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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. (a+b)(a-b)=
y-y1=m(x-x1)
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.
A²-b²
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.
2. How do you calculate the probability of two events in a row? (Probability of A and B)
T1 * r^(n-1)
x² + 2xy + y²
(x+y)(x-y)
Probability A * Probability B
3. What is the area of a cylinder?
1/x^a
Less
y = kx
2(pi)r(r+h)
4. What is the factored version of x² + 2xy + y² ?
(x+y)²
(pi)r^2
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.
An ange whose vertex is the center of the circle
5. Quadratic Formula
2Length + 2width [or (length + width) x 2]
2x2x2x5x5
b±[vb²-4ac]/2a
(y2-y1)/(x2-x1)
6. When a line crosses two parallel lines - ________.
y-y1=m(x-x1)
2(pi)r(r+h)
The four big angles are equal and the four small angles are equal
Percentage Change = Difference/Original * 100
7. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).
8. In a parabola - if the first term is positive - the parabola ________.
A²-b²
Opens up
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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
9. What is the formula for the diagonal of any square?
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.
S*v2
Total distance/total time
Pi*d
10. Perimeter (circumference) of a circle
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2 pi r
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
The distance across the circle through the center of the circle.The diameter is twice the radius.
11. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
b±[vb²-4ac]/2a
The average - mean - median - or mode.
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.
12. What is 'absolute value' - and how is it represented?
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13. Surface Area of rectangular prism
(pi)r^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.
2lw+2lh+2wh
(x+y)(x-y)
14. What is the volume of a cylinder?
S^2
?r²
Bh
(pi)r^2(h)
15. What is inversely proportional?
4/3pir^3
y = k/x
An ange whose vertex is the center of the circle
1/2 h (b1 + b2)
16. How do you find the nth term of an arithmetic sequence?
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
Sum of the lengths of the sides
y2-y1/x2-x1
T1 + (n-1)d
17. Circumference of a circle
y2-y1/x2-x1
?d OR 2?r
x² -2xy + y²
Lw
18. 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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19. Surface Area of Sphere
4pir^2
Probability A + Probability B
A=?r2
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.
20. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
1/1
2Length + 2width [or (length + width) x 2]
(x1+x2)/2 - (y1+y2)/2
21. perimeter of square
4s
4pir^2
(a+b)(a-b)
4/3pir^3
22. Perimeter of rectangle
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.
x²-y²
2l+2w
N x M
23. Perimeter of a square
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
4s (where s = length of a side)
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'.
The four big angles are equal and the four small angles are equal
24. What is the factored version of x² -2xy + y² ?
(x-y)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.
4s (where s = length of a side)
Negative
25. What is the sum of the inside angles of an n-sided polygon?
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.
Order does matter for a permutation - but does not matter for a combination.
Last term
(n-2)180
26. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
1/3Bh
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 four big angles are equal and the four small angles are equal
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.
27. What is the side ratio for a Right Isosceles triangle?
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(a-b)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
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.
28. Volume of prism
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Lwh
Bh
x² + 2xy + y²
29. Define the 'Third side' rule for triangles
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30. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
N x M
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/x^a
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.
31. What is a 'Right isosceles' triangle?
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. Given event A: A + notA = 1.
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.
Middle term
32. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.
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33. What is the point-slope form?
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 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.
(x+y)(x-y)
(y-y1)=m(x-x1)
34. If x² = 144 - does v144 = x?
Equal
2l+2w
Last term
Not necessarily. This is a trick question - because x could be either positive or negative.
35. What is the prime factorization of 200?
Order does matter for a permutation - but does not matter for a combination.
2x2x2x5x5
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.
A+b
36. What is the area of a solid rectangle?
Probability A * Probability B
S^2
2(lw+wh+lh)
x°/360 times (?r²) - where x is the degrees in the angle
37. Area of Rectangle
2 pi r
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.
1/x^a
Lw
38. Perimeter of polygon
Sum of the lengths of the sides
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Total distance/total time
A=bh
39. Lines reflected over the x or y axis have ____ slopes.
2(pi)r(r+h)
Negative
1/2bh
Sum of terms/number of terms
40. How do you find the sum of an arithmetic sequence?
1/x^a
(a+b)²
(n/2) * (t1+tn)
(x1+x2)/2 - (y1+y2)/2
41. Area of Parallelogram
A+b
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.
Bh
42. 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.
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.
S² - where s = length of a side
(0 -0)
43. How do you multiply and divide square roots?
y-y1=m(x-x1)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
½(base x height) [or (base x height)÷2]
1. Given event A: A + notA = 1.
44. Define the formula for calculating slope.
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.
(y-y1)=m(x-x1)
The four big angles are equal and the four small angles are equal
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
45. How do you calculate the surface area of a rectangular box?
(a+b)(a²-ab+b²)
2Length + 2width [or (length + width) x 2]
(x+y)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.
46. a²+2ab+b²
Sum of the lengths of the sides
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
(a+b)²
47. How do you calculate the percentage of change?
1.7
1/3pir^2*h
Percentage Change = Difference/Original * 100
Less
48. Define a factorial of a number - and how it is written.
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.
(pi)r^2(h)
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.
Bh
49. Rough est. of v1 =
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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
T1 * r^(n-1)
1
50. What is the side ratio for a 30:60:90 triangle?
(y2-y1)/(x2-x1)
Probability A * Probability B
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Bh