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

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2. (a+b)(c+d)
Ac+ad+bc+bd
(y2-y1)/(x2-x1)
1/2 h (b1 + b2)
Pi*r^2

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

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4. When you reverse FOIL - the term that needs to add out is the _____
Total distance/total time
T1 + (n-1)d
Middle term
(n-2)180

5. What is the 'distributive law'?
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.
Opens up
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.
x²-y²

6. Circumference of cirlce using diameter
Pi*d
Lw
Opens up
2(lw+wh+lh)

7. Circumference of a circle using radius
2(lw+wh+lh)
2pi*r
The four big angles are equal and the four small angles are equal
(a+b)(a-b)

8. What is the prime factorization of 200?
Pi*r^2
(a-b)²
?r²
2x2x2x5x5

9. Surface Area of Cylinder
2pir^2 + 2pir*h
y2-y1/x2-x1
b±[vb²-4ac]/2a
Sum of the lengths of the sides

10. What is the 'Third side' rule for triangles?
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.
Bh
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.

11. Define the mode of a set of numbers.
Less
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.
T1 * r^(n-1)/(r-1)
Not necessarily. This is a trick question - because x could be either positive or negative.

12. What is the factored version of x² -2xy + y² ?
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
(0 -0)
(x-y)²
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.

13. Volume of sphere
4/3pir^3
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.
(x1+x2)/2 - (y1+y2)/2
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

14. Quadratic Formula
2pi*r
(n/2) * (t1+tn)
b±[vb²-4ac]/2a
2lw+2lh+2wh

15. Volume of Cylinder
Pir^2h
A²-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
x²-y²

16. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
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)
Order does matter for a permutation - but does not matter for a combination.

17. Area of Circle
(x-y)²
Pi*r^2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Opens down

18. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Opens down
y = kx
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.
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.

19. Rough est. of v3 =
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.
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.
1.7

20. Define 'proportionate' values
2l+2w
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'.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.

21. a³-b³
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(a-b)(a²+ab+b²)
Opens down
y2-y1/x2-x1

22. What is the point-slope form?
(y-y1)=m(x-x1)
?d OR 2?r
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1

23. How do you multiply and divide square roots?
Opens down
Part of a circle connecting two points on the circle.
(a-b)(a²+ab+b²)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

24. What is the average?
Middle term
2(pi)r
Sum of terms/number of terms
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.

25. Explain the special properties of zero.
Ac+ad+bc+bd
Bh
1.4
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.

26. What'S the most important thing to remember about charts you'll see on the GRE?
1/x^a
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.
2Length + 2width [or (length + width) x 2]
The set of points which are all the same distance (the radius) from a certain point (the center).

27. What is inversely proportional?
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.
y = k/x
T1 * r^(n-1)
An ange whose vertex is the center of the circle

28. Rough est. of v2 =
1.4
Order does matter for a permutation - but does not matter for a combination.
Last term
Equal

29. What is the unfactored version of (x-y)² ?
½(base x height) [or (base x height)÷2]
x² -2xy + y²
Groups - teams - or committees.
Bh

30. The probability of an event happening and the probability of an event NOT happening must add up to what number?
y = k/x
x² + 2xy + y²
1. Given event A: A + notA = 1.
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.

31. In a parabola - if the first term is positive - the parabola ________.
(a+b)(a-b)
Number of desired outcomes/number of total outcomes
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Opens up

32. 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
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.
(x+y)²
Ac+ad+bc+bd

33. What is a '30:60:90' triangle?
1/2bh
2x2x2x5x5
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
?r²

34. Define a factorial of a number - and how it is written.
The average - mean - median - or mode.
Less
The distance across the circle through the center of the circle.The diameter is twice the radius.
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.

35. Rough est. of v1 =
1
Sum of terms/number of terms
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.
Bh

36. If something is possible but not certain - what is the numeric range of probability of it happening?
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 = k/x
Between 0 and 1.
(y-y1)=m(x-x1)

37. Perimeter of polygon
Between 0 and 1.
(x1+x2)/2 - (y1+y2)/2
Sum of the lengths of the sides
(pi)r^2(h)

38. How do you calculate the surface area of a rectangular box?
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.
(x1+x2)/2 - (y1+y2)/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.
Sum of terms/number of terms

39. How do you find the sum of a geometric sequence?
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.
Lwh
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
T1 * r^(n-1)/(r-1)

40. What is the probability?
Negative
(a-b)(a²+ab+b²)
Number of desired outcomes/number of total outcomes
Lwh

41. In a coordinate system - what is the origin?
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.
Order does matter for a permutation - but does not matter for a combination.
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.
(0 -0)

42. Perimeter (circumference) of a circle
y2-y1/x2-x1
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2 pi r
The distance across the circle through the center of the circle.The diameter is twice the radius.

43. Perimeter of a square
1. Given event A: A + notA = 1.
Between 0 and 1.
4s (where s = length of a side)
Pi*r^2

44. How do you solve a permutation?
Groups - teams - or committees.
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
Less
Between 0 and 1.

45. Slope
(y2-y1)/(x2-x1)
The average - mean - median - or mode.
(x+y)²
?r²

46. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Part of a circle connecting two points on the circle.
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
2pi*r

47. What is the area of a cylinder?
2pi*r
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(r+h)
Probability A * Probability B

48. x^a * x^b = x^__
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.
Opens down
A+b
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

49. What is the volume of a cylinder?
Pir^2h
(pi)r^2(h)
(n degrees/360) * (pi)r^2
b±[vb²-4ac]/2a

50. What is the side ratio for a 30:60:90 triangle?
1.4
Bh
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x²-y²