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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. Area of a circle
2(lw+wh+lh)
?r²
A²-b²
Equal

2. What is the factored version of (x+y)(x-y) ?
2lw+2lh+2wh
Between 0 and 1.
Pi*r^2
x²-y²

3. What is the area of a triangle?
Last term
T1 * r^(n-1)
Order does matter for a permutation - but does not matter for a combination.
1/2bh

4. perimeter of square
4s
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.
2pir^2 + 2pir*h
Not necessarily. This is a trick question - because x could be either positive or negative.

5. Rough est. of v2 =
A=bh
Less
1.4
y2-y1/x2-x1

6. Rough est. of v3 =
1.7
Total distance/total time
4pir^2
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

7. The length of one side of any triangle is ____ than the sum of the other two sides.
?r²
x² + 2xy + y²
Less
A=bh

8. Perimeter of rectangle
½(base x height) [or (base x height)÷2]
y = k/x
2l+2w
1.4

9. What is the side ratio for a Right Isosceles triangle?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2pi*r
(a-b)(a²+ab+b²)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

10. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
1/3pir^2*h
Part of a circle connecting two points on the circle.
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.

11. 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.
Bh
Pi*d
Opens down

12. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
2pi*r
(n degrees/360) * (pi)r^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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

13. What is the 'Third side' rule for triangles?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Negative
4s (where s = length of a side)
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.

14. What is directly proportional?
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.
2pi*r
Number of desired outcomes/number of total outcomes
y = kx

15. In a parabola - if the first term is positive - the parabola ________.
(x1+x2)/2 - (y1+y2)/2
4/3pir^3
Opens up
2(pi)r(r+h)

16. What is the distance formula?
y = kx
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
(y-y1)=m(x-x1)
Sqr( x2 -x1) + (y2- y1)

17. Volume of prism
Bh
Last term
Probability A + Probability B
1/x^a

18. 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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19. How do you calculate the probability of two events in a row? (Probability of A and B)
Opens up
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1/1
Probability A * Probability B

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

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21. What is an 'equilateral' triangle?
Less
?d OR 2?r
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2pi*r

22. What is the area of a 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
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.
(pi)r^2
1.4

23. What is the formula for the diagonal of any square?
T1 + (n-1)d
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.
(0 -0)
S*v2

24. Area of Trapezoid
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
2Length + 2width [or (length + width) x 2]
1/2 h (b1 + b2)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

25. a²-b²
(a-b)(a²+ab+b²)
2(pi)r(r+h)
Opens down
(a-b)(a+b)

26. What is the side ratio for a 30:60:90 triangle?
A segment connecting the center of a circle to any point on the circle
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Number of desired outcomes/number of total outcomes

27. x^-a =
1/x^a
(a+b)²
The total # of possible outcomes.
Lwh

28. a²+2ab+b²
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.
Probability A + Probability B
(a+b)²
x² -2xy + y²

29. What are the side ratios for a 30:60:90 triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
4s
Opens up
Between 0 and 1.

30. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Total distance/total time
1/2 h (b1 + 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
(0 -0)

31. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
1/2bh
Middle term
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.

32. If something is possible but not certain - what is the numeric range of probability of it happening?
Lw
T1 + (n-1)d
Between 0 and 1.
A²-b²

33. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
1/x^a
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.
x² + 2xy + y²
Sum of the lengths of the sides

34. Area of Circles
A=?r2
x² -2xy + y²
½(base x height) [or (base x height)÷2]
(n degrees/360) * (pi)r^2

35. Define 'proportionate' values
Negative
C =?d
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

36. Area of Triangle
1/2bh
(x+y)(x-y)
1/3pir^2*h
2Length + 2width [or (length + width) x 2]

37. Perimeter of a rectangle
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.
x²-y²
(a+b)(a-b)
2Length + 2width [or (length + width) x 2]

38. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
2(pi)r
N x M
2 pi r
Ac+ad+bc+bd

39. Area of a triangle
½(base x height) [or (base x height)÷2]
?d OR 2?r
y = kx
T1 * r^(n-1)/(r-1)

40. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
x²-y²
(a-b)(a²+ab+b²)
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.

41. What is a '30:60:90' triangle?
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
Not necessarily. This is a trick question - because x could be either positive or negative.
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'.
2l+2w

42. In intersecting lines - opposite angles are _____.
(a+b)²
Equal
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
T1 * r^(n-1)/(r-1)

43. x^a * x^b = x^__
2(pi)r
2lw+2lh+2wh
A+b
Pir^2h

44. Volume of Cone
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1/3pir^2*h
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.
S² - where s = length of a side

45. What is the point-slope form?
(x+y)²
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
(y-y1)=m(x-x1)

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

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47. Does order matter for a permutation? How about for a combination?
C =?d
(n-2)180
Order does matter for a permutation - but does not matter for a combination.
(pi)r^2(h)

48. Surface Area of rectangular prism
2lw+2lh+2wh
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Bh
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

49. Surface Area of Cylinder
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2pir^2 + 2pir*h

50. How do you calculate the surface area of a rectangular box?
x² + 2xy + y²
The distance from one point on the circle to another point on the circle.
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.
Middle term