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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. How do you find the nth term of an arithmetic sequence?
N x M
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
T1 + (n-1)d
(a-b)(a²+ab+b²)
2. Rough est. of v1 =
1
2lw+2lh+2wh
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
1/2 h (b1 + b2)
3. How do you find the nth term of a geometric sequence?
T1 * r^(n-1)
A segment connecting the center of a circle to any point on the circle
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.
(pi)r^2(h)
4. Surface Area of rectangular prism
2lw+2lh+2wh
(x-y)²
1
Negative
5. In a coordinate system - what is the origin?
Total distance/total time
(0 -0)
Pi*r^2
(n-2)180
6. How do you calculate the probability of two events in a row? (Probability of A and B)
y = k/x
Probability A * Probability B
(x-y)²
A=bh
7. Circumference Formula
(n-2)180
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.
C =?d
b±[vb²-4ac]/2a
8. Perimeter of a rectangle
N x M
Last term
2Length + 2width [or (length + width) x 2]
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
9. How do you multiply and divide square roots?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
The average - mean - median - or mode.
N x M
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
10. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.
11. (a+b)(c+d)
Ac+ad+bc+bd
(n degrees/360) * 2(pi)r
(x+y)²
1/2 h (b1 + b2)
12. Circumference of cirlce using diameter
Opens up
Pi*d
C =?d
2(pi)r
13. What is the point-slope form?
S² - where s = length of a side
The four big angles are equal and the four small angles are equal
(pi)r^2
(y-y1)=m(x-x1)
14. Volume of Cylinder
(a-b)(a+b)
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.
Pir^2h
Number of desired outcomes/number of total outcomes
15. Area of Triangle
T1 * r^(n-1)
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.
1/2bh
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.
16. a²-2ab+b²
2(pi)r(r+h)
The average - mean - median - or mode.
T1 + (n-1)d
(a-b)²
17. 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.
1
y2-y1/x2-x1
A segment connecting the center of a circle to any point on the circle
18. What is the factored version of x² -2xy + y² ?
(x-y)²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
(a-b)(a²+ab+b²)
y-y1=m(x-x1)
19. Volume of prism
C =?d
x² -2xy + y²
Bh
Order does matter for a permutation - but does not matter for a combination.
20. What is the unfactored version of (x-y)² ?
x² -2xy + y²
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.
(0 -0)
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.
21. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
1. Given event A: A + notA = 1.
1/2 h (b1 + b2)
A=?r2
22. Volume of pyramid
T1 + (n-1)d
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
1
1/3Bh
23. Circumference of a circle
?d OR 2?r
Bh
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.
4/3pir^3
24. What is the probability?
Negative
4s
(x-y)²
Number of desired outcomes/number of total outcomes
25. What is a '30:60:90' triangle?
(n/2) * (t1+tn)
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
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
26. x^a * x^b = x^__
Bh
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.
(a+b)(a-b)
A+b
27. For a bell curve - what three terms might be used to describe the number in the middle?
Bh
The average - mean - median - or mode.
S^2
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.
28. 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.
(pi)r^2
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
y2-y1/x2-x1
29. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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.
Less
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
30. (a+b)(a-b)=
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(y2-y1)/(x2-x1)
A²-b²
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.
31. Volume of sphere
(n-2)180
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
32. What is the area of a circle?
1
(pi)r^2
(a-b)(a²+ab+b²)
Order does matter for a permutation - but does not matter for a combination.
33. Area of Circle
Pi*r^2
2 pi r
Number of desired outcomes/number of total outcomes
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
34. What is the factored version of x² + 2xy + y² ?
(x+y)²
2pi*r
2(pi)r(r+h)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
35. What is the area of a triangle?
1.4
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.
1/2bh
The set of points which are all the same distance (the radius) from a certain point (the center).
36. In a parabola - if the first term is positive - the parabola ________.
y = k/x
Opens up
2x2x2x5x5
4s
37. When you reverse FOIL - the term that needs to add out is the _____
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.
x² + 2xy + y²
Middle term
1/3pir^2*h
38. How do you find the slope?
The distance across the circle through the center of the circle.The diameter is twice the radius.
Lw
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.
y2-y1/x2-x1
39. How do you calculate the surface area of a rectangular box?
The average - mean - median - or mode.
x°/360 times (2 pi r) - where x is the degrees in the angle
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.
Between 0 and 1.
40. a² - b² is equal to
4/3pir^3
Total distance/total time
(a+b)(a-b)
A²-b²
41. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
y2-y1/x2-x1
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.
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
42. Sector
Part of a circle connecting two points on the circle.
2l+2w
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
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.
43. What is the 'distributive law'?
½(base x height) [or (base x height)÷2]
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
2pir^2 + 2pir*h
44. Area of rectangle - square - parallelogram
A=bh
A segment connecting the center of a circle to any point 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.
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.
45. What is the circumference of a circle?
Negative
2(pi)r
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Probability A * Probability B
46. a²+2ab+b²
(a+b)²
(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.
?d OR 2?r
47. What is the 'Third side' rule for triangles?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
x² + 2xy + y²
S² - where s = length of a side
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.
48. Area of a square
Sqr( x2 -x1) + (y2- y1)
Opens up
S² - where s = length of a side
Last term
49. Define the range of a set of numbers.
A segment connecting the center of a circle to any point on the circle
(x1+x2)/2 - (y1+y2)/2
2(lw+wh+lh)
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.
50. Define the 'Third side' rule for triangles