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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 'distributive law'?
1/1
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.
Probability A * Probability B
An ange whose vertex is the center of the circle
2. Rough est. of v1 =
1
Pi*d
(x+y)(x-y)
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.
3. a²+2ab+b²
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.
T1 * r^(n-1)/(r-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
(a+b)²
4. Define 'proportionate' values
(a-b)²
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
x² + 2xy + y²
5. Area of Circle
Pi*r^2
?r²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2(pi)r(r+h)
6. Volume of Cylinder
An ange whose vertex is the center of the circle
Pir^2h
Between 0 and 1.
Sum of the lengths of the sides
7. Circumference Formula
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
C =?d
Last term
8. Volume of sphere
2(lw+wh+lh)
4/3pir^3
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
Lw
9. What is the length of an arc?
(n degrees/360) * 2(pi)r
Sum of the lengths of the sides
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
10. a²-b²
(a-b)(a+b)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
N x M
11. Central Angle
A segment connecting the center of a circle to any point on the circle
Ac+ad+bc+bd
4pir^2
An ange whose vertex is the center of the circle
12. How do you find the sum of an arithmetic sequence?
(n/2) * (t1+tn)
y2-y1/x2-x1
1/2 h (b1 + b2)
2pi*r
13. Area of a trapezoid
1/x^a
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Percentage Change = Difference/Original * 100
14. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
4s
(x+y)²
N x M
2(pi)r(r+h)
15. x^-a =
T1 + (n-1)d
(n degrees/360) * (pi)r^2
Part of a circle connecting two points on the circle.
1/x^a
16. What is the volume of a solid rectangle?
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.
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.
Lwh
(pi)r^2
17. What is the circumference of a circle?
The four big angles are equal and the four small angles are equal
2(pi)r
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
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
18. 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.
y = k/x
Last term
The distance from one point on the circle to another point on the circle.
19. Arc
N x M
Part of a circle connecting two points on the circle.
A=?r2
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
20. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
(n degrees/360) * (pi)r^2
(x+y)²
Lw
21. In a coordinate system - what is the origin?
Groups - teams - or committees.
(0 -0)
?r²
2(pi)r(r+h)
22. Volume of Cone
1/3pir^2*h
A²-b²
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
(a+b)²
23. Area of a triangle
Bh
½(base x height) [or (base x height)÷2]
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Middle term
24. What is the point-slope form?
(x+y)²
(y-y1)=m(x-x1)
A=bh
(x+y)(x-y)
25. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Order does matter for a permutation - but does not matter for a combination.
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.
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.
26. 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.
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.
2pir^2 + 2pir*h
2(pi)r(r+h)
27. What must be true before a quadratic equation can be solved?
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28. What number goes on the bottom of a probability fraction?
Negative
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(x1+x2)/2 - (y1+y2)/2
The total # of possible outcomes.
29. What is the equation of a line?
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30. Does order matter for a permutation? How about for a combination?
Lw
The distance from one point on the circle to another point on the circle.
Order does matter for a permutation - but does not matter for a combination.
2(pi)r(r+h)
31. Volume of pyramid
1/3Bh
4s (where s = length of a side)
(x+y)(x-y)
The total # of possible outcomes.
32. List two odd behaviors of exponents
Ac+ad+bc+bd
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.
(a+b)²
2pir^2 + 2pir*h
33. How do you calculate a diagonal inside a 3-dimensional rectangular box?
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
?r²
1.4
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
34. How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
Pi*d
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
35. How do you calculate the probability of two events in a row? (Probability of A and B)
(n/2) * (t1+tn)
Probability A * Probability B
Number of desired outcomes/number of total outcomes
The distance from one point on the circle to another point on the circle.
36. What is 'absolute value' - and how is it represented?
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37. How do you calculate the percentage of change?
T1 * r^(n-1)
Probability A * Probability B
(pi)r^2(h)
Percentage Change = Difference/Original * 100
38. Area of a square
Middle term
Total distance/total time
S² - where s = length of a side
Negative
39. How do you find the nth term of an arithmetic sequence?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
T1 + (n-1)d
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Pi*d
40. Area of Trapezoid
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.
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.
(a+b)(a-b)
41. For a bell curve - what three terms might be used to describe the number in the middle?
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 average - mean - median - or mode.
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
42. Chord
A=bh
The distance from one point on the circle to another point on the circle.
Bh
Groups - teams - or committees.
43. Perimeter of rectangle
Between 0 and 1.
Sum of the lengths of the sides
2l+2w
A=bh
44. Explain the difference between a digit and a number.
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45. To divide powers with the same base...
2(pi)r
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.
Lwh
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
46. When a line crosses two parallel lines - ________.
The four big angles are equal and the four small angles are equal
(y-y1)=m(x-x1)
Not necessarily. This is a trick question - because x could be either positive or negative.
Arrangements - orders - schedules - or lists.
47. How do you find the slope?
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.
y2-y1/x2-x1
x² -2xy + y²
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.
48. What are the side ratios for a 30:60:90 triangle?
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.
2(lw+wh+lh)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Sqr( x2 -x1) + (y2- y1)
49. Define a factorial of a number - and how it is written.
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.
(n degrees/360) * 2(pi)r
4s
Opens up
50. When you reverse FOIL - the term that needs to multiply out is the _____
2l+2w
Arrangements - orders - schedules - or lists.
S² - where s = length of a side
Last term