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GRE Math 2

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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?
Sum of the lengths of the sides
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
4s (where s = length of a side)

2. a² - b² is equal to
T1 * r^(n-1)/(r-1)
x² -2xy + y²
x² + 2xy + y²
(a+b)(a-b)

3. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
(n degrees/360) * 2(pi)r
(x+y)(x-y)
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. 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

4. Volume of pyramid
Middle term
Probability A + Probability B
2pir^2 + 2pir*h
1/3Bh

5. Explain the special properties of zero.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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 set of points which are all the same distance (the radius) from a certain point (the center).
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.

6. Circumference Formula
C =?d
1/2 h (b1 + b2)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Ac+ad+bc+bd

7. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Part of a circle connecting two points on the circle.
Bh
x°/360 times (?r²) - where x is the degrees in the angle
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.

8. Define the 'Third side' rule for triangles

9. What is the side ratio for a 30:60:90 triangle?
1/3Bh
1/2bh
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.

10. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
T1 * r^(n-1)
x² + 2xy + y²

11. Lines reflected over the x or y axis have ____ slopes.
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.
y-y1=m(x-x1)
Negative
T1 * r^(n-1)

12. What is the factored version of x² + 2xy + y² ?
(x+y)²
4pir^2
A segment connecting the center of a circle to any point on the circle
Middle term

13. Area of a square
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
S² - where s = length of a side
2(pi)r(r+h)
N x M

14. a²+2ab+b²
Last term
Total distance/total time
(a+b)²
4/3pir^3

15. x^a * x^b = x^__
4/3pir^3
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
(n-2)180

16. To divide powers with the same base...
The distance from one point on the circle to another point on the circle.
(a-b)²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1. Given event A: A + notA = 1.

17. Perimeter (circumference) of a circle
b±[vb²-4ac]/2a
2 pi r
Lw
4pir^2

18. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
2Length + 2width [or (length + width) x 2]
y2-y1/x2-x1
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 part of a circle that looks like a piece of pie. A sector is bounded by 2 radii and an arc of the circle.

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

20. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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
1/2 h (b1 + b2)
2(lw+wh+lh)

21. Area of Circle
2(pi)r(r+h)
1/2bh
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.
Pi*r^2

22. How do you solve a permutation?
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
N x M
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

23. What is the prime factorization of 200?
4pir^2
2x2x2x5x5
2 pi r
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

24. Perimeter of polygon
1/2bh
2(pi)r
Sum of the lengths of the sides
S² - where s = length of a side

25. Chord
(a-b)(a²+ab+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 from one point on the circle to another point on the circle.
1/2bh

26. When you reverse FOIL - the term that needs to add out is the _____
Middle term
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)(a²+ab+b²)
x²-y²

27. What is a '30:60:90' triangle?
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.
2x2x2x5x5
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 degrees/360) * 2(pi)r

28. What is the factored version of (x+y)(x-y) ?
The total # of possible outcomes.
4/3pir^3
x²-y²
(y-y1)=m(x-x1)

29. What is the 'distributive law'?
4s
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.
2lw+2lh+2wh
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'.

30. Arc
Part of a circle connecting two points on the circle.
The four big angles are equal and the four small angles are equal
Sum of terms/number of terms
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

31. Define a factorial of a number - and how it is written.
(x+y)(x-y)
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.
Arrangements - orders - schedules - or lists.
Opens down

32. The probability of an event happening and the probability of an event NOT happening must add up to what number?
(n degrees/360) * 2(pi)r
1. Given event A: A + notA = 1.
1
x°/360 times (2 pi r) - where x is the degrees in the angle

33. When a line crosses two parallel lines - ________.
The four big angles are equal and the four small angles are equal
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.
2Length + 2width [or (length + width) x 2]
A²-b²

34. Surface Area of Cylinder
The four big angles are equal and the four small angles are equal
2pir^2 + 2pir*h
2(lw+wh+lh)
(pi)r^2

35. The length of one side of any triangle is ____ than the sum of the other two sides.
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
Less
x² -2xy + y²
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

36. Circumference of cirlce using diameter
?d OR 2?r
2Length + 2width [or (length + width) x 2]
Pi*d
Probability A + Probability B

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

38. How do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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)(a²-ab+b²)
2(pi)r

39. What is the average?
1
x°/360 times (?r²) - where x is the degrees in the angle
Sum of terms/number of terms
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5

40. What'S the most important thing to remember about charts you'll see on the GRE?
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.
1/3pir^2*h
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
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.

41. How do you multiply and divide square roots?
2lw+2lh+2wh
Groups - teams - or committees.
A=?r2
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

42. Area of a triangle
The average - mean - median - or mode.
½(base x height) [or (base x height)÷2]
1/x^a
4s

43. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
S^2
Probability A + Probability B
Lwh
1.7

44. In a parabola - if the first term is positive - the parabola ________.
2pir^2 + 2pir*h
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
Opens up
The set of points which are all the same distance (the radius) from a certain point (the center).

45. What is the volume of a solid rectangle?
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
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 average - mean - median - or mode.
Lwh

46. Slope
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.
2l+2w
(y2-y1)/(x2-x1)
S^2

47. Area of Square
A=?r2
S^2
Opens down
An ange whose vertex is the center of the circle

48. If x² = 144 - does v144 = x?
4pir^2
Not necessarily. This is a trick question - because x could be either positive or negative.
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

49. Circumference of a circle
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.
1.7
?d OR 2?r
Pi*r^2

50. What do combination problems usually ask for?
Groups - teams - or committees.
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
x² + 2xy + y²