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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. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
b±[vb²-4ac]/2a
y2-y1/x2-x1
4pir^2
2. Circumference Formula
C =?d
Pir^2h
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)180
3. What is the 'Third side' rule for triangles?
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(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.
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.
4. What is the surface area of a cylinder?
The four big angles are equal and the four small angles are equal
2(pi)r(r+h)
A+b
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
5. How do you calculate the probability of two events in a row? (Probability of A and B)
(y2-y1)/(x2-x1)
(a+b)(a-b)
Probability A * Probability B
(n-2)180
6. In a coordinate system - identify the quadrants and describe their location.
(a-b)²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
The average - mean - median - or mode.
(pi)r^2
7. 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.
Opens down
(a-b)²
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.
8. a²-b²
S*v2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
(a-b)(a+b)
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
9. How do you calculate the percentage of change?
Not necessarily. This is a trick question - because x could be either positive or negative.
Lwh
Arrangements - orders - schedules - or lists.
Percentage Change = Difference/Original * 100
10. To divide powers with the same base...
1.4
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
4s (where s = length of a side)
11. The length of one side of any triangle is ____ than the sum of the other two sides.
Sqr( x2 -x1) + (y2- y1)
Less
(x+y)²
2l+2w
12. Area of Rectangle
Lw
1.4
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
1/3Bh
13. Area of Circle
Pi*r^2
(n/2) * (t1+tn)
Lw
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.
14. Surface Area of rectangular prism
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(pi)r^2
Bh
2lw+2lh+2wh
15. When you reverse FOIL - the term that needs to multiply out is the _____
(a-b)(a+b)
(x1+x2)/2 - (y1+y2)/2
Last term
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'.
16. a³+b³
(x1+x2)/2 - (y1+y2)/2
(a-b)(a²+ab+b²)
A=bh
(a+b)(a²-ab+b²)
17. Circumference of a circle using radius
4s (where s = length of a side)
(y2-y1)/(x2-x1)
2pi*r
(n degrees/360) * (pi)r^2
18. Perimeter of rectangle
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2l+2w
y-y1=m(x-x1)
Bh
19. What is the distance formula?
Sqr( x2 -x1) + (y2- y1)
2pir^2 + 2pir*h
T1 * r^(n-1)/(r-1)
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.
20. What do combination problems usually ask for?
1/1
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.
Groups - teams - or committees.
1. Given event A: A + notA = 1.
21. When you reverse FOIL - the term that needs to add out is the _____
2(pi)r(r+h)
1/x^a
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'.
Middle term
22. Area of Parallelogram
(x-y)²
Bh
S^2
Lwh
23. Volume of Cone
1/3pir^2*h
1.4
2pir^2 + 2pir*h
y-y1=m(x-x1)
24. Define the range of a set of numbers.
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.
T1 + (n-1)d
Total distance/total time
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.
25. What is the point-slope form?
2 pi r
x² -2xy + y²
(y-y1)=m(x-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.
26. Circumference of cirlce using diameter
1.7
Pi*d
2(lw+wh+lh)
An ange whose vertex is the center of the circle
27. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
(x+y)(x-y)
2(pi)r
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.
x°/360 times (?r²) - where x is the degrees in the angle
28. What is the unfactored version of x²-y² ?
x² -2xy + y²
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2l+2w
(x+y)(x-y)
29. What is the length of an arc?
(n degrees/360) * (pi)r^2
x²-y²
(n degrees/360) * 2(pi)r
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
30. What is the area of a sector?
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.
b±[vb²-4ac]/2a
(a+b)²
(n degrees/360) * (pi)r^2
31. What is the factored version of x² -2xy + y² ?
(x-y)²
Equal
(y2-y1)/(x2-x1)
The distance from one point on the circle to another point on the circle.
32. What is the factored version of x² + 2xy + y² ?
Pi*d
1/2bh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(x+y)²
33. Perimeter of a rectangle
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
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.
1/2 h (b1 + b2)
2Length + 2width [or (length + width) x 2]
34. What is the prime factorization of 200?
2x2x2x5x5
T1 * r^(n-1)
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.
?d OR 2?r
35. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.
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36. What number goes on the bottom of a probability fraction?
(a-b)(a²+ab+b²)
The distance across the circle through the center of the circle.The diameter is twice the radius.
S*v2
The total # of possible outcomes.
37. Chord
2lw+2lh+2wh
The distance from one point on the circle to another point on the circle.
2pi*r
Pir^2h
38. What is a 'Right isosceles' triangle?
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.
T1 + (n-1)d
(n-2)180
x²-y²
39. What is the circumference of a circle?
The distance from one point on the circle to another point on the circle.
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.
Bh
40. x^-a =
Probability A * Probability B
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
1/x^a
41. Explain the special properties of zero.
(n degrees/360) * (pi)r^2
Number of desired outcomes/number of total outcomes
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
42. How do you find the midpoint?
(a-b)(a²+ab+b²)
T1 * r^(n-1)
(n-2)180
(x1+x2)/2 - (y1+y2)/2
43. If x² = 144 - does v144 = x?
S² - where s = length of a side
Not necessarily. This is a trick question - because x could be either positive or negative.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Opens down
44. Volume of pyramid
N x M
1/3Bh
y = k/x
(y2-y1)/(x2-x1)
45. Lines reflected over the x or y axis have ____ slopes.
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.
Order does matter for a permutation - but does not matter for a combination.
T1 * r^(n-1)/(r-1)
Negative
46. What is a '30:60:90' triangle?
(n-2)180
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
Pir^2h
½(b1 +b2) x h [or (b1 +b2) x h÷2]
47. Point-Slope form
Less
y-y1=m(x-x1)
2lw+2lh+2wh
x°/360 times (?r²) - where x is the degrees in the angle
48. Define the mode of a set of numbers.
Sum of the lengths of the sides
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.
x°/360 times (?r²) - where x is the degrees in the angle
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
49. Surface Area of Sphere
A+b
4pir^2
A=bh
2(pi)r
50. Slope
(y2-y1)/(x2-x1)
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.
1/3Bh
?r²