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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. List two odd behaviors of exponents
S*v2
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. Given event A: A + notA = 1.
(x+y)²

2. What is the unfactored version of (x-y)² ?
Probability A + Probability B
?r²
x² + 2xy + y²
x² -2xy + y²

3. 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.
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
Bh

4. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
A²-b²
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'.
Arrangements - orders - schedules - or lists.

5. What number goes on the bottom of a probability fraction?
The distance from one point on the circle to another point on the circle.
The total # of possible outcomes.
2lw+2lh+2wh
Total distance/total time

6. What is the average speed?
Total distance/total time
T1 * r^(n-1)
Opens down
Bh

7. Define the range of a set of numbers.
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.
2pir^2 + 2pir*h
A=?r2
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.

8. What is a '30:60:90' triangle?
The distance across the circle through the center of the circle.The diameter is twice the radius.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

9. Sector
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.
x°/360 times (?r²) - where x is the degrees in the angle
2Length + 2width [or (length + width) x 2]
4s (where s = length of a side)

10. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
(pi)r^2
4/3pir^3

11. What is the factored version of x² + 2xy + y² ?
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.
x²-y²
(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.

12. What is the side ratio for a 30:60:90 triangle?
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Sum of the lengths of the sides
A circle'S perimeter is roughly 3x its diameter (the formula is pd).

13. In a parabola - if the first term is negative - the parabola ________.
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=?r2
Pir^2h
Opens down

14. What is the factored version of x² -2xy + y² ?
Less
(x-y)²
The average - mean - median - or mode.
S*v2

15. What is the formula for the diagonal of any square?
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.
Between 0 and 1.
(pi)r^2(h)
S*v2

16. Area of a square
T1 * r^(n-1)/(r-1)
Ac+ad+bc+bd
S² - where s = length of a side
1/x^a

17. Define 'proportionate' values
The total # of possible outcomes.
(x+y)(x-y)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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

18. Area of Circles
x² -2xy + y²
(a+b)(a-b)
A=?r2
1/2bh

19. Surface Area of Sphere
4pir^2
y = kx
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.
Equal

20. x^-a =
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
1/x^a

21. Area of a trapezoid
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.
1/2bh
2(pi)r(r+h)
½(b1 +b2) x h [or (b1 +b2) x h÷2]

22. Area of Circle
y-y1=m(x-x1)
(a-b)(a²+ab+b²)
Pi*r^2
2l+2w

23. 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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24. Volume of prism
Pi*d
Bh
(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.

25. Slope
(pi)r^2
(y2-y1)/(x2-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.
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.

26. Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
4s (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.
S² - where s = length of a side

27. What is the 'distributive law'?
Total distance/total time
(n-2)180
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.
x² + 2xy + y²

28. How do you multiply powers with the same base?
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.
Bh
Bh
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

29. What is the circumference of a circle?
Equal
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.
2(pi)r
Sum of terms/number of terms

30. What is the point-slope form?
A=?r2
(y-y1)=m(x-x1)
(x+y)(x-y)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.

31. Area of Square
1/x^a
½(base x height) [or (base x height)÷2]
S^2
x°/360 times (?r²) - where x is the degrees in the angle

32. What is the surface area of a cylinder?
(a-b)(a²+ab+b²)
2(pi)r(r+h)
Bh
A²-b²

33. Area of a circle
Bh
S^2
?r²
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.

34. Lines reflected over the x or y axis have ____ slopes.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
1/3pir^2*h
Lw
Negative

35. What do permutation problems often ask for?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Arrangements - orders - schedules - or lists.
Sum of terms/number of terms
Bh

36. Area of Parallelogram
Bh
1
4s
Order does matter for a permutation - but does not matter for a combination.

37. Rough est. of v3 =
1.7
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)
The distance across the circle through the center of the circle.The diameter is twice the radius.

38. If something is possible but not certain - what is the numeric range of probability of it happening?
x°/360 times (?r²) - where x is the degrees in the angle
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Between 0 and 1.
A=bh

39. The length of one side of any triangle is ____ than the sum of the other two sides.
x°/360 times (2 pi r) - where x is the degrees in the angle
Sqr( x2 -x1) + (y2- y1)
Less
A²-b²

40. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Bh
½(base x height) [or (base x height)÷2]
(a+b)(a-b)
1. Given event A: A + notA = 1.

41. x^a * x^b = x^__
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Pir^2h
A+b
Opens up

42. What is the prime factorization of 200?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Arrangements - orders - schedules - or lists.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
2x2x2x5x5

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

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44. Circumference of cirlce using diameter
2Length + 2width [or (length + width) x 2]
Pi*d
Middle term
4s

45. a²+2ab+b²
(a+b)²
(x+y)²
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
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

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

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47. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
y2-y1/x2-x1
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.
(x+y)(x-y)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

48. What is the average?
An ange whose vertex is the center of the circle
(0 -0)
x²-y²
Sum of terms/number of terms

49. Area of Rectangle
(x+y)²
Last term
Lw
Order does matter for a permutation - but does not matter for a combination.

50. What is the side ratio for a Right Isosceles triangle?
Equal
Percentage Change = Difference/Original * 100
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
S^2