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Test your basic knowledge |
GRE Math 2
Start Test
Study First
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. Area of Triangle
1/2bh
(a-b)(a²+ab+b²)
(n/2) * (t1+tn)
(n-2)180
2. Area of a square
½(b1 +b2) x h [or (b1 +b2) x h÷2]
S² - where s = length of a side
?r²
y = k/x
3. What is the prime factorization of 200?
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.
1/2 h (b1 + b2)
1/3Bh
2x2x2x5x5
4. 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.
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.
1
2Length + 2width [or (length + width) x 2]
5. What is the 'Third side' rule for triangles?
2pir^2 + 2pir*h
1. Given event A: A + notA = 1.
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
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.
6. What is 'absolute value' - and how is it represented?
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7. a²-b²
(a-b)(a+b)
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
8. Does order matter for a permutation? How about for a combination?
T1 * r^(n-1)
Order does matter for a permutation - but does not matter for a combination.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
9. Rough est. of v2 =
1.4
1/3Bh
1/2 h (b1 + b2)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
10. What is the formula for the diagonal of any square?
x² -2xy + y²
x°/360 times (2 pi r) - where x is the degrees in the angle
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.
S*v2
11. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
S² - where s = length of a side
Last term
1/x^a
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.
12. What is the probability?
Number of desired outcomes/number of total outcomes
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A+b
2pir^2 + 2pir*h
13. What is the unfactored version of (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.
1.4
x² + 2xy + y²
2(pi)r(r+h)
14. How do you find the sum of an arithmetic sequence?
1/3pir^2*h
The total # of possible outcomes.
A=?r2
(n/2) * (t1+tn)
15. x^a * x^b = x^__
2lw+2lh+2wh
A+b
Negative
(0 -0)
16. To divide powers with the same base...
y2-y1/x2-x1
½(base x height) [or (base x height)÷2]
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
x°/360 times (2 pi r) - where x is the degrees in the angle
17. Volume of Cylinder
x°/360 times (?r²) - where x is the degrees in the angle
Pir^2h
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.
Probability A * Probability B
18. (a+b)(c+d)
2x2x2x5x5
A=bh
Not necessarily. This is a trick question - because x could be either positive or negative.
Ac+ad+bc+bd
19. (a+b)(a-b)=
Between 0 and 1.
A segment connecting the center of a circle to any point on the circle
A²-b²
The total # of possible outcomes.
20. a²+2ab+b²
The distance from one point on the circle to another point on the circle.
(y2-y1)/(x2-x1)
1/2bh
(a+b)²
21. 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.
?d OR 2?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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
22. Rough est. of v1 =
2(pi)r(r+h)
A+b
(x+y)(x-y)
1
23. What is the unfactored version of x²-y² ?
(x+y)(x-y)
2(pi)r(r+h)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1/3Bh
24. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
Part of a circle connecting two points on the circle.
(x-y)²
1
25. What is the length of an arc?
4s (where s = length of a side)
(n degrees/360) * 2(pi)r
Number of desired outcomes/number of total outcomes
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
26. Central Angle
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.
An ange whose vertex is the center of the circle
S² - where s = length of a side
(pi)r^2
27. Point-Slope form
2x2x2x5x5
½(b1 +b2) x h [or (b1 +b2) x h÷2]
?d OR 2?r
y-y1=m(x-x1)
28. What is directly proportional?
The average - mean - median - or mode.
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.
y = kx
A=bh
29. List two odd behaviors of exponents
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.
Sum of terms/number of terms
y = kx
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
30. Define the range of a set of numbers.
(x+y)(x-y)
2pi*r
2x2x2x5x5
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.
31. Circumference of a circle
4pir^2
(a+b)(a-b)
Probability A + Probability B
?d OR 2?r
32. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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.
1/2 h (b1 + b2)
y-y1=m(x-x1)
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
33. What is the average?
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.
N x M
Sum of terms/number of terms
Opens up
34. Volume of sphere
A segment connecting the center of a circle to any point on the circle
2pi*r
The length of any one side of a triangle must be less than the sum of the other two sides. It must also be greater than the difference between the other two sides. So - 'A' will always be < B+C - and > B-C or C-B.
4/3pir^3
35. If x² = 144 - does v144 = x?
Equal
2pi*r
1/3Bh
Not necessarily. This is a trick question - because x could be either positive or negative.
36. How do you find the slope?
Number of desired outcomes/number of total outcomes
(0 -0)
y2-y1/x2-x1
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
37. What is the 'distributive law'?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Opens up
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.
1.7
38. Perimeter of a square
Probability A + Probability B
4s (where s = length of a side)
2(pi)r(r+h)
T1 * r^(n-1)
39. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Negative
(a-b)(a+b)
Opens down
40. The length of one side of any triangle is ____ than the sum of the other two sides.
b±[vb²-4ac]/2a
Less
Probability A * Probability B
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.
41. a² - b² is equal to
2(pi)r(r+h)
(a+b)(a-b)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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
42. If something is certain to happen - how is the probability of this event expressed mathematically?
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.
Sqr( x2 -x1) + (y2- y1)
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.
1/1
43. Perimeter of rectangle
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.
2pi*r
2l+2w
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.
44. x^-a =
1/x^a
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.
Equal
1/3pir^2*h
45. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
2(pi)r
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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.
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.
46. What is inversely proportional?
y = k/x
A²-b²
2lw+2lh+2wh
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
47. Define the formula for calculating slope.
Sum of the lengths of the sides
Pir^2h
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
N x M
48. What is the surface area of a cylinder?
2(pi)r(r+h)
2 pi r
4/3pir^3
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.
49. In a coordinate system - what is the origin?
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
y = kx
Probability A + Probability B
(0 -0)
50. a³-b³
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.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(a-b)(a²+ab+b²)
1/2 h (b1 + b2)