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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. When you reverse FOIL - the term that needs to add out is the _____
Middle term
C =?d
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.
Less
2. Arc
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.
1
Part of a circle connecting two points on the circle.
y = kx
3. What is the unfactored version of (x+y)² ?
(a+b)²
x² + 2xy + y²
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
1.4
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
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
5. Volume of prism
Bh
Part of a circle connecting two points on the circle.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
6. Rough est. of v1 =
2(pi)r
1
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.
7. Define the mode of a set of numbers.
Sqr( x2 -x1) + (y2- y1)
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/x^a
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.
8. 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.
(x+y)²
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.
2pi*r
9. What is directly proportional?
y = kx
Opens down
(x+y)(x-y)
The set of points which are all the same distance (the radius) from a certain point (the center).
10. Circumference of a circle using radius
Bh
2pi*r
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(a-b)(a²+ab+b²)
11. Explain the special properties of zero.
Opens down
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.
Equal
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.
12. What number goes on the bottom of a probability fraction?
y-y1=m(x-x1)
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.
A²-b²
The total # of possible outcomes.
13. What is the volume of a solid rectangle?
The set of points which are all the same distance (the radius) from a certain point (the center).
Lwh
Pir^2h
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.
14. Area of a trapezoid
Equal
½(b1 +b2) x h [or (b1 +b2) x h÷2]
The set of points which are all the same distance (the radius) from a certain point (the center).
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.
15. Rough est. of v3 =
(pi)r^2
Total distance/total time
1.7
2(pi)r
16. What is the point-slope form?
(y-y1)=m(x-x1)
1. Given event A: A + notA = 1.
Bh
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.
17. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(0 -0)
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.
18. Perimeter (circumference) of a circle
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.
Opens up
2 pi r
2(pi)r(r+h)
19. a²-b²
1/1
(a-b)(a+b)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1
20. Chord
The distance from one point on the circle to another point on the circle.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2x2x2x5x5
(n degrees/360) * 2(pi)r
21. Quadratic Formula
S*v2
Not necessarily. This is a trick question - because x could be either positive or negative.
(a+b)(a-b)
b±[vb²-4ac]/2a
22. What is the length of an arc?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(n degrees/360) * 2(pi)r
2(pi)r(r+h)
The set of points which are all the same distance (the radius) from a certain point (the center).
23. Circumference of cirlce using diameter
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
(n degrees/360) * 2(pi)r
An ange whose vertex is the center of the circle
Pi*d
24. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
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.
Probability A + Probability B
N x M
25. What is the surface area of a cylinder?
(n degrees/360) * (pi)r^2
2(pi)r(r+h)
x°/360 times (2 pi r) - where x is the degrees in the angle
A+b
26. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
A²-b²
Sum of terms/number of terms
1/2bh
27. The probability of an event happening and the probability of an event NOT happening must add up to what number?
A segment connecting the center of a circle to any point on the circle
1/1
1. Given event A: A + notA = 1.
?r²
28. Perimeter of polygon
b±[vb²-4ac]/2a
x² -2xy + y²
Sum of the lengths of the sides
S^2
29. (a+b)(c+d)
Ac+ad+bc+bd
2 pi r
S*v2
Negative
30. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
Bh
Probability A * Probability B
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.
31. Slope
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.
2(pi)r(r+h)
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.
(y2-y1)/(x2-x1)
32. Area of Rectangle
?d OR 2?r
Lw
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.
33. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
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34. Perimeter of rectangle
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.
2l+2w
Groups - teams - or committees.
1
35. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
1/1
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.
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.
Ac+ad+bc+bd
36. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
The average - mean - median - or mode.
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.
y = kx
37. If something is certain to happen - how is the probability of this event expressed mathematically?
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.
4/3pir^3
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.
1/1
38. Diameter
A²-b²
(x+y)²
The distance across the circle through the center of the circle.The diameter is twice the radius.
Bh
39. x^a * x^b = x^__
Part of a circle connecting two points on the circle.
4s
A+b
(pi)r^2
40. Does order matter for a permutation? How about for a combination?
2Length + 2width [or (length + width) x 2]
(pi)r^2
Order does matter for a permutation - but does not matter for a combination.
The average - mean - median - or mode.
41. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
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-b)(a²+ab+b²)
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 x M
42. Define the range of a set of numbers.
1.7
T1 + (n-1)d
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.
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.
43. Perimeter of a square
4s (where s = length of a side)
(y-y1)=m(x-x1)
x² -2xy + y²
2(pi)r(r+h)
44. In a coordinate system - identify the quadrants and describe their location.
A segment connecting the center of a circle to any point on the circle
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2(pi)r(r+h)
45. Circumference of a circle
?d OR 2?r
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.
N x M
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
46. What is the 'Third side' rule for triangles?
(a+b)²
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.
1
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.
47. Area of a sector
(pi)r^2
Opens down
1.7
x°/360 times (?r²) - where x is the degrees in the angle
48. What is the side ratio for a 30:60:90 triangle?
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.
(x1+x2)/2 - (y1+y2)/2
1
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
49. What is 'absolute value' - and how is it represented?
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50. Central Angle
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.
1.7
A segment connecting the center of a circle to any point on the circle
An ange whose vertex is the center of the circle