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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 average?
x°/360 times (?r²) - where x is the degrees in the angle
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.
Sum of terms/number of terms

2. If x² = 144 - does v144 = x?
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.
(a-b)(a+b)
Equal
Not necessarily. This is a trick question - because x could be either positive or negative.

3. Radius (Radii)
(a+b)(a-b)
x² -2xy + y²
A segment connecting the center of a circle to any point on the circle
y = k/x

4. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
2l+2w
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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.
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.

5. What is the circumference of a circle?
1/1
2(pi)r
The total # of possible outcomes.
T1 + (n-1)d

6. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

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7. Quadratic Formula
y = k/x
b±[vb²-4ac]/2a
N x M
x² -2xy + y²

8. Area of Rectangle
Lw
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(a-b)²

9. What is the distance formula?
Sqr( x2 -x1) + (y2- y1)
The distance across the circle through the center of the circle.The diameter is twice the radius.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
y2-y1/x2-x1

10. The probability of an event happening and the probability of an event NOT happening must add up to what number?
C =?d
1. Given event A: A + notA = 1.
?d OR 2?r
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.

11. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.

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12. What is the volume of a solid rectangle?
Total distance/total time
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2(lw+wh+lh)
Lwh

13. What is the prime factorization of 200?
?r²
2x2x2x5x5
(x+y)(x-y)
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.

14. a³+b³
Lwh
(a+b)(a²-ab+b²)
(a-b)(a²+ab+b²)
½(base x height) [or (base x height)÷2]

15. To divide powers with the same base...
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Sqr( x2 -x1) + (y2- y1)
A²-b²

16. Volume of Cylinder
?r²
Pir^2h
1.4
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. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
Probability A + Probability B
(n/2) * (t1+tn)
y = k/x

18. What is the unfactored version of x²-y² ?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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)
Ac+ad+bc+bd

19. What are the side ratios for a 30:60:90 triangle?
Less
Pir^2h
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2Length + 2width [or (length + width) x 2]

20. a²+2ab+b²
(x+y)²
S^2
Lwh
(a+b)²

21. Point-Slope form
y-y1=m(x-x1)
Sum of terms/number of terms
4pir^2
A=bh

22. What is the probability?
1.4
T1 * r^(n-1)
Number of desired outcomes/number of total outcomes
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

23. What is the formula for the diagonal of any square?
S*v2
Order does matter for a permutation - but does not matter for a combination.
1/3Bh
2pi*r

24. What is the factored version of x² -2xy + y² ?
½(base x height) [or (base x height)÷2]
(x-y)²
Pir^2h
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

25. In a parabola - if the first term is negative - the parabola ________.
(y2-y1)/(x2-x1)
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.
Opens down
?d OR 2?r

26. Perimeter of a square
4s (where s = length of a side)
(a+b)(a²-ab+b²)
(a-b)(a²+ab+b²)
2(pi)r(r+h)

27. What is an 'equilateral' triangle?
1/2bh
4s
2pi*r
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

28. Define 'proportionate' values
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(0 -0)
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.

29. Area of a triangle
The distance across the circle through the center of the circle.The diameter is twice the radius.
½(base x height) [or (base x height)÷2]
The total # of possible outcomes.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

30. Area of a circle
An ange whose vertex is the center of the circle
?r²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1/x^a

31. How do you multiply powers with the same base?
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.
4s
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2lw+2lh+2wh

32. How do you find the nth term of a geometric sequence?
T1 * r^(n-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.
Opens up
2lw+2lh+2wh

33. How do you find the sum of an arithmetic sequence?
Lw
(n/2) * (t1+tn)
(y2-y1)/(x2-x1)
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.

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

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35. What is the area of a sector?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(n degrees/360) * (pi)r^2
Probability A * Probability B
(pi)r^2

36. For a bell curve - what three terms might be used to describe the number in the middle?
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.
The average - mean - median - or mode.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

37. When you reverse FOIL - the term that needs to add out is the _____
(a-b)²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Middle term
(x1+x2)/2 - (y1+y2)/2

38. Surface Area of Cylinder
(a+b)(a-b)
Percentage Change = Difference/Original * 100
(n degrees/360) * (pi)r^2
2pir^2 + 2pir*h

39. What is the surface area of a cylinder?
Between 0 and 1.
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'.
2(pi)r(r+h)
4s

40. Volume of prism
Bh
(pi)r^2
Opens down
y = k/x

41. Area of a trapezoid
2x2x2x5x5
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
4s
½(b1 +b2) x h [or (b1 +b2) x h÷2]

42. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
Groups - teams - or committees.
T1 * r^(n-1)
(n/2) * (t1+tn)

43. What is directly proportional?
Less
y = kx
Probability A + Probability B
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.

44. What is the unfactored version of (x-y)² ?
4pir^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.
Last term
x² -2xy + y²

45. List two odd behaviors of exponents
1/3Bh
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
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.

46. How do you find the sum of a geometric sequence?
T1 * r^(n-1)/(r-1)
Opens down
(x+y)²
1/3pir^2*h

47. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
Probability A + Probability B
Sum of terms/number of terms
1/3Bh

48. How do you multiply and divide square roots?
Percentage Change = Difference/Original * 100
1/1
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The four big angles are equal and the four small angles are equal

49. What is the 'distributive law'?
2(pi)r(r+h)
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.
2(pi)r
x²-y²

50. a²-2ab+b²
(a-b)²
1/2 h (b1 + b2)
1/2bh
(a-b)(a+b)