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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 the surface area of a rectangular box?
(a-b)(a+b)
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.
(n/2) * (t1+tn)
b±[vb²-4ac]/2a
2. What is the volume of a cylinder?
Ac+ad+bc+bd
(pi)r^2(h)
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
3. What is the equation of a line?
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4. Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Lwh
y2-y1/x2-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.
5. What do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
Groups - teams - or committees.
A+b
x² -2xy + y²
6. Quadratic Formula
(a-b)²
b±[vb²-4ac]/2a
The average - mean - median - or mode.
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.
7. x^a * x^b = x^__
A+b
(0 -0)
y = k/x
A²-b²
8. How do you multiply powers with the same base?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
4s (where s = length of a side)
The four big angles are equal and the four small angles are equal
2(lw+wh+lh)
9. What is a 'Right isosceles' triangle?
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.
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 set of points which are all the same distance (the radius) from a certain point (the center).
10. Perimeter of rectangle
Lwh
Arrangements - orders - schedules - or lists.
2l+2w
2(pi)r(r+h)
11. Volume of Cone
Sum of the lengths of the sides
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/3pir^2*h
(n degrees/360) * 2(pi)r
12. Point-Slope form
Percentage Change = Difference/Original * 100
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2(pi)r(r+h)
y-y1=m(x-x1)
13. perimeter of square
4s
(a-b)(a+b)
Order does matter for a permutation - but does not matter for a combination.
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.
14. a²+2ab+b²
Bh
Sum of the lengths of the sides
(a+b)²
1/2bh
15. When a line crosses two parallel lines - ________.
C =?d
The set of points which are all the same distance (the radius) from a certain point (the center).
The four big angles are equal and the four small angles are equal
(a+b)²
16. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the angle
Opens down
Bh
(a-b)(a+b)
17. Area of a sector
1/3Bh
C =?d
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.
x°/360 times (?r²) - where x is the degrees in the angle
18. Define the 'Third side' rule for triangles
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19. a² - b² is equal to
(a+b)(a-b)
Pir^2h
The set of points which are all the same distance (the radius) from a certain point (the center).
4pir^2
20. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
The average - mean - median - or mode.
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
21. What is the point-slope form?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
(y-y1)=m(x-x1)
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 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.
22. In a coordinate system - what is the origin?
(0 -0)
(x+y)(x-y)
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.
x² + 2xy + y²
23. Area of Trapezoid
Last term
1/2 h (b1 + b2)
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
4pir^2
24. a³+b³
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(a+b)(a²-ab+b²)
(n/2) * (t1+tn)
Number of desired outcomes/number of total outcomes
25. a²-b²
(pi)r^2
(a-b)(a²+ab+b²)
4/3pir^3
(a-b)(a+b)
26. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
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 + (n-1)d
x² + 2xy + y²
27. Volume of sphere
4/3pir^3
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Pir^2h
2x2x2x5x5
28. Circumference of cirlce using diameter
2(pi)r(r+h)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Pi*d
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
29. What is the factored version of x² -2xy + y² ?
An ange whose vertex is the center of the circle
(x-y)²
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a+b)(a²-ab+b²)
30. Rough est. of v1 =
2 pi r
1/1
Lwh
1
31. Area of a trapezoid
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
x² + 2xy + y²
4s
½(b1 +b2) x h [or (b1 +b2) x h÷2]
32. What is the distance formula?
Pir^2h
Bh
(n degrees/360) * (pi)r^2
Sqr( x2 -x1) + (y2- y1)
33. Does order matter for a permutation? How about for a combination?
Bh
2 pi r
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.
Order does matter for a permutation - but does not matter for a combination.
34. Circle
2 pi r
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.
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.
The set of points which are all the same distance (the radius) from a certain point (the center).
35. Area of a triangle
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.
½(base x height) [or (base x height)÷2]
Order does matter for a permutation - but does not matter for a combination.
1/3pir^2*h
36. Define the mode of a set of numbers.
T1 * r^(n-1)
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.
(x1+x2)/2 - (y1+y2)/2
2 pi r
37. What is the average speed?
4s
Total distance/total time
2(lw+wh+lh)
(x+y)²
38. Surface Area of Sphere
The distance across the circle through the center of the circle.The diameter is twice the radius.
(a+b)(a-b)
4pir^2
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.
39. (a+b)(a-b)=
y = k/x
A²-b²
Pi*d
(n/2) * (t1+tn)
40. Chord
(n/2) * (t1+tn)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The distance from one point on the circle to another point on the circle.
C =?d
41. How do you find the sum of a geometric sequence?
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
T1 * r^(n-1)/(r-1)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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
42. What is the surface area of a cylinder?
(a-b)(a+b)
2(pi)r(r+h)
A segment connecting the center of a circle to any point on the circle
Arrangements - orders - schedules - or lists.
43. Perimeter of a rectangle
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2Length + 2width [or (length + width) x 2]
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.
44. Central Angle
2(pi)r
An ange whose vertex is the center of the circle
N x M
The distance from one point on the circle to another point on the circle.
45. What is the unfactored version of (x-y)² ?
x² -2xy + y²
A+b
y2-y1/x2-x1
Sum of terms/number of terms
46. What is the sum of the inside angles of an n-sided polygon?
(n-2)180
Lw
C =?d
Pi*d
47. What is the factored version of x² + 2xy + y² ?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(n-2)180
(x+y)²
The average - mean - median - or mode.
48. Area of rectangle - square - parallelogram
A=bh
(a+b)²
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x² + 2xy + y²
49. The length of one side of any triangle is ____ than the sum of the other two sides.
Less
Not necessarily. This is a trick question - because x could be either positive or negative.
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
Pi*r^2
50. a²-2ab+b²
(a-b)²
S^2
(x+y)²
?d OR 2?r