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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.
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
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
(a-b)(a²+ab+b²)

2. When you reverse FOIL - the term that needs to add out is the _____
2(pi)r(r+h)
Middle term
(a+b)(a-b)
x² + 2xy + y²

3. If x² = 144 - does v144 = x?
(a-b)²
Not necessarily. This is a trick question - because x could be either positive or negative.
Sum of the lengths of the sides
½(base x height) [or (base x height)÷2]

4. What is the probability?
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.
Number of desired outcomes/number of total outcomes
y-y1=m(x-x1)
(x-y)²

5. What is the surface area of a cylinder?
A²-b²
2(pi)r(r+h)
4/3pir^3
The four big angles are equal and the four small angles are equal

6. What is the point-slope form?
Not necessarily. This is a trick question - because x could be either positive or negative.
(y-y1)=m(x-x1)
1/2 h (b1 + b2)
½(base x height) [or (base x height)÷2]

7. a²-2ab+b²
Lwh
Number of desired outcomes/number of total outcomes
2(pi)r(r+h)
(a-b)²

8. What is the 'Third side' rule for triangles?
The total # of possible outcomes.
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. Given event A: A + notA = 1.
Opens down

9. length of a sector
S² - where s = length of a side
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.
x°/360 times (2 pi r) - where x is the degrees in the angle
(y2-y1)/(x2-x1)

10. a³-b³
1/3pir^2*h
(a-b)(a²+ab+b²)
(n-2)180
Bh

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

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

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13. How do you solve a permutation?
Order does matter for a permutation - but does not matter for a combination.
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
Percentage Change = Difference/Original * 100
(x-y)²

14. Quadratic Formula
Not necessarily. This is a trick question - because x could be either positive or negative.
b±[vb²-4ac]/2a
A²-b²
Sqr( x2 -x1) + (y2- y1)

15. How do you calculate the percentage of change?
2x2x2x5x5
Percentage Change = Difference/Original * 100
Last term
4/3pir^3

16. Rough est. of v1 =
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
1
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.
Opens down

17. Area of Rectangle
1/2 h (b1 + b2)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Lw
Percentage Change = Difference/Original * 100

18. Area of Triangle
1/2bh
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
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.
Arrangements - orders - schedules - or lists.

19. What is the average speed?
Negative
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Total distance/total time
An ange whose vertex is the center of the circle

20. What is the factored version of x² + 2xy + y² ?
y2-y1/x2-x1
(x+y)²
Percentage Change = Difference/Original * 100
Pi*r^2

21. Circumference Formula
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.
C =?d
S² - where s = length of a side
y = k/x

22. What number goes on the bottom of a probability fraction?
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
A segment connecting the center of a circle to any point on the circle
?d OR 2?r
The total # of possible outcomes.

23. Area of a circle
?r²
Arrangements - orders - schedules - or lists.
The total # of possible outcomes.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

24. What do combination problems usually ask for?
T1 * r^(n-1)/(r-1)
A²-b²
y = kx
Groups - teams - or committees.

25. To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
A²-b²
1/3pir^2*h
Less

26. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2(lw+wh+lh)
(a+b)²
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.

27. How do you find the sum of a geometric sequence?
(a+b)(a²-ab+b²)
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.
Groups - teams - or committees.
T1 * r^(n-1)/(r-1)

28. What'S the most important thing to remember about charts you'll see on the GRE?
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.
1/2 h (b1 + b2)
A=?r2
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

29. Volume of Cylinder
Less
Pir^2h
Not necessarily. This is a trick question - because x could be either positive or negative.
T1 + (n-1)d

30. What is the distance formula?
½(base x height) [or (base x height)÷2]
Sqr( x2 -x1) + (y2- y1)
Percentage Change = Difference/Original * 100
The set of points which are all the same distance (the radius) from a certain point (the center).

31. How do you calculate the probability of two events in a row? (Probability of A and B)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Number of desired outcomes/number of total outcomes
A+b
Probability A * Probability B

32. Perimeter of polygon
Sum of the lengths of the sides
1.7
(n degrees/360) * (pi)r^2
x² + 2xy + y²

33. Define the 'Third side' rule for triangles

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34. In a coordinate system - what is the origin?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(0 -0)
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'.
Opens up

35. Slope
(y2-y1)/(x2-x1)
1. Given event A: A + notA = 1.
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
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

36. List two odd behaviors of exponents
N x M
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.
S*v2
(x1+x2)/2 - (y1+y2)/2

37. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.

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38. How do you find the midpoint?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x°/360 times (2 pi r) - where x is the degrees in the angle
x² + 2xy + y²
(x1+x2)/2 - (y1+y2)/2

39. What are the side ratios for a 30:60:90 triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Lwh
x°/360 times (2 pi r) - where x is the degrees in the angle
T1 * r^(n-1)/(r-1)

40. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
The distance across the circle through the center of the circle.The diameter is twice the radius.
Pir^2h
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.

41. What is the unfactored version of (x-y)² ?
S*v2
1/3Bh
A=bh
x² -2xy + y²

42. What is the unfactored version of x²-y² ?
2x2x2x5x5
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.
Sum of terms/number of terms
(x+y)(x-y)

43. In a parabola - if the first term is positive - the parabola ________.
Opens down
Last term
(a-b)²
Opens up

44. What is the prime factorization of 200?
(a+b)²
(a+b)(a-b)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2x2x2x5x5

45. Diameter
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.
x² + 2xy + y²
The distance across the circle through the center of the circle.The diameter is twice the radius.
Lw

46. Rough est. of v3 =
1.7
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
Pi*d

47. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
Sum of the lengths of the sides
(a-b)(a+b)
Pi*r^2

48. Surface Area of Cylinder
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(h)
A²-b²
2pir^2 + 2pir*h

49. What is the area of a solid rectangle?
2(lw+wh+lh)
(n-2)180
y-y1=m(x-x1)
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.

50. Area of Square
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Pir^2h
S^2
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.