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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?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(x+y)²
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1/2 h (b1 + b2)

2. Volume of Cylinder
Part of a circle connecting two points on the circle.
(n/2) * (t1+tn)
Pir^2h
Probability A * Probability B

3. a²+2ab+b²
(a+b)²
Sqr( x2 -x1) + (y2- y1)
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.
x°/360 times (?r²) - where x is the degrees in the angle

4. Lines reflected over the x or y axis have ____ slopes.
(a-b)²
Negative
(n-2)180
Less

5. In a coordinate system - identify the quadrants and describe their location.
(a+b)(a-b)
x°/360 times (?r²) - where x is the degrees in the angle
The average - mean - median - or mode.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

6. What is the 'distributive law'?
2lw+2lh+2wh
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.
Total distance/total time
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.

7. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
(a-b)(a²+ab+b²)
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. 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
1/3Bh

8. Rough est. of v1 =
Lwh
A=?r2
b±[vb²-4ac]/2a
1

9. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
1/2bh
Ac+ad+bc+bd
Probability A + Probability B

10. Area of a trapezoid
4s
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
½(b1 +b2) x h [or (b1 +b2) x h÷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.

11. What are the side ratios for a 30:60:90 triangle?
Bh
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1. Given event A: A + notA = 1.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

12. length of a sector
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.
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 set of points which are all the same distance (the radius) from a certain point (the center).
x°/360 times (2 pi r) - where x is the degrees in the angle

13. Define 'proportionate' values
y = k/x
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(0 -0)
The set of points which are all the same distance (the radius) from a certain point (the center).

14. Define the range of a set of numbers.
T1 * r^(n-1)
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
N x M

15. 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
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2lw+2lh+2wh
1

16. Sector
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.
Probability A + Probability B
2(pi)r(r+h)
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.

17. What is the area of a solid rectangle?
x°/360 times (2 pi r) - where x is the degrees in the angle
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2(lw+wh+lh)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

18. What is the area of a circle?
The set of points which are all the same distance (the radius) from a certain point (the center).
x²-y²
An ange whose vertex is the center of the circle
(pi)r^2

19. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
S² - where s = length of a side
2x2x2x5x5
x²-y²

20. Surface Area of rectangular prism
Probability A * Probability B
Groups - teams - or committees.
T1 + (n-1)d
2lw+2lh+2wh

21. Surface Area of Sphere
4pir^2
The distance across the circle through the center of the circle.The diameter is twice the radius.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.

22. Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
x°/360 times (?r²) - where x is the degrees in the angle
?r²
Groups - teams - or committees.

23. (a+b)(c+d)
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.
Less
Ac+ad+bc+bd
1.7

24. For a bell curve - what three terms might be used to describe the number in the middle?
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.
Part of a circle connecting two points on the circle.
S*v2
The average - mean - median - or mode.

25. Area of a square
Opens down
S² - where s = length of a side
The set of points which are all the same distance (the radius) from a certain point (the center).
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.

26. How do you multiply and divide square roots?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a-b)²
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
x°/360 times (?r²) - where x is the degrees in the angle

27. x^-a =
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1/x^a
(a-b)(a²+ab+b²)
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.

28. What is the point-slope form?
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.
Arrangements - orders - schedules - or lists.
S^2
(y-y1)=m(x-x1)

29. How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1/1
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.
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.

30. If something is certain to happen - how is the probability of this event expressed mathematically?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/1
S² - where s = length of a side
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.

31. What is the circumference of a circle?
Lw
2(pi)r
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.
4pir^2

32. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
2pi*r
N x M
½(base x height) [or (base x height)÷2]

33. What is the area of a cylinder?
2pi*r
Part of a circle connecting two points on the circle.
(a-b)(a²+ab+b²)
2(pi)r(r+h)

34. Slope
(y2-y1)/(x2-x1)
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.
A=bh
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

35. Circumference of a circle
?d OR 2?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.
(pi)r^2
4s (where s = length of a side)

36. What is the unfactored version of x²-y² ?
(x+y)(x-y)
N x M
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Number of desired outcomes/number of total outcomes

37. Rough est. of v3 =
A segment connecting the center of a circle to any point on the circle
1.7
Opens up
Sum of terms/number of terms

38. In a parabola - if the first term is positive - the parabola ________.
(x-y)²
1/3pir^2*h
1.7
Opens up

39. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
The set of points which are all the same distance (the radius) from a certain point (the center).
(a-b)(a+b)
2(pi)r(r+h)

40. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
2Length + 2width [or (length + width) x 2]
x² + 2xy + y²
Less
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.

41. How do you find the nth term of a geometric sequence?
T1 * r^(n-1)
(a-b)(a²+ab+b²)
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.
Lw

42. What is the area of a sector?
(n degrees/360) * (pi)r^2
The set of points which are all the same distance (the radius) from a certain point (the center).
1/x^a
x²-y²

43. Explain the special properties of zero.
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.
The distance from one point on the circle to another point on the circle.
Sqr( x2 -x1) + (y2- y1)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

44. If something is possible but not certain - what is the numeric range of probability of it happening?
(n degrees/360) * 2(pi)r
2l+2w
Between 0 and 1.
T1 * r^(n-1)/(r-1)

45. Rough est. of v2 =
Bh
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'.
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.

46. To divide powers with the same base...
Sum of the lengths of the sides
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1
Number of desired outcomes/number of total outcomes

47. What is the factored version of x² + 2xy + y² ?
(n degrees/360) * 2(pi)r
(x+y)²
4s
A=?r2

48. Perimeter of a rectangle
(n-2)180
2Length + 2width [or (length + width) x 2]
1/2bh
x²-y²

49. What is a 'Right isosceles' triangle?
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.
Equal
Order does matter for a permutation - but does not matter for a combination.
(y2-y1)/(x2-x1)

50. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Sqr( x2 -x1) + (y2- y1)
(n degrees/360) * 2(pi)r
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.
Bh