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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. Lines reflected over the x or y axis have ____ slopes.
(a+b)(a²-ab+b²)
Between 0 and 1.
Negative
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
2. Volume of Cone
4s (where s = length of a side)
x°/360 times (?r²) - where x is the degrees in the angle
1/3pir^2*h
Part of a circle connecting two points on the circle.
3. Volume of sphere
4/3pir^3
2(pi)r
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
4. What is an 'equilateral' triangle?
1. Given event A: A + notA = 1.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Pi*d
(n-2)180
5. What is the equation of a line?
6. What is directly proportional?
An ange whose vertex is the center of the circle
1/3pir^2*h
y = kx
The distance across the circle through the center of the circle.The diameter is twice the radius.
7. How do you calculate the probability of two events in a row? (Probability of A and B)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
4s (where s = length of a side)
Probability A * Probability B
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.
8. Perimeter of rectangle
2l+2w
(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. 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
9. If something is certain to happen - how is the probability of this event expressed mathematically?
2pir^2 + 2pir*h
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Probability A * Probability B
1/1
10. What is the formula for the diagonal of any square?
Ac+ad+bc+bd
The set of points which are all the same distance (the radius) from a certain point (the center).
Sum of the lengths of the sides
S*v2
11. Define the mode of a set of numbers.
(x-y)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.
The total # of possible outcomes.
Pir^2h
12. What is the area of a circle?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Lwh
(pi)r^2
y = k/x
13. What is the factored version of x² -2xy + y² ?
1/x^a
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(x-y)²
S² - where s = length of a side
14. What are the side ratios for a 30:60:90 triangle?
(a-b)(a²+ab+b²)
Opens down
2x2x2x5x5
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
15. What is the 'Third side' rule for triangles?
Not necessarily. This is a trick question - because x could be either positive or negative.
x² -2xy + y²
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
16. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
A+b
Probability A + Probability B
17. Surface Area of rectangular prism
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.
2 pi r
2lw+2lh+2wh
Bh
18. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
?d OR 2?r
(0 -0)
2pi*r
19. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
Negative
Lwh
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
20. What is the factored version of (x+y)(x-y) ?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x²-y²
Ac+ad+bc+bd
y2-y1/x2-x1
21. Arc
S^2
2 pi r
Middle term
Part of a circle connecting two points on the circle.
22. How do you multiply powers with the same base?
2Length + 2width [or (length + width) x 2]
Less
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
23. Area of a square
(n-2)180
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
4s
S² - where s = length of a side
24. a³-b³
(a-b)(a²+ab+b²)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
2(pi)r(r+h)
Equal
25. perimeter of square
(x+y)²
4s
The set of points which are all the same distance (the radius) from a certain point (the center).
The average - mean - median - or mode.
26. What is inversely proportional?
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.
y = k/x
(n degrees/360) * 2(pi)r
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.
27. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(x+y)²
(y2-y1)/(x2-x1)
Probability A + Probability B
28. What is the area of a sector?
(n degrees/360) * (pi)r^2
(a+b)²
x²-y²
A=bh
29. In a parabola - if the first term is negative - the parabola ________.
Sum of the lengths of the sides
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Opens down
y2-y1/x2-x1
30. What is the average speed?
2pi*r
?d OR 2?r
Total distance/total time
(pi)r^2(h)
31. Explain the special properties of zero.
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.
Percentage Change = Difference/Original * 100
Part of a circle connecting two points on the circle.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
32. Perimeter of a rectangle
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.
Arrangements - orders - schedules - or lists.
2Length + 2width [or (length + width) x 2]
Negative
33. Area of a trapezoid
Pi*d
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(a-b)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.
34. What is the sum of the inside angles of an n-sided polygon?
(n-2)180
(a-b)(a²+ab+b²)
The four big angles are equal and the four small angles are equal
x² + 2xy + y²
35. What is the point-slope form?
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.
(y-y1)=m(x-x1)
Bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
36. Chord
The distance from one point on the circle to another point on the circle.
T1 + (n-1)d
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2(lw+wh+lh)
37. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Pir^2h
Not necessarily. This is a trick question - because x could be either positive or negative.
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.
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.
38. How do you calculate a diagonal inside a 3-dimensional rectangular box?
Part of a circle connecting two points on the circle.
x² + 2xy + y²
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(a+b)(a²-ab+b²)
39. x^a * x^b = x^__
x²-y²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
A+b
Opens up
40. What is the area of a cylinder?
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.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Opens down
2(pi)r(r+h)
41. Volume of pyramid
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'.
1/3Bh
1/2 h (b1 + b2)
(n degrees/360) * 2(pi)r
42. What is the area of a solid rectangle?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2(lw+wh+lh)
S² - where s = length of a side
43. Area of a triangle
½(base x height) [or (base x height)÷2]
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
The average - mean - median - or mode.
y = k/x
44. Define the range of a set of numbers.
(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.
2pir^2 + 2pir*h
(n/2) * (t1+tn)
45. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
1/3Bh
Number of desired outcomes/number of total outcomes
Order does matter for a permutation - but does not matter for a combination.
46. Perimeter (circumference) of a circle
Bh
2 pi r
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
47. Perimeter of polygon
Sum of the lengths of the sides
(a-b)(a²+ab+b²)
An ange whose vertex is the center of the circle
?r²
48. How do you find the sum of a geometric sequence?
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.
T1 * r^(n-1)/(r-1)
2(pi)r(r+h)
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.
49. What is a 'Right isosceles' triangle?
1/2 h (b1 + b2)
C =?d
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.
2(pi)r
50. Surface Area of Sphere
4pir^2
2(pi)r
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.
Pi*d