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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 calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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
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.
1. Given event A: A + notA = 1.
2. a²-2ab+b²
Lwh
N x M
(a-b)²
2pi*r
3. Rough est. of v2 =
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.
1
1.4
2(pi)r(r+h)
4. What is a '30:60:90' triangle?
1. Given event A: A + notA = 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
T1 + (n-1)d
Sqr( x2 -x1) + (y2- y1)
5. What is the surface area of a cylinder?
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.
Less
2(pi)r(r+h)
1/2 h (b1 + b2)
6. a³+b³
(a+b)(a²-ab+b²)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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.
S*v2
7. What is a 'Right isosceles' triangle?
(y2-y1)/(x2-x1)
Pi*r^2
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.
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.
8. What is the probability?
Number of desired outcomes/number of total outcomes
Pi*d
T1 * r^(n-1)
1/3pir^2*h
9. Define 'proportionate' values
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.
y = kx
(a-b)(a+b)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
10. Area of rectangle - square - parallelogram
Between 0 and 1.
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=bh
Lw
11. Lines reflected over the x or y axis have ____ slopes.
Negative
2(lw+wh+lh)
4/3pir^3
N x M
12. To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Bh
(y-y1)=m(x-x1)
2l+2w
13. Central Angle
Part of a circle connecting two points on the circle.
x² + 2xy + y²
An ange whose vertex is the center of the circle
b±[vb²-4ac]/2a
14. The probability of an event happening and the probability of an event NOT happening must add up to what number?
Number of desired outcomes/number of total outcomes
1. Given event A: A + notA = 1.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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.
15. Area of Parallelogram
Bh
Probability A + Probability B
1. Given event A: A + notA = 1.
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.
16. List two odd behaviors of exponents
2(pi)r(r+h)
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
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
17. What is the area of a circle?
(pi)r^2
Groups - teams - or committees.
Ac+ad+bc+bd
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
18. Does order matter for a permutation? How about for a combination?
(a-b)(a+b)
Order does matter for a permutation - but does not matter for a combination.
The set of points which are all the same distance (the radius) from a certain point (the center).
The total # of possible outcomes.
19. What is the volume of a cylinder?
(pi)r^2(h)
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. 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.
Arrangements - orders - schedules - or lists.
20. Circumference of cirlce using diameter
b±[vb²-4ac]/2a
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Pi*d
Pi*r^2
21. Circumference of a circle using radius
N x M
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.
y = k/x
2pi*r
22. What is the formula for the diagonal of any square?
y2-y1/x2-x1
An ange whose vertex is the center of the circle
b±[vb²-4ac]/2a
S*v2
23. Area of Square
C =?d
2(pi)r(r+h)
S^2
Between 0 and 1.
24. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
(n/2) * (t1+tn)
T1 + (n-1)d
T1 * r^(n-1)
25. Slope
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.
x°/360 times (2 pi r) - where x is the degrees in the angle
(x+y)(x-y)
(y2-y1)/(x2-x1)
26. How do you solve a permutation?
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.
4pir^2
2lw+2lh+2wh
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
27. What is the factored version of x² -2xy + y² ?
A=?r2
2x2x2x5x5
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(x-y)²
28. 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.
y-y1=m(x-x1)
T1 * r^(n-1)
The total # of possible outcomes.
29. What do permutation problems often ask for?
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.
1
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.
Arrangements - orders - schedules - or lists.
30. length of a sector
The distance from one point on the circle to another point on the circle.
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'.
x°/360 times (2 pi r) - where x is the degrees in the angle
Sum of terms/number of terms
31. x^a * x^b = x^__
Groups - teams - or committees.
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.
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.
A+b
32. How do you find the 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.
The distance across the circle through the center of the circle.The diameter is twice the radius.
Percentage Change = Difference/Original * 100
y2-y1/x2-x1
33. What'S the most important thing to remember about charts you'll see on the GRE?
Sum of terms/number of terms
Lw
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.
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.
34. a²-b²
(a-b)(a+b)
(a-b)²
(n-2)180
1. Given event A: A + notA = 1.
35. Perimeter of polygon
(n degrees/360) * (pi)r^2
Sum of the lengths of the sides
The set of points which are all the same distance (the radius) from a certain point (the center).
½(base x height) [or (base x height)÷2]
36. Area of Circles
(pi)r^2(h)
A=?r2
(a+b)²
?d OR 2?r
37. Area of Circle
Pi*r^2
(x+y)(x-y)
Total distance/total time
The set of points which are all the same distance (the radius) from a certain point (the center).
38. Define the range of a set of numbers.
Sum of terms/number of terms
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.
Pi*r^2
39. Perimeter of a rectangle
2 pi r
2Length + 2width [or (length + width) x 2]
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.
1/3pir^2*h
40. What is the volume of a solid rectangle?
2lw+2lh+2wh
Lwh
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
41. What is directly proportional?
y = kx
Pi*d
?d OR 2?r
Number of desired outcomes/number of total outcomes
42. What is the area of a sector?
(x-y)²
(n degrees/360) * (pi)r^2
Less
Ac+ad+bc+bd
43. Volume of Cylinder
Probability A * Probability B
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.
Middle term
Pir^2h
44. Area of a triangle
½(base x height) [or (base x height)÷2]
S² - where s = length of a side
A²-b²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
45. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.
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46. Circumference Formula
C =?d
Sum of terms/number of terms
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
47. a³-b³
?r²
(a-b)(a²+ab+b²)
2 pi r
T1 * r^(n-1)
48. In a coordinate system - identify the quadrants and describe their location.
T1 + (n-1)d
N x M
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1/2bh
49. What is the equation of a line?
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50. How do you calculate the surface area of a rectangular box?
Ac+ad+bc+bd
2pir^2 + 2pir*h
Lwh
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.