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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. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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.
The distance across the circle through the center of the circle.The diameter is twice the radius.
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

2. Define the range of a set of numbers.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
(n/2) * (t1+tn)
Total distance/total time

3. Volume of prism
(y-y1)=m(x-x1)
Bh
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
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

4. What is the unfactored version of (x+y)² ?
N x M
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.
x² + 2xy + y²
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.

5. What is the prime factorization of 200?
(pi)r^2
Sum of the lengths of the sides
x°/360 times (?r²) - where x is the degrees in the angle
2x2x2x5x5

6. The length of one side of any triangle is ____ than the sum of the other two sides.
Less
(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.
The total # of possible outcomes.

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

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8. Circumference of cirlce using diameter
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.
1/3Bh
Pi*d
?d OR 2?r

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

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10. What is the average speed?
Between 0 and 1.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Total distance/total time
Not necessarily. This is a trick question - because x could be either positive or negative.

11. How do you find the slope?
A=bh
?d OR 2?r
x°/360 times (?r²) - where x is the degrees in the angle
y2-y1/x2-x1

12. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
(n degrees/360) * (pi)r^2
½(base x height) [or (base x height)÷2]
Probability A + Probability B
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.

13. 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.
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'.
y-y1=m(x-x1)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

14. Quadratic Formula
(x+y)(x-y)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Pi*d
b±[vb²-4ac]/2a

15. Area of Trapezoid
Opens down
T1 * r^(n-1)
1/2 h (b1 + b2)
?r²

16. Define the 'Third side' rule for triangles

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17. Area of Rectangle
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a-b)²
A=bh
Lw

18. What are the side ratios for a 30:60:90 triangle?
Lw
The set of points which are all the same distance (the radius) from a certain point (the center).
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x² -2xy + y²

19. What is the factored version of x² -2xy + y² ?
1/2 h (b1 + b2)
(x-y)²
Number of desired outcomes/number of total outcomes
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.

20. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
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(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.
(a-b)²
N x M

21. Perimeter of polygon
1.7
1. Given event A: A + notA = 1.
Sum of the lengths of the sides
2lw+2lh+2wh

22. What is the area of a solid rectangle?
2(lw+wh+lh)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Between 0 and 1.
2 pi r

23. (a+b)(a-b)=
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
x°/360 times (?r²) - where x is the degrees in the angle
A²-b²
Opens down

24. Area of a square
Pir^2h
S² - where s = length of a side
y = kx
(n-2)180

25. What is the area of a 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.
x²-y²
1/2bh
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

26. Volume of sphere
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Last term
4/3pir^3
1.4

27. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).
1/2bh

28. Chord
(0 -0)
Between 0 and 1.
T1 + (n-1)d
The distance from one point on the circle to another point on the circle.

29. What is a 'Right isosceles' triangle?
1. Given event A: A + notA = 1.
Number of desired outcomes/number of total outcomes
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

30. 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.
1/3Bh
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(n-2)180

31. In intersecting lines - opposite angles are _____.
2(pi)r(r+h)
Equal
2 pi r
C =?d

32. Perimeter of a rectangle
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. 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*v2
2Length + 2width [or (length + width) x 2]

33. What is the unfactored version of x²-y² ?
(x+y)(x-y)
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.
T1 * r^(n-1)/(r-1)
1/3pir^2*h

34. If x² = 144 - does v144 = x?
(x+y)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.
Not necessarily. This is a trick question - because x could be either positive or negative.
T1 * r^(n-1)/(r-1)

35. Rough est. of v2 =
1/3Bh
1.4
The distance across the circle through the center of the circle.The diameter is twice the radius.
(x-y)²

36. Perimeter of a square
(n/2) * (t1+tn)
2pir^2 + 2pir*h
4s (where s = length of a side)
Probability A + Probability B

37. What is the factored version of (x+y)(x-y) ?
Opens down
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.
A=?r2
x²-y²

38. What'S the most important thing to remember about charts you'll see on the GRE?
(n-2)180
(x1+x2)/2 - (y1+y2)/2
Equal
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.

39. What is the volume of a cylinder?
2(pi)r
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.
Last term
(pi)r^2(h)

40. Surface Area of Cylinder
Not necessarily. This is a trick question - because x could be either positive or negative.
2pir^2 + 2pir*h
2(pi)r(r+h)
A=bh

41. How do you calculate the surface area of a rectangular box?
Sum of terms/number of terms
(n degrees/360) * 2(pi)r
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+b)(a²-ab+b²)

42. Define 'proportionate' values
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.
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
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2(lw+wh+lh)

43. Perimeter of rectangle
Sqr( x2 -x1) + (y2- y1)
2l+2w
Middle term
1

44. a² - b² is equal to
2lw+2lh+2wh
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(a+b)(a-b)
Opens up

45. What is the average?
N x M
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.
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.
Sum of terms/number of terms

46. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(y2-y1)/(x2-x1)
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.

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

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48. What do combination problems usually ask for?
2pi*r
(a+b)²
Groups - teams - or committees.
2Length + 2width [or (length + width) x 2]

49. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
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.
(n degrees/360) * 2(pi)r
1.4

50. Area of Square
The distance across the circle through the center of the circle.The diameter is twice the radius.
Part of a circle connecting two points on the circle.
The average - mean - median - or mode.
S^2