)/2

33. a²-2ab+b²
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(a-b)²
2pir^2 + 2pir*h
x²-y²

34. Area of a circle
A segment connecting the center of a circle to any point on the circle
?r²
(y-y1)=m(x-x1)
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

35. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
The four big angles are equal and the four small angles are equal
½(base x height) [or (base x height)÷2]
1. Given event A: A + notA = 1.

36. Area of Square
(y2-y1)/(x2-x1)
S^2
y = kx
The four big angles are equal and the four small angles are equal

37. How do you multiply and divide square roots?
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.
(0 -0)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(n/2) * (t1+tn)

38. What is the surface area of a cylinder?
2Length + 2width [or (length + width) x 2]
2(pi)r(r+h)
Opens up
(a+b)(a-b)

39. Quadratic Formula
(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.
b±[vb²-4ac]/2a
Number of desired outcomes/number of total outcomes

40. How do you calculate the surface area of a rectangular box?
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 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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Sum of terms/number of terms

41. Circumference of a 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.
Negative
?d OR 2?r
Pir^2h

42. Rough est. of v3 =
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
A=?r2
1.7
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.

43. How do you find the slope?
1/x^a
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.
y2-y1/x2-x1
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.

44. To divide powers with the same base...
Probability A + Probability B
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.
(a-b)²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

45. What is the 'Third side' rule for triangles?
½(base x height) [or (base x height)÷2]
1/2bh
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 four big angles are equal and the four small angles are equal

46. What'S the most important thing to remember about charts you'll see on the GRE?
2pir^2 + 2pir*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.
Pi*r^2
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

47. What is the area of a circle?
2l+2w
2pi*r
1
(pi)r^2

48. Rough est. of v1 =
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 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.
2Length + 2width [or (length + width) x 2]
1

49. perimeter of square
Negative
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.
x°/360 times (2 pi r) - where x is the degrees in the angle
4s

50. Perimeter (circumference) of a circle
2 pi r
2Length + 2width [or (length + width) x 2]
(a+b)²
4/3pir^3