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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. What is the area of a circle?
Arrangements - orders - schedules - or lists.
(pi)r^2
T1 + (n-1)d
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.
2. Perimeter of polygon
1.7
2lw+2lh+2wh
½(base x height) [or (base x height)÷2]
Sum of the lengths of the sides
3. Define the range of a set of numbers.
N x M
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.
S^2
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.
4. Diameter
1. Given event A: A + notA = 1.
Lw
The distance across the circle through the center of the circle.The diameter is twice the radius.
2(pi)r(r+h)
5. Surface Area of Cylinder
Between 0 and 1.
The set of points which are all the same distance (the radius) from a certain point (the center).
2pir^2 + 2pir*h
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
6. (a+b)(a-b)=
Arrangements - orders - schedules - or lists.
A²-b²
(x+y)(x-y)
C =?d
7. a²+2ab+b²
½(base x height) [or (base x height)÷2]
(a+b)²
Probability A + Probability B
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'.
8. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
T1 * r^(n-1)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(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.
9. To divide powers with the same base...
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
N x M
10. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
(pi)r^2(h)
The distance from one point on the circle to another point on the circle.
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.
S^2
11. Area of a circle
2x2x2x5x5
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.
?r²
x°/360 times (2 pi r) - where x is the degrees in the angle
12. If x² = 144 - does v144 = x?
1/3Bh
Not necessarily. This is a trick question - because x could be either positive or negative.
Pir^2h
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.
13. Explain the special properties of zero.
(pi)r^2
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Part of a circle connecting two points on the circle.
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.
14. What is the side ratio 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.
Probability A * Probability B
(x1+x2)/2 - (y1+y2)/2
1/3pir^2*h
15. Define 'proportionate' values
Lwh
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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. 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.
16. Perimeter (circumference) of a circle
(pi)r^2(h)
2 pi r
The four big angles are equal and the four small angles are equal
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
17. How do you find the nth term of an arithmetic sequence?
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
T1 + (n-1)d
y = k/x
18. Circumference of a circle using radius
2pi*r
Less
1/2bh
2(pi)r(r+h)
19. Perimeter of a rectangle
S*v2
2(pi)r
2Length + 2width [or (length + width) x 2]
Probability A + Probability B
20. What'S the most important thing to remember about charts you'll see on the GRE?
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
21. What is the factored version of (x+y)(x-y) ?
(a-b)²
x²-y²
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2Length + 2width [or (length + width) x 2]
22. Area of a triangle
Lw
½(base x height) [or (base x height)÷2]
x°/360 times (?r²) - where x is the degrees in the angle
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.
23. Rough est. of v1 =
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.
(x1+x2)/2 - (y1+y2)/2
1
Less
24. a² - b² is equal to
2(pi)r
(a+b)(a-b)
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.
Last term
25. Arc
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.
Percentage Change = Difference/Original * 100
A+b
26. Area of Parallelogram
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/x^a
(n degrees/360) * (pi)r^2
Bh
27. What is the 'distributive law'?
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 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
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.
28. If something is possible but not certain - what is the numeric range of probability of it happening?
Equal
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.
Between 0 and 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.
29. a²-2ab+b²
N x M
(a-b)²
(x1+x2)/2 - (y1+y2)/2
Groups - teams - or committees.
30. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
T1 * r^(n-1)/(r-1)
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
A=bh
31. Volume of Cylinder
S^2
1.7
Number of desired outcomes/number of total outcomes
Pir^2h
32. Volume of pyramid
2(pi)r(r+h)
Number of desired outcomes/number of total outcomes
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'.
1/3Bh
33. What is the equation of a line?
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34. Point-Slope form
y-y1=m(x-x1)
(n-2)180
2 pi r
Probability A + Probability B
35. Area of Triangle
(a-b)(a+b)
Pi*r^2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1/2bh
36. Radius (Radii)
4pir^2
A segment connecting the center of a circle to any point on the circle
2(pi)r
2Length + 2width [or (length + width) x 2]
37. Area of Trapezoid
Last term
Opens down
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)
38. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
Negative
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Sum of terms/number of terms
39. How do you find the slope?
y2-y1/x2-x1
The total # of possible outcomes.
(a+b)(a-b)
C =?d
40. Define the formula for calculating slope.
Lw
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
?r²
41. a³-b³
Order does matter for a permutation - but does not matter for a combination.
(n degrees/360) * 2(pi)r
2Length + 2width [or (length + width) x 2]
(a-b)(a²+ab+b²)
42. What number goes on the bottom of a probability fraction?
Bh
?d OR 2?r
The total # of possible outcomes.
½(base x height) [or (base x height)÷2]
43. In a parabola - if the first term is negative - the parabola ________.
2x2x2x5x5
Pi*r^2
Opens down
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.
44. a²-b²
(a-b)(a+b)
The distance from one point on the circle to another point on the circle.
1/x^a
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.
45. What is the volume of a solid rectangle?
Lwh
Pi*d
A=bh
Ac+ad+bc+bd
46. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
N x M
Groups - teams - or committees.
T1 * r^(n-1)
Equal
47. What is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Pi*d
(x1+x2)/2 - (y1+y2)/2
T1 + (n-1)d
48. Quadratic Formula
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
T1 * r^(n-1)/(r-1)
Lwh
b±[vb²-4ac]/2a
49. 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.
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.
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.
(n-2)180
50. What do permutation problems often ask for?
S² - where s = length of a side
Opens up
y-y1=m(x-x1)
Arrangements - orders - schedules - or lists.