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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. How do you find the sum of a geometric sequence?
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
T1 * r^(n-1)/(r-1)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
½(b1 +b2) x h [or (b1 +b2) x h÷2]

2. Slope
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
(y2-y1)/(x2-x1)
A+b
(x+y)²

3. What is the unfactored version of (x+y)² ?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x² + 2xy + y²
1/x^a

4. What is the 'Third side' rule for triangles?
T1 * r^(n-1)/(r-1)
y-y1=m(x-x1)
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.
2pi*r

5. In a coordinate system - identify the quadrants and describe their location.
Negative
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
2pir^2 + 2pir*h

6. What is 'absolute value' - and how is it represented?

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7. Surface Area of Sphere
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.
(x+y)²
?r²

8. What is inversely proportional?
Arrangements - orders - schedules - or lists.
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.
y = k/x
1/2bh

9. The probability of an event happening and the probability of an event NOT happening must add up to what number?
x² -2xy + y²
(x-y)²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1. Given event A: A + notA = 1.

10. In a parabola - if the first term is negative - the parabola ________.
x°/360 times (?r²) - where x is the degrees in the angle
Last term
b±[vb²-4ac]/2a
Opens down

11. Circumference of a circle
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.
?d OR 2?r
(n/2) * (t1+tn)
Number of desired outcomes/number of total outcomes

12. What'S the most important thing to remember about charts you'll see on the GRE?
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 -2xy + y²
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.
1/x^a

13. What is the factored version of x² + 2xy + y² ?
Sum of terms/number of terms
1/2bh
Last term
(x+y)²

14. If something is possible but not certain - what is the numeric range of probability of it happening?
(n degrees/360) * (pi)r^2
Between 0 and 1.
Pi*r^2
2 pi r

15. How do you multiply powers with the same base?
The total # of possible outcomes.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
4/3pir^3
y = kx

16. What is the area of a solid rectangle?
2Length + 2width [or (length + width) x 2]
T1 * r^(n-1)
1.4
2(lw+wh+lh)

17. In a parabola - if the first term is positive - the parabola ________.
b±[vb²-4ac]/2a
y = k/x
Opens up
2pir^2 + 2pir*h

18. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Total distance/total time
Probability A + Probability B
½(b1 +b2) x h [or (b1 +b2) x h÷2]
x² + 2xy + y²

19. Area of a trapezoid
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
1. Given event A: A + notA = 1.
S*v2
½(b1 +b2) x h [or (b1 +b2) x h÷2]

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

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21. Volume of sphere
T1 * r^(n-1)/(r-1)
4/3pir^3
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.
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

22. Area of Rectangle
Lw
The set of points which are all the same distance (the radius) from a certain point (the center).
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
(n degrees/360) * 2(pi)r

23. Diameter
x°/360 times (2 pi r) - where x is the degrees in the angle
(n degrees/360) * 2(pi)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.
The distance across the circle through the center of the circle.The diameter is twice the radius.

24. What is an 'equilateral' triangle?
Sqr( x2 -x1) + (y2- y1)
T1 * r^(n-1)/(r-1)
An ange whose vertex is the center of the circle
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

25. Area of Trapezoid
Sqr( x2 -x1) + (y2- y1)
(n degrees/360) * 2(pi)r
1/2 h (b1 + b2)
1/2bh

26. Perimeter of a square
Sqr( x2 -x1) + (y2- y1)
4s (where s = length of a side)
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.
1/3Bh

27. In intersecting lines - opposite angles are _____.
Total distance/total time
Equal
Between 0 and 1.
(a-b)(a+b)

28. Area of a triangle
An ange whose vertex is the center of the circle
Last term
Less
½(base x height) [or (base x height)÷2]

29. x^-a =
?d OR 2?r
1/x^a
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'.
1/2bh

30. Arc
Arrangements - orders - schedules - or lists.
Part of a circle connecting two points on the circle.
T1 + (n-1)d
Number of desired outcomes/number of total outcomes

31. (a+b)(a-b)=
A²-b²
1/x^a
Sum of terms/number of terms
Bh

32. What are the side ratios for a 30:60:90 triangle?
1/3Bh
2pir^2 + 2pir*h
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/x^a

33. (a+b)(c+d)
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.
Less
(pi)r^2
Ac+ad+bc+bd

34. What is the area of a triangle?
(a-b)²
Probability A * Probability B
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/2bh

35. Surface Area of Cylinder
1/1
The average - mean - median - or mode.
2pir^2 + 2pir*h
2lw+2lh+2wh

36. What is the side ratio for a Right Isosceles triangle?
(y-y1)=m(x-x1)
A+b
?d OR 2?r
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

37. Perimeter (circumference) of a circle
(x-y)²
2 pi r
x°/360 times (2 pi r) - where x is the degrees in the angle
4s (where s = length of a side)

38. Circumference of a circle using radius
Less
2pi*r
Part of a circle connecting two points on the circle.
2Length + 2width [or (length + width) x 2]

39. What is the length of an arc?
2(pi)r(r+h)
(n degrees/360) * 2(pi)r
2lw+2lh+2wh
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'.

40. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
(pi)r^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.
S*v2
1.7

41. The length of one side of any triangle is ____ than the sum of the other two sides.
An ange whose vertex is the center of the circle
Middle term
Less
(a+b)²

42. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the angle
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
C =?d
4s (where s = length of a side)

43. What is the area of a cylinder?
2(pi)r(r+h)
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.
1. Given event A: A + notA = 1.
½(base x height) [or (base x height)÷2]

44. What is the area of a sector?
Pi*r^2
4s
(n degrees/360) * (pi)r^2
(x+y)²

45. Circumference Formula
Total distance/total time
C =?d
Less
2lw+2lh+2wh

46. What is the factored version of x² -2xy + y² ?
(x-y)²
Order does matter for a permutation - but does not matter for a combination.
Less
1/x^a

47. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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.
(0 -0)
(n degrees/360) * (pi)r^2
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

48. Area of Square
(n degrees/360) * 2(pi)r
4/3pir^3
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
S^2

49. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
Opens down
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The average - mean - median - or mode.

50. List two odd behaviors of exponents
(a-b)(a+b)
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.
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.
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.