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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. Area of Circles
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
A=?r2
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.
1/1
2. Area of Circle
Arrangements - orders - schedules - or lists.
A=bh
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.
Pi*r^2
3. Arc
The set of points which are all the same distance (the radius) from a certain point (the center).
x°/360 times (2 pi r) - where x is the degrees in the angle
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.
Part of a circle connecting two points on the circle.
4. What are the side ratios for a 30:60:90 triangle?
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.
A=?r2
The four big angles are equal and the four small angles are equal
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
5. List two odd behaviors of exponents
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.
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
1. Given event A: A + notA = 1.
Lwh
6. Area of a triangle
Ac+ad+bc+bd
½(base x height) [or (base x height)÷2]
Less
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
7. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
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8. Explain the special properties of zero.
y2-y1/x2-x1
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. 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
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.
9. Volume of pyramid
2lw+2lh+2wh
Pir^2h
4s
1/3Bh
10. Circumference of cirlce using diameter
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.
2pir^2 + 2pir*h
Pi*d
2(pi)r(r+h)
11. Area of a trapezoid
Probability A + Probability B
x°/360 times (2 pi r) - where x is the degrees in the angle
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Between 0 and 1.
12. Area of Triangle
The distance from one point on the circle to another point on the circle.
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.
1/2bh
(x-y)²
13. In a parabola - if the first term is positive - the parabola ________.
Arrangements - orders - schedules - or lists.
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.
Opens up
1. Given event A: A + notA = 1.
14. Area of a sector
(y-y1)=m(x-x1)
x°/360 times (?r²) - where x is the degrees in the angle
2(pi)r(r+h)
The distance across the circle through the center of the circle.The diameter is twice the radius.
15. What is the formula for the diagonal of any square?
(x+y)²
A²-b²
The set of points which are all the same distance (the radius) from a certain point (the center).
S*v2
16. Define the range of a set of numbers.
2pi*r
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
Not necessarily. This is a trick question - because x could be either positive or negative.
17. What number goes on the bottom of a probability fraction?
Less
The total # of possible outcomes.
(pi)r^2(h)
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.
18. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
(a+b)²
Number of desired outcomes/number of total outcomes
Opens down
19. What is an 'equilateral' triangle?
(x+y)(x-y)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
C =?d
(pi)r^2
20. Circumference of a circle
?d OR 2?r
1/2bh
Between 0 and 1.
2(pi)r(r+h)
21. length of a sector
Arrangements - orders - schedules - or lists.
x°/360 times (2 pi r) - where x is the degrees in the angle
2lw+2lh+2wh
b±[vb²-4ac]/2a
22. What is the volume of a cylinder?
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.
2pi*r
(pi)r^2(h)
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.
23. Area of Rectangle
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.
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
Sqr( x2 -x1) + (y2- y1)
Lw
24. Perimeter (circumference) of a circle
Total distance/total time
4s (where s = length of a side)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2 pi r
25. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
S*v2
Probability A + Probability B
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.
Arrangements - orders - schedules - or lists.
26. Point-Slope form
Equal
1.7
y-y1=m(x-x1)
Groups - teams - or committees.
27. Define the formula for calculating slope.
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 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.
(x1+x2)/2 - (y1+y2)/2
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
28. Volume of prism
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.
Pir^2h
Bh
4s (where s = length of a side)
29. Define a factorial of a number - and how it is written.
2l+2w
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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
The total # of possible outcomes.
30. x^a * x^b = x^__
(a-b)(a²+ab+b²)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
(pi)r^2
A+b
31. The length of one side of any triangle is ____ than the sum of the other two sides.
The set of points which are all the same distance (the radius) from a certain point (the center).
(x+y)(x-y)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Less
32. Rough est. of v3 =
1.7
y = kx
C =?d
A=bh
33. How do you find the sum of a geometric sequence?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
T1 * r^(n-1)/(r-1)
A segment connecting the center of a circle to any point on the circle
Arrangements - orders - schedules - or lists.
34. What must be true before a quadratic equation can be solved?
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35. Explain the difference between a digit and a number.
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36. a³-b³
Equal
(a-b)(a²+ab+b²)
2lw+2lh+2wh
Opens down
37. Perimeter of polygon
The four big angles are equal and the four small angles are equal
Sum of the lengths of the sides
1/3pir^2*h
4/3pir^3
38. Area of Square
x² + 2xy + y²
b±[vb²-4ac]/2a
Percentage Change = Difference/Original * 100
S^2
39. Perimeter of rectangle
2l+2w
4s
The total # of possible outcomes.
Part of a circle connecting two points on the circle.
40. x^-a =
The four big angles are equal and the four small angles are equal
(a+b)²
1/x^a
Sqr( x2 -x1) + (y2- y1)
41. What is the sum of the inside angles of an n-sided polygon?
(n-2)180
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'.
?r²
x²-y²
42. What is the area of a circle?
(pi)r^2
Total distance/total time
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.
43. 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.
Bh
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.
x² -2xy + y²
44. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
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.
Opens up
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
45. When a line crosses two parallel lines - ________.
Pi*d
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
The four big angles are equal and the four small angles are equal
1.4
46. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
4/3pir^3
N x M
The distance across the circle through the center of the circle.The diameter is twice the radius.
Less
47. What is the average?
Last term
Opens down
Sum of terms/number of terms
Lwh
48. Central Angle
Pi*r^2
Pi*d
y = k/x
An ange whose vertex is the center of the circle
49. (a+b)(c+d)
The set of points which are all the same distance (the radius) from a certain point (the center).
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Between 0 and 1.
Ac+ad+bc+bd
50. The probability of an event happening and the probability of an event NOT happening must add up to what number?
1. Given event A: A + notA = 1.
The average - mean - median - or mode.
(x+y)²
Lw