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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. What is the volume of a solid rectangle?
(x1+x2)/2 - (y1+y2)/2
An ange whose vertex is the center of the circle
Lwh
1.4
2. List two odd behaviors of exponents
4pir^2
(pi)r^2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
3. Circumference of a circle using radius
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(n degrees/360) * (pi)r^2
N x M
2pi*r
4. 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.
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.
4s (where s = length of a side)
1/2bh
5. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
(a+b)²
2lw+2lh+2wh
Probability A * Probability B
6. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
?d OR 2?r
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
(n/2) * (t1+tn)
Sqr( x2 -x1) + (y2- y1)
7. What is the unfactored version of (x-y)² ?
x² -2xy + y²
y = kx
1/1
x°/360 times (?r²) - where x is the degrees in the angle
8. How do you calculate a diagonal inside a 3-dimensional rectangular box?
(n/2) * (t1+tn)
N x M
(pi)r^2(h)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
9. a³+b³
(a+b)(a²-ab+b²)
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)(a²+ab+b²)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
10. 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
Number of desired outcomes/number of total outcomes
S² - where s = length of a side
Equal
11. What is the area of a cylinder?
1/x^a
(a-b)(a+b)
2(pi)r(r+h)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
12. What is the point-slope form?
(y-y1)=m(x-x1)
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.
?r²
C =?d
13. When a line crosses two parallel lines - ________.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
x² -2xy + y²
Number of desired outcomes/number of total outcomes
The four big angles are equal and the four small angles are equal
14. Area of a sector
1/2bh
A+b
x°/360 times (?r²) - where x is the degrees in the angle
Bh
15. Area of Circle
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.
Part of a circle connecting two points on the circle.
Pi*r^2
16. Perimeter of a square
4s (where s = length of a side)
Last term
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
17. What is a 'Right isosceles' triangle?
x°/360 times (?r²) - where x is the degrees in the angle
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.
2(lw+wh+lh)
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.
18. How do you multiply powers with the same base?
S² - where s = length of a side
Sqr( x2 -x1) + (y2- y1)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
19. How do you solve a permutation?
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
2(pi)r(r+h)
(a-b)²
Opens down
20. What is the length of an arc?
2 pi r
(n degrees/360) * 2(pi)r
A segment connecting the center of a circle to any point on the circle
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.
21. Arc
?d OR 2?r
Total distance/total time
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.
Part of a circle connecting two points on the circle.
22. Volume of pyramid
Total distance/total time
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.
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.
1/3Bh
23. What do combination problems usually ask for?
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. Given event A: A + notA = 1.
N x M
Groups - teams - or committees.
24. What'S the most important thing to remember about charts you'll see on the GRE?
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.
T1 + (n-1)d
1/3pir^2*h
T1 * r^(n-1)/(r-1)
25. Volume of sphere
1/1
?r²
A=bh
4/3pir^3
26. What is the volume of a cylinder?
Number of desired outcomes/number of total outcomes
(pi)r^2(h)
Pi*d
1/2bh
27. Explain the difference between a digit and a number.
28. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
29. When you reverse FOIL - the term that needs to add out is the _____
(a-b)²
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
Last term
30. What is 'absolute value' - and how is it represented?
31. Does order matter for a permutation? How about for a combination?
Sum of the lengths of the sides
4/3pir^3
x°/360 times (2 pi r) - where x is the degrees in the angle
Order does matter for a permutation - but does not matter for a combination.
32. Area of a triangle
(a+b)(a²-ab+b²)
½(base x height) [or (base x height)÷2]
x² -2xy + y²
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.
33. Area of Trapezoid
1/2 h (b1 + b2)
T1 * r^(n-1)/(r-1)
A=bh
T1 + (n-1)d
34. What is the area of a triangle?
2x2x2x5x5
2lw+2lh+2wh
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.
1/2bh
35. What is the unfactored version of (x+y)² ?
(x-y)²
A=bh
x² + 2xy + y²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
36. What is the factored version of x² -2xy + y² ?
(x-y)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.
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.
Pi*d
37. Surface Area of rectangular prism
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.
2lw+2lh+2wh
y = kx
Sum of the lengths of the sides
38. Chord
The distance from one point on the circle to another point on the circle.
N x M
(0 -0)
(pi)r^2(h)
39. What is the average?
S² - where s = length of a side
2lw+2lh+2wh
(x+y)²
Sum of terms/number of terms
40. What is the circumference of a circle?
Equal
Pir^2h
2(pi)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.
41. What number goes on the bottom of a probability fraction?
x°/360 times (2 pi r) - where x is the degrees in the angle
The total # of possible outcomes.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2(pi)r
42. Define the range of a set of numbers.
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.
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.
2pir^2 + 2pir*h
(0 -0)
43. What is the equation of a line?
44. What is the area of a solid rectangle?
2(lw+wh+lh)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(a-b)²
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 percentage of change?
Between 0 and 1.
Percentage Change = Difference/Original * 100
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
46. What is the probability?
2l+2w
Number of desired outcomes/number of total outcomes
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.
A²-b²
47. What is the 'Third side' rule for triangles?
(x1+x2)/2 - (y1+y2)/2
T1 * r^(n-1)
Percentage Change = Difference/Original * 100
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. Circle
(0 -0)
Order does matter for a permutation - but does not matter for a combination.
The total # of possible outcomes.
The set of points which are all the same distance (the radius) from a certain point (the center).
49. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
Sqr( x2 -x1) + (y2- y1)
2(pi)r(r+h)
Ac+ad+bc+bd
50. What is the side ratio for a 30:60:90 triangle?
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
2pi*r
Not necessarily. This is a trick question - because x could be either positive or negative.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.