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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 average?
Sum of terms/number of terms
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
4s (where s = length of a side)
Equal

2. 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
1/2 h (b1 + b2)
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.
(x-y)²

3. How do you find the sum of a geometric sequence?
S*v2
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.
2x2x2x5x5
T1 * r^(n-1)/(r-1)

4. Area of Circles
2 pi r
A=?r2
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.
(a-b)(a²+ab+b²)

5. (a+b)(a-b)=
(a+b)²
x²-y²
A²-b²
Order does matter for a permutation - but does not matter for a combination.

6. Explain the special properties of zero.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
S^2
Opens down

7. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Sqr( x2 -x1) + (y2- y1)
(a+b)(a-b)
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.
?r²

8. Define a factorial of a number - and how it is written.
2lw+2lh+2wh
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
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.
x°/360 times (2 pi r) - where x is the degrees in the angle

9. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
4s
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
(a+b)(a-b)

10. a²+2ab+b²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Total distance/total time
(a+b)²
Probability A * Probability B

11. x^-a =
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
A segment connecting the center of a circle to any point on the circle
Less
1/x^a

12. Area of a triangle
1.7
½(base x height) [or (base x height)÷2]
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.
1/2bh

13. Central Angle
(x1+x2)/2 - (y1+y2)/2
1. Given event A: A + notA = 1.
An ange whose vertex is the center of the circle
(pi)r^2(h)

14. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
x°/360 times (?r²) - where x is the degrees in the angle
The set of points which are all the same distance (the radius) from a certain point (the center).
(pi)r^2

15. (a+b)(c+d)
The average - mean - median - or mode.
1/2 h (b1 + b2)
The four big angles are equal and the four small angles are equal
Ac+ad+bc+bd

16. Define the 'Third side' rule for triangles

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17. What is the area of a circle?
(pi)r^2
(n/2) * (t1+tn)
The distance across the circle through the center of the circle.The diameter is twice the radius.
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.

18. How do you find the sum of an arithmetic sequence?
Bh
The average - mean - median - or mode.
(a+b)(a-b)
(n/2) * (t1+tn)

19. How do you find the nth term of an arithmetic sequence?
(n-2)180
A+b
T1 + (n-1)d
x°/360 times (2 pi r) - where x is the degrees in the angle

20. Area of a circle
1
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.
?r²
(a-b)(a+b)

21. Circumference of a circle using radius
(a-b)(a+b)
Negative
2pi*r
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

22. What is the prime factorization of 200?
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.
2x2x2x5x5
Equal
y-y1=m(x-x1)

23. 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.
1
(n-2)180
Sqr( x2 -x1) + (y2- y1)

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

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25. What is the area of a cylinder?
x² -2xy + y²
(a+b)(a-b)
2(pi)r(r+h)
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.

26. Volume of Cone
Ac+ad+bc+bd
x²-y²
1/3pir^2*h
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2

27. When you reverse FOIL - the term that needs to add out is the _____
Opens up
The four big angles are equal and the four small angles are equal
Middle term
1

28. a²-b²
x²-y²
(a-b)(a²+ab+b²)
(a-b)(a+b)
A segment connecting the center of a circle to any point on the circle

29. Volume of pyramid
Sum of the lengths of the sides
1/3Bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

30. How do you find the midpoint?
A=bh
(a-b)(a²+ab+b²)
1/3Bh
(x1+x2)/2 - (y1+y2)/2

31. What'S the most important thing to remember about charts you'll see on the GRE?
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.
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.
2pi*r
2(pi)r

32. What is the length of an arc?
1/2bh
x² + 2xy + y²
Probability A + Probability B
(n degrees/360) * 2(pi)r

33. Surface Area of Sphere
4pir^2
Equal
2lw+2lh+2wh
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

34. Area of a sector
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.
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
x°/360 times (?r²) - where x is the degrees in the angle

35. Define the range of a set of numbers.
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.
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.
(0 -0)
Arrangements - orders - schedules - or lists.

36. Circle
The set of points which are all the same distance (the radius) from a certain point (the center).
Ac+ad+bc+bd
(a-b)(a²+ab+b²)
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.

37. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
The four big angles are equal and the four small angles are equal
The average - mean - median - or mode.
S² - where s = length of a side
N x M

38. What is a 'Right isosceles' triangle?
Order does matter for a permutation - but does not matter for a combination.
Opens down
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.
(n degrees/360) * 2(pi)r

39. Area of Trapezoid
1/2bh
Less
1/2 h (b1 + b2)
A segment connecting the center of a circle to any point on the circle

40. Chord
Probability A * Probability B
Groups - teams - or committees.
The distance from one point on the circle to another point on the circle.
The set of points which are all the same distance (the radius) from a certain point (the center).

41. How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
4/3pir^3
(x-y)²
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.

42. What is the 'distributive law'?
The distance across the circle through the center of the circle.The diameter is twice the radius.
Middle term
(a+b)(a²-ab+b²)
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.

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

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44. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
(y-y1)=m(x-x1)
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
(x-y)²

45. Volume of Cylinder
The average - mean - median - or mode.
Part of a circle connecting two points on the circle.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Pir^2h

46. How do you find the nth term of a geometric sequence?
T1 * r^(n-1)
Not necessarily. This is a trick question - because x could be either positive or negative.
Percentage Change = Difference/Original * 100
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

47. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
4s
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.
Total distance/total time
2(pi)r(r+h)

48. What is directly proportional?
2lw+2lh+2wh
?r²
y = kx
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.

49. Slope
(0 -0)
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.
(y2-y1)/(x2-x1)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.

50. perimeter of square
S*v2
4s
The average - mean - median - or mode.
A=bh