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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. 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.
Last term
1.7
A=?r2

2. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
Pir^2h
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(n-2)180

3. Area of Circle
Pi*r^2
2Length + 2width [or (length + width) x 2]
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
T1 + (n-1)d

4. What is the factored version of (x+y)(x-y) ?
1/x^a
x²-y²
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)²

5. To divide powers with the same base...
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.
(x+y)²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(0 -0)

6. 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.
(a-b)(a+b)
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'.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

7. What is the area of a circle?
1/3pir^2*h
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(pi)r^2

8. How do you solve a permutation?
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
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
y-y1=m(x-x1)

9. What is the equation of a line?

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10. How do you find the nth term of an arithmetic sequence?
(a-b)(a²+ab+b²)
T1 + (n-1)d
2pi*r
Lwh

11. What is an 'equilateral' triangle?
A segment connecting the center of a circle to any point on the circle
N x M
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

12. What is the area of a triangle?
Lwh
Last term
1/2bh
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.

13. What is the factored version of x² -2xy + y² ?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x 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
(a+b)(a²-ab+b²)
(x-y)²

14. Surface Area of Sphere
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
Arrangements - orders - schedules - or lists.
Equal
4pir^2

15. Perimeter of a rectangle
S² - where s = length of a side
2(pi)r(r+h)
A=bh
2Length + 2width [or (length + width) x 2]

16. What is the formula for the diagonal of any square?
2Length + 2width [or (length + width) x 2]
1/2 h (b1 + b2)
y = k/x
S*v2

17. Surface Area of rectangular prism
2lw+2lh+2wh
(y-y1)=m(x-x1)
y = kx
?r²

18. a²-b²
½(base x height) [or (base x height)÷2]
(a-b)(a+b)
(a-b)(a²+ab+b²)
(pi)r^2(h)

19. a²-2ab+b²
2(pi)r
(a-b)²
Ac+ad+bc+bd
Bh

20. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(n degrees/360) * (pi)r^2

21. What is the surface area of a cylinder?
2(pi)r(r+h)
4s
2 pi r
Sqr( x2 -x1) + (y2- y1)

22. List two odd behaviors of exponents
S² - where s = length of a side
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.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Order does matter for a permutation - but does not matter for a combination.

23. If x² = 144 - does v144 = x?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Pi*r^2
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Not necessarily. This is a trick question - because x could be either positive or negative.

24. a³+b³
The set of points which are all the same distance (the radius) from a certain point (the center).
(a+b)(a²-ab+b²)
1/3pir^2*h
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.

25. Explain the difference between a digit and a number.

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26. Volume of pyramid
4s
C =?d
The four big angles are equal and the four small angles are equal
1/3Bh

27. What is the volume of a cylinder?
(pi)r^2(h)
(x+y)²
Total distance/total time
?r²

28. Area of a triangle
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
Ac+ad+bc+bd
?d OR 2?r
½(base x height) [or (base x height)÷2]

29. Circumference of cirlce using diameter
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'.
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.
Pi*d

30. Volume of prism
Bh
Percentage Change = Difference/Original * 100
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)(x-y)

31. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Sum of the lengths of the sides
Ac+ad+bc+bd
Groups - teams - or committees.

32. What is the average?
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.
2(pi)r(r+h)
A segment connecting the center of a circle to any point on the circle
Sum of terms/number of terms

33. 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.
2(pi)r
Not necessarily. This is a trick question - because x could be either positive or negative.
N x M

34. When a line crosses two parallel lines - ________.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Probability A + Probability B
The four big angles are equal and the four small angles are equal
2(pi)r

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

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36. What is the unfactored version of (x+y)² ?
(x+y)²
2lw+2lh+2wh
(pi)r^2
x² + 2xy + y²

37. What is the probability?
2(lw+wh+lh)
Number of desired outcomes/number of total outcomes
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'.
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.

38. What is the point-slope form?
?r²
Between 0 and 1.
(y-y1)=m(x-x1)
(pi)r^2(h)

39. What is directly proportional?
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
y = kx
A+b

40. (a+b)(c+d)
Ac+ad+bc+bd
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.
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.
Pi*d

41. x^a * x^b = x^__
The total # of possible outcomes.
(x+y)(x-y)
Order does matter for a permutation - but does not matter for a combination.
A+b

42. Radius (Radii)
2(lw+wh+lh)
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 segment connecting the center of a circle to any point on the circle
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

43. Perimeter 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.
The total # of possible outcomes.
y = k/x
2l+2w

44. Point-Slope form
4/3pir^3
1/2bh
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.
y-y1=m(x-x1)

45. What is the area of a solid rectangle?
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.
Between 0 and 1.
2(lw+wh+lh)
Less

46. In a parabola - if the first term is positive - the parabola ________.
Opens up
4s (where s = length of a side)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1.7

47. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
An ange whose vertex is the center of the circle
(n/2) * (t1+tn)
S*v2
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.

48. How do you find the sum of a geometric sequence?
?r²
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
T1 * r^(n-1)/(r-1)

49. a²+2ab+b²
Bh
(x+y)²
T1 * r^(n-1)
(a+b)²

50. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
4s
2x2x2x5x5
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.
The distance from one point on the circle to another point on the circle.