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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. length of a sector
Last term
A=?r2
(a+b)(a²-ab+b²)
x°/360 times (2 pi r) - where x is the degrees in the angle
2. When a line crosses two parallel lines - ________.
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.
x°/360 times (2 pi r) - where x is the degrees in the angle
Between 0 and 1.
3. How do you calculate a diagonal inside a 3-dimensional rectangular box?
(a-b)(a²+ab+b²)
?r²
x²-y²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
4. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
Number of desired outcomes/number of total outcomes
(x+y)²
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.
5. 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.
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.
4s
Probability A * Probability B
6. Quadratic Formula
1
1/2bh
2(pi)r(r+h)
b±[vb²-4ac]/2a
7. For a bell curve - what three terms might be used to describe the number in the middle?
2(pi)r(r+h)
4/3pir^3
The average - mean - median - or mode.
(x1+x2)/2 - (y1+y2)/2
8. When you reverse FOIL - the term that needs to multiply out is the _____
2x2x2x5x5
2(pi)r
Last term
x°/360 times (?r²) - where x is the degrees in the angle
9. If something is possible but not certain - what is the numeric range of probability of it happening?
Sum of terms/number of terms
(a+b)(a-b)
1/x^a
Between 0 and 1.
10. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
N x M
Sqr( x2 -x1) + (y2- y1)
(n degrees/360) * (pi)r^2
11. How do you multiply powers with the same base?
Opens up
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
b±[vb²-4ac]/2a
(0 -0)
12. Slope
(y2-y1)/(x2-x1)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Pir^2h
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.
13. What is the distance formula?
The four big angles are equal and the four small angles are equal
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Sum of terms/number of terms
Sqr( x2 -x1) + (y2- y1)
14. Sector
(a-b)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.
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.
The distance from one point on the circle to another point on the circle.
15. What must be true before a quadratic equation can be solved?
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16. How do you find the nth term of a geometric sequence?
Pi*d
T1 * r^(n-1)
The four big angles are equal and the four small angles are equal
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
17. What is a '30:60:90' triangle?
Ac+ad+bc+bd
(y2-y1)/(x2-x1)
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. Given event A: A + notA = 1.
18. In intersecting lines - opposite angles are _____.
(x+y)²
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
The average - mean - median - or mode.
19. What is an 'equilateral' triangle?
The distance across the circle through the center of the circle.The diameter is twice the radius.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
The distance from one point on the circle to another point on the circle.
Sum of the lengths of the sides
20. In a coordinate system - identify the quadrants and describe their location.
Pir^2h
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2pi*r
2(pi)r(r+h)
21. What is 'absolute value' - and how is it represented?
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22. Explain the difference between a digit and a number.
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23. What is the sum of the inside angles of an n-sided polygon?
The set of points which are all the same distance (the radius) from a certain point (the center).
(n-2)180
Opens down
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.
24. In a coordinate system - what is the origin?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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
(0 -0)
Negative
25. What number goes on the bottom of a probability fraction?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
The total # of possible outcomes.
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
2 pi r
26. Area of a triangle
The set of points which are all the same distance (the radius) from a certain point (the center).
A=bh
A segment connecting the center of a circle to any point on the circle
½(base x height) [or (base x height)÷2]
27. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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)
y = k/x
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
28. Circumference of a circle using radius
2pi*r
Opens up
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.
Middle term
29. What is the area of a cylinder?
4s
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(pi)r(r+h)
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.
30. a³-b³
S*v2
(a-b)(a²+ab+b²)
4s (where s = length of a side)
T1 * r^(n-1)
31. What is the equation of a line?
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32. Surface Area of Cylinder
Probability A * Probability B
1.4
(y-y1)=m(x-x1)
2pir^2 + 2pir*h
33. How do you find the sum of a geometric sequence?
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.
T1 * r^(n-1)/(r-1)
(a+b)(a-b)
2Length + 2width [or (length + width) x 2]
34. Define a factorial of a number - and how it is written.
Probability A + Probability B
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.
(x1+x2)/2 - (y1+y2)/2
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.
35. Area of Circle
T1 * r^(n-1)
The average - mean - median - or mode.
Pi*r^2
1.7
36. Area of Triangle
An ange whose vertex is the center of the circle
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.
1/2bh
1/3Bh
37. The length of one side of any triangle is ____ than the sum of the other two sides.
(pi)r^2(h)
Pir^2h
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Less
38. Surface Area of rectangular prism
(n/2) * (t1+tn)
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
2lw+2lh+2wh
39. Area of rectangle - square - parallelogram
(a-b)(a+b)
1.7
A=bh
y2-y1/x2-x1
40. What is the probability?
x² -2xy + y²
2 pi r
1.7
Number of desired outcomes/number of total outcomes
41. Circumference Formula
y2-y1/x2-x1
(n-2)180
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.
C =?d
42. Volume of pyramid
1/3Bh
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
1/x^a
(0 -0)
43. Surface Area of Sphere
(n/2) * (t1+tn)
N x M
4pir^2
1/2bh
44. (a+b)(c+d)
Probability A * Probability B
2lw+2lh+2wh
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.
Ac+ad+bc+bd
45. What is the factored version of x² + 2xy + y² ?
(x+y)²
Bh
Probability A + Probability B
Percentage Change = Difference/Original * 100
46. 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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Sum of terms/number of terms
(y2-y1)/(x2-x1)
47. Volume of sphere
4/3pir^3
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.
(n/2) * (t1+tn)
Less
48. Perimeter of rectangle
Probability A * Probability B
2(pi)r(r+h)
2(pi)r(r+h)
2l+2w
49. (a+b)(a-b)=
y2-y1/x2-x1
A²-b²
(a-b)²
Sum of the lengths of the sides
50. Explain the special properties of zero.
Lwh
Number of desired outcomes/number of total outcomes
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.
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.