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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 side ratio for a Right Isosceles triangle?
The set of points which are all the same distance (the radius) from a certain point (the center).
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2(pi)r(r+h)
(n/2) * (t1+tn)

2. Define the range of a set of numbers.
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.
1/2 h (b1 + b2)
1/1
C =?d

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

4. What is the area of a circle?
Sum of terms/number of terms
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.
1.7
(pi)r^2

5. What is the unfactored version of (x-y)² ?
Bh
x² -2xy + y²
1/2bh
(a-b)²

6. a² - b² is equal to
(a+b)(a-b)
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.
1.4
Sqr( x2 -x1) + (y2- y1)

7. Slope
An ange whose vertex is the center of the circle
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(y2-y1)/(x2-x1)
N x M

8. Point-Slope form
b±[vb²-4ac]/2a
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)r^2(h)
y-y1=m(x-x1)

9. Surface Area of Cylinder
(n/2) * (t1+tn)
2pir^2 + 2pir*h
2x2x2x5x5
x°/360 times (2 pi r) - where x is the degrees in the angle

10. Chord
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
The distance from one point on the circle to another point on the circle.
The average - mean - median - or mode.

11. Area of a trapezoid
x°/360 times (?r²) - where x is the degrees in the angle
Opens up
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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.

12. What do permutation problems often ask for?
Middle term
Arrangements - orders - schedules - or lists.
1/1
C =?d

13. length of a sector
1
x°/360 times (2 pi r) - where x is the degrees in the angle
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Sum of terms/number of terms

14. Surface Area of rectangular prism
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.
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.
2lw+2lh+2wh
Not necessarily. This is a trick question - because x could be either positive or negative.

15. In a parabola - if the first term is negative - the parabola ________.
1/x^a
Pi*r^2
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.
Opens down

16. Surface Area of Sphere
(x1+x2)/2 - (y1+y2)/2
S*v2
1
4pir^2

17. Perimeter of a rectangle
1/2bh
Bh
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2Length + 2width [or (length + width) x 2]

18. What is the formula for the diagonal of any square?
(a+b)(a-b)
2(pi)r
?d OR 2?r
S*v2

19. Central Angle
Probability A * Probability B
(n degrees/360) * 2(pi)r
1.7
An ange whose vertex is the center of the circle

20. Lines reflected over the x or y axis have ____ slopes.
T1 + (n-1)d
Negative
?r²
Pi*r^2

21. When you reverse FOIL - the term that needs to multiply out is the _____
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Between 0 and 1.
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.
Last term

22. Rough est. of v1 =
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.
T1 * r^(n-1)/(r-1)
Not necessarily. This is a trick question - because x could be either positive or negative.
1

23. Area of a sector
Lw
1/1
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
x°/360 times (?r²) - where x is the degrees in the angle

24. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
2pir^2 + 2pir*h
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2 pi r

25. What is the average speed?
Total distance/total time
Not necessarily. This is a trick question - because x could be either positive or negative.
The total # of possible outcomes.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

26. Area of rectangle - square - parallelogram
1/1
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
A=bh
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'.

27. List two odd behaviors of exponents
T1 + (n-1)d
y-y1=m(x-x1)
4/3pir^3
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.

28. What is the equation of a line?

29. How do you find the nth term of an arithmetic sequence?
(x+y)²
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.
2lw+2lh+2wh
T1 + (n-1)d

30. What is the factored version of x² -2xy + y² ?
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(x-y)²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

31. Rough est. of v2 =
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
1.4
A segment connecting the center of a circle to any point on the circle
(a+b)(a-b)

32. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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)
x² -2xy + y²

33. Area of Trapezoid
A segment connecting the center of a circle to any point on the circle
1/2 h (b1 + b2)
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

34. Perimeter of a square
Bh
1/3Bh
Pi*r^2
4s (where s = length of a side)

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

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

37. Area of a circle
?r²
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.
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.
1/3Bh

38. In a coordinate system - what is the origin?
Pir^2h
(0 -0)
S*v2
Part of a circle connecting two points on the circle.

39. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
The distance from one point on the circle to another point on the circle.
Between 0 and 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.

40. Quadratic Formula
Opens up
Pir^2h
The total # of possible outcomes.
b±[vb²-4ac]/2a

41. What is the distance formula?
Sqr( x2 -x1) + (y2- y1)
Opens up
T1 + (n-1)d
x² + 2xy + y²

42. a²-b²
(a-b)(a+b)
1/3Bh
(pi)r^2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

43. Area of Square
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.
S^2
1/2bh
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'.

44. Area of Circle
Pi*r^2
Number of desired outcomes/number of total outcomes
Opens up
2lw+2lh+2wh

45. What is the area of a solid rectangle?
(pi)r^2
2(pi)r(r+h)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2(lw+wh+lh)

46. What are the side ratios for a 30:60:90 triangle?
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/x^a
(y-y1)=m(x-x1)

47. x^a * x^b = x^__
A segment connecting the center of a circle to any 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.
A+b
Arrangements - orders - schedules - or lists.

48. To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(n-2)180
2(pi)r(r+h)
2(lw+wh+lh)

49. How do you multiply powers with the same base?
Probability A + Probability B
A segment connecting the center of a circle to any point on the circle
Pi*r^2
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

50. x^-a =
(a+b)(a²-ab+b²)
1/x^a
Probability A + Probability B
The distance from one point on the circle to another point on the circle.