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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. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
S*v2
y2-y1/x2-x1
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2. What is the circumference of a circle?
2Length + 2width [or (length + width) x 2]
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Opens up
2(pi)r
3. 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.
2pi*r
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
S^2
4. Chord
A+b
2Length + 2width [or (length + width) x 2]
The distance from one point on the circle to another point on the circle.
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.
5. How do you solve a permutation?
Probability A * Probability B
4pir^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
x°/360 times (?r²) - where x is the degrees in the angle
6. What'S the most important thing to remember about charts you'll see on the GRE?
2pi*r
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.
(y2-y1)/(x2-x1)
T1 * r^(n-1)
7. In intersecting lines - opposite angles are _____.
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
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Equal
x°/360 times (?r²) - where x is the degrees in the angle
8. Circumference Formula
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
½(base x height) [or (base x height)÷2]
The four big angles are equal and the four small angles are equal
C =?d
9. 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.
Sum of the lengths of the sides
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Middle term
10. 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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11. What is the area of a triangle?
(y-y1)=m(x-x1)
1/2bh
(a+b)²
½(base x height) [or (base x height)÷2]
12. In a coordinate system - what is the origin?
(0 -0)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
A segment connecting the center of a circle to any point on the circle
Sum of the lengths of the sides
13. Perimeter of a square
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
4s (where s = length of a side)
1/3Bh
b±[vb²-4ac]/2a
14. What is the area of a sector?
(x+y)²
Arrangements - orders - schedules - or lists.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(n degrees/360) * (pi)r^2
15. Circumference of cirlce using diameter
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
(x1+x2)/2 - (y1+y2)/2
Pi*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.
16. a³-b³
Middle term
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1.7
(a-b)(a²+ab+b²)
17. Sector
T1 * r^(n-1)/(r-1)
(x-y)²
x² + 2xy + y²
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.
18. What is the equation of a line?
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19. Area of a square
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(n degrees/360) * (pi)r^2
S² - where s = length of a side
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
20. For a bell curve - what three terms might be used to describe the number in the middle?
1/2bh
1/x^a
The average - mean - median - or mode.
Less
21. a² - b² is equal to
(a+b)(a-b)
x² + 2xy + y²
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.
?d OR 2?r
22. What is the average speed?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Total distance/total time
2pir^2 + 2pir*h
(pi)r^2
23. What is directly proportional?
y = kx
Pi*r^2
The total # of possible outcomes.
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.
24. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
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.
x°/360 times (?r²) - where x is the degrees in the angle
2(pi)r(r+h)
25. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
Middle term
The distance from one point on the circle to another point on the circle.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
26. Quadratic Formula
2Length + 2width [or (length + width) x 2]
b±[vb²-4ac]/2a
(y-y1)=m(x-x1)
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.
27. What is the area of a circle?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
(pi)r^2
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
28. What is the sum of the inside angles of an n-sided polygon?
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.
The distance from one point on the circle to another point on the circle.
(n-2)180
2l+2w
29. What is the volume of a cylinder?
Middle term
(pi)r^2(h)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
1/1
30. How do you calculate the surface area of a rectangular box?
1/2bh
C =?d
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.
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.
31. How do you multiply powers with the same base?
(y2-y1)/(x2-x1)
Pi*r^2
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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
32. What is the unfactored version of x²-y² ?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(x+y)(x-y)
Part of a circle connecting two points on the circle.
2(pi)r(r+h)
33. When a line crosses two parallel lines - ________.
The four big angles are equal and the four small angles are equal
4/3pir^3
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Pi*r^2
34. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
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35. (a+b)(c+d)
Ac+ad+bc+bd
The distance from one point on the circle to another point on the circle.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
½(base x height) [or (base x height)÷2]
36. 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
1/x^a
Opens down
2(pi)r(r+h)
37. Volume of sphere
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.
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 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.
4/3pir^3
38. In a coordinate system - identify the quadrants and describe their location.
Less
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Lwh
Pi*d
39. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
1/2 h (b1 + b2)
2x2x2x5x5
(x1+x2)/2 - (y1+y2)/2
40. Surface Area of Sphere
Sum of the lengths of the sides
A=?r2
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
4pir^2
41. Rough est. of v1 =
A=bh
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
y-y1=m(x-x1)
1
42. What are the side ratios for a 30:60:90 triangle?
2lw+2lh+2wh
Total distance/total time
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Pi*d
43. Radius (Radii)
2l+2w
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A segment connecting the center of a circle to any point on the circle
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.
44. Central Angle
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.
(y2-y1)/(x2-x1)
An ange whose vertex is the center of the circle
x² -2xy + y²
45. What is a '30:60:90' triangle?
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
Between 0 and 1.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
46. Define the range of a set of numbers.
Part of a circle connecting two points on the circle.
?d OR 2?r
½(b1 +b2) x h [or (b1 +b2) x h÷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.
47. Area of Circles
Part of a circle connecting two points on the circle.
Opens up
Opens down
A=?r2
48. Explain the difference between a digit and a number.
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49. What is the point-slope form?
(y-y1)=m(x-x1)
Middle term
(a+b)(a²-ab+b²)
b±[vb²-4ac]/2a
50. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the angle
1/2bh
(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.