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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 kind of triangle is this: has two sides of equal length - and a 90 degree angle?
(a+b)(a-b)
The average - mean - median - or mode.
Number of desired outcomes/number of total outcomes
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.

2. Slope
(y2-y1)/(x2-x1)
(a-b)(a+b)
Pi*d
x°/360 times (?r²) - where x is the degrees in the angle

3. Quadratic Formula
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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
b±[vb²-4ac]/2a
T1 + (n-1)d

4. What is the side ratio for a Right Isosceles triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Opens up
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Groups - teams - or committees.

5. What is a '30:60:90' triangle?
2pi*r
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.
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
(n-2)180

6. Area of a triangle
½(base x height) [or (base x height)÷2]
(y2-y1)/(x2-x1)
(n degrees/360) * (pi)r^2
Percentage Change = Difference/Original * 100

7. Volume of sphere
x°/360 times (?r²) - where x is the degrees in the angle
4/3pir^3
1/x^a
Negative

8. How do you find the nth term of a geometric sequence?
T1 * r^(n-1)
(n degrees/360) * 2(pi)r
An ange whose vertex is the center of the circle
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

9. What is the factored version of (x+y)(x-y) ?
2(pi)r(r+h)
The length of any one side of a triangle must be less than the sum of the other two sides. It must also be greater than the difference between the other two sides. So - 'A' will always be < B+C - and > B-C or C-B.
x²-y²
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.

10. Circumference of cirlce using diameter
A²-b²
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Pi*d

11. Rough est. of v1 =
4s
(pi)r^2
(x+y)²
1

12. a² - b² is equal to
(a+b)(a-b)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(a-b)(a+b)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

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

14. What is the length of an arc?
(a-b)²
(n degrees/360) * 2(pi)r
x°/360 times (2 pi r) - where x is the degrees in the angle
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.

15. How do you find the sum of a geometric sequence?
4/3pir^3
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
Order does matter for a permutation - but does not matter for a combination.
T1 * r^(n-1)/(r-1)

16. Area of Rectangle
C =?d
Lw
(a+b)(a-b)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

17. Surface Area of Sphere
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
(x-y)²
y2-y1/x2-x1
4pir^2

18. What is the distance formula?
(a-b)(a+b)
Sqr( x2 -x1) + (y2- y1)
(a-b)²
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

19. Define the mode of a set of numbers.
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.
Percentage Change = Difference/Original * 100
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
The distance from one point on the circle to another point on the circle.

20. a²-b²
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/x^a
(x+y)²
(a-b)(a+b)

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

22. Area of Trapezoid
(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.
Pi*d
1/2 h (b1 + b2)

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

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

25. How do you calculate a diagonal inside a 3-dimensional rectangular box?
S² - where s = length of a side
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.
x²-y²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

26. How do you solve a permutation?
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.
Lw
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
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.

27. To divide powers with the same base...
y2-y1/x2-x1
x²-y²
2pir^2 + 2pir*h
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

28. In a coordinate system - identify the quadrants and describe their location.
Last term
1.4
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
?d OR 2?r

29. Volume of pyramid
2(pi)r(r+h)
1/3Bh
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
½(base x height) [or (base x height)÷2]

30. a²+2ab+b²
(a+b)²
y = kx
Pir^2h
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

31. In a parabola - if the first term is positive - the parabola ________.
4s (where s = length of a side)
Not necessarily. This is a trick question - because x could be either positive or negative.
Opens up
(a-b)(a+b)

32. What is directly proportional?
y = kx
b±[vb²-4ac]/2a
?d OR 2?r
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.

33. Arc
Part of a circle connecting two points on the circle.
A=bh
Pi*r^2
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

34. In intersecting lines - opposite angles are _____.
Total distance/total time
2(lw+wh+lh)
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
Equal

35. Surface Area of Cylinder
(n/2) * (t1+tn)
A²-b²
2pir^2 + 2pir*h
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.

36. Rough est. of v3 =
1.7
½(base x height) [or (base x height)÷2]
Ac+ad+bc+bd
2 pi r

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

38. Define the formula for calculating slope.
b±[vb²-4ac]/2a
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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 across the circle through the center of the circle.The diameter is twice the radius.

39. How do you calculate the probability of two events in a row? (Probability of A and B)
1/1
Probability A * Probability B
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.
(a-b)²

40. Define 'proportionate' values
(a-b)(a+b)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Equal
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

41. Chord
The distance from one point on the circle to another point on the circle.
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.
2lw+2lh+2wh
4s (where s = length of a side)

42. Area of Square
S^2
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.
y2-y1/x2-x1
The length of any one side of a triangle must be less than the sum of the other two sides. It must also be greater than the difference between the other two sides. So - 'A' will always be < B+C - and > B-C or C-B.

43. What is the formula for the diagonal of any square?
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)²
S*v2
y = k/x

44. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
1/3Bh
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.
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.

45. Point-Slope form
2Length + 2width [or (length + width) x 2]
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Sum of the lengths of the sides
y-y1=m(x-x1)

46. What is the unfactored version of x²-y² ?
(n degrees/360) * (pi)r^2
?r²
(x+y)(x-y)
1/3Bh

47. What is the factored version of x² + 2xy + y² ?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(x+y)²
Last term
A segment connecting the center of a circle to any point on the circle

48. How do you multiply and divide square roots?
x² + 2xy + y²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
y2-y1/x2-x1
(x-y)²

49. What is the unfactored version of (x-y)² ?
x² -2xy + y²
Pir^2h
Last term
Percentage Change = Difference/Original * 100

50. What is the prime factorization of 200?
The set of points which are all the same distance (the radius) from a certain point (the center).
1.7
1
2x2x2x5x5