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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. If x² = 144 - does v144 = x?
Bh
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Not necessarily. This is a trick question - because x could be either positive or negative.
2Length + 2width [or (length + width) x 2]

2. What is the factored version of (x+y)(x-y) ?
y = k/x
(x1+x2)/2 - (y1+y2)/2
x²-y²
1/2bh

3. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
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
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Ac+ad+bc+bd

4. Area of a square
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.
(a+b)(a²-ab+b²)
S² - where s = length of a side
The distance from one point on the circle to another point on the circle.

5. What is the area of a triangle?
1/2bh
The four big angles are equal and the four small angles are equal
A²-b²
T1 * r^(n-1)/(r-1)

6. Lines reflected over the x or y axis have ____ slopes.
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.
Negative
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.
(x-y)²

7. If something is possible but not certain - what is the numeric range of probability of it happening?
A segment connecting the center of a circle to any point on the circle
Sqr( x2 -x1) + (y2- y1)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Between 0 and 1.

8. What is the unfactored version of (x-y)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.
x² -2xy + y²
The average - mean - median - or mode.
T1 + (n-1)d

9. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
Equal
Probability A * Probability B
1. Given event A: A + notA = 1.

10. What is the unfactored version of (x+y)² ?
Opens up
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 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.
x² + 2xy + y²

11. Central Angle
An ange whose vertex is the center of the circle
2(lw+wh+lh)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Probability A + Probability B

12. What is the formula for the diagonal of any square?
1/2bh
S*v2
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 total # of possible outcomes.

13. Point-Slope form
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.
Pi*d
y-y1=m(x-x1)
(a-b)(a+b)

14. How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2(pi)r(r+h)
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.
1/1

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

16. What is the area of a solid rectangle?
2(pi)r
2 pi r
b±[vb²-4ac]/2a
2(lw+wh+lh)

17. Volume of Cylinder
(x+y)²
An ange whose vertex is the center of the circle
Pir^2h
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.

18. What is the side ratio for a Right Isosceles triangle?
x² + 2xy + y²
2 pi r
(n degrees/360) * 2(pi)r
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.

19. Define the formula for calculating slope.
S² - where s = length of a side
y2-y1/x2-x1
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(a+b)(a-b)

20. What is the average speed?
Total distance/total time
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.
Pi*r^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.

21. Arc
Part of a circle connecting two points on the circle.
Equal
1/1
1.7

22. Explain the special properties of zero.
2Length + 2width [or (length + width) x 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.
(n degrees/360) * 2(pi)r
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.

23. Surface Area of rectangular prism
Number of desired outcomes/number of total outcomes
2lw+2lh+2wh
S^2
An ange whose vertex is the center of the circle

24. Volume of Cone
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.
1/3pir^2*h
y2-y1/x2-x1
Last term

25. What is the surface area of a cylinder?
2(pi)r(r+h)
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.
Number of desired outcomes/number of total outcomes
?d OR 2?r

26. What is the distance formula?
Sqr( x2 -x1) + (y2- y1)
The total # of possible outcomes.
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.
2pir^2 + 2pir*h

27. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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
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.
An ange whose vertex is the center of the circle
x°/360 times (?r²) - where x is the degrees in the angle

28. a³-b³
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.
N x M
(a-b)(a²+ab+b²)
2Length + 2width [or (length + width) x 2]

29. Circumference of cirlce using diameter
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*d
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.
2pi*r

30. How do you find the midpoint?
2pi*r
T1 + (n-1)d
x°/360 times (?r²) - where x is the degrees in the angle
(x1+x2)/2 - (y1+y2)/2

31. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Last term
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.
(n degrees/360) * 2(pi)r
(n-2)180

32. Slope
x°/360 times (2 pi r) - where x is the degrees in the angle
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 distance from one point on the circle to another point on the circle.
(y2-y1)/(x2-x1)

33. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
4pir^2
Percentage Change = Difference/Original * 100
2l+2w

34. Area of a circle
?r²
T1 + (n-1)d
(pi)r^2
Lw

35. What is inversely proportional?
y = k/x
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.
1. Given event A: A + notA = 1.
S*v2

36. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
(a-b)(a²+ab+b²)
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
y2-y1/x2-x1
The average - mean - median - or mode.

37. What is the average?
Sum of terms/number of terms
Pi*d
Order does matter for a permutation - but does not matter for a combination.
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.

38. 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.
N x M
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.
4s

39. Volume of prism
Part of a circle connecting two points on the circle.
Bh
1.4
1/1

40. Perimeter of a square
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
4s (where s = length of a side)
1/1

41. How do you find the sum of a geometric sequence?
Not necessarily. This is a trick question - because x could be either positive or negative.
Sum of the lengths of the sides
Pi*d
T1 * r^(n-1)/(r-1)

42. Quadratic Formula
b±[vb²-4ac]/2a
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(a-b)²
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.

43. a³+b³
T1 * r^(n-1)/(r-1)
2lw+2lh+2wh
(a+b)(a²-ab+b²)
(a+b)(a-b)

44. When you reverse FOIL - the term that needs to add out is the _____
1/x^a
Middle term
x°/360 times (?r²) - where x is the degrees in the angle
(x+y)(x-y)

45. In a coordinate system - what is the origin?
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
Pi*r^2
(0 -0)
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. What is the 'distributive law'?
Total distance/total time
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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

47. How do you solve a permutation?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Last term
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.
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

48. Perimeter (circumference) of a circle
2 pi r
2x2x2x5x5
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.
The distance across the circle through the center of the circle.The diameter is twice the radius.

49. Area of a triangle
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'.
½(base x height) [or (base x height)÷2]
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 = k/x

50. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Groups - teams - or committees.
Probability A + Probability B
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.