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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 Parallelogram
Bh
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1.7
4s (where s = length of a side)
2. What is inversely proportional?
(x+y)²
Order does matter for a permutation - but does not matter for a combination.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
y = k/x
3. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
A=bh
C =?d
1/3Bh
4. Area of Triangle
x²-y²
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
Bh
1/2bh
5. Surface Area of Sphere
x² + 2xy + y²
4pir^2
y = kx
The distance from one point on the circle to another point on the circle.
6. When you reverse FOIL - the term that needs to add out is the _____
N x M
Middle term
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.
x²-y²
7. For a bell curve - what three terms might be used to describe the number in the middle?
The average - mean - median - or mode.
b±[vb²-4ac]/2a
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.
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.
8. What is the equation of a line?
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9. x^-a =
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.
Between 0 and 1.
1/x^a
4s (where s = length of a side)
10. What number goes on the bottom of a probability fraction?
(x1+x2)/2 - (y1+y2)/2
The total # of possible outcomes.
1/x^a
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.
11. If x² = 144 - does v144 = x?
?d OR 2?r
y = k/x
(x+y)(x-y)
Not necessarily. This is a trick question - because x could be either positive or negative.
12. What do combination problems usually ask for?
Less
Groups - teams - or committees.
Opens down
(a+b)²
13. What is the average?
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
T1 + (n-1)d
Sum of terms/number of terms
14. Slope
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(y2-y1)/(x2-x1)
4s
Pi*r^2
15. Area of a triangle
½(base x height) [or (base x height)÷2]
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.
Pi*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.
16. Diameter
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
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 distance across the circle through the center of the circle.The diameter is twice the radius.
17. Rough est. of v1 =
1
S*v2
½(base x height) [or (base x height)÷2]
2x2x2x5x5
18. Explain the special properties of zero.
2(lw+wh+lh)
(n degrees/360) * 2(pi)r
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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.
19. What must be true before a quadratic equation can be solved?
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20. What is the unfactored version of (x-y)² ?
x² -2xy + y²
y2-y1/x2-x1
1/2bh
(pi)r^2
21. What are the side ratios for a 30:60:90 triangle?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
An ange whose vertex is the center of the circle
The set of points which are all the same distance (the radius) from a certain point (the center).
22. (a+b)(c+d)
x² + 2xy + y²
(a-b)(a²+ab+b²)
x°/360 times (2 pi r) - where x is the degrees in the angle
Ac+ad+bc+bd
23. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
(pi)r^2
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
N x M
1.4
24. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.
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25. Define the formula for calculating slope.
The four big angles are equal and the four small angles are equal
Probability A + Probability B
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
26. What is the unfactored version of (x+y)² ?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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
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.
27. Circumference of a circle
?d OR 2?r
Probability A * Probability B
4/3pir^3
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.
28. Area of Square
Less
(n/2) * (t1+tn)
S^2
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
29. What is the point-slope form?
Bh
2 pi r
(y-y1)=m(x-x1)
The four big angles are equal and the four small angles are equal
30. What is the formula for the diagonal of any square?
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
S*v2
The distance from one point on the circle to another point on the circle.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
31. What'S the most important thing to remember about charts you'll see on the GRE?
Arrangements - orders - schedules - or lists.
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.
2l+2w
(a+b)²
32. Point-Slope form
½(b1 +b2) x h [or (b1 +b2) x h÷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.
y-y1=m(x-x1)
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
33. What is the circumference of a circle?
Bh
(x+y)(x-y)
2(pi)r
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.
34. Quadratic Formula
b±[vb²-4ac]/2a
The distance from one point on the circle to another point on the circle.
The set of points which are all the same distance (the radius) from a certain point (the center).
Bh
35. What is the factored version of (x+y)(x-y) ?
Lw
y-y1=m(x-x1)
x²-y²
T1 * r^(n-1)/(r-1)
36. Sector
(a-b)(a²+ab+b²)
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.
1/2bh
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.
37. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
The distance across the circle through the center of the circle.The diameter is twice the radius.
2pir^2 + 2pir*h
Groups - teams - or committees.
38. In a coordinate system - what is the origin?
1.7
(0 -0)
Sum of terms/number of terms
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
39. What do permutation problems often ask for?
b±[vb²-4ac]/2a
1/2bh
Arrangements - orders - schedules - or lists.
The total # of possible outcomes.
40. perimeter of square
Equal
4s
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.
1/2bh
41. What is the unfactored version of x²-y² ?
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)(x-y)
Lwh
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.
42. How do you find the midpoint?
Part of a circle connecting two points on the circle.
2(pi)r
(x1+x2)/2 - (y1+y2)/2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
43. Perimeter of a rectangle
b±[vb²-4ac]/2a
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.
y2-y1/x2-x1
2Length + 2width [or (length + width) x 2]
44. How do you find the nth term of a geometric sequence?
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.
T1 * r^(n-1)
Order does matter for a permutation - but does not matter for a combination.
Probability A + Probability B
45. Area of a trapezoid
The four big angles are equal and the four small angles are equal
y2-y1/x2-x1
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(a+b)²
46. How do you find the sum of a geometric sequence?
T1 * r^(n-1)/(r-1)
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.
Sum of the lengths of the sides
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 Circle
Pi*r^2
2(lw+wh+lh)
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)(a²-ab+b²)
48. Define the range of a set of numbers.
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.
1.7
4s (where s = length of a side)
The distance from one point on the circle to another point on the circle.
49. Circumference Formula
2Length + 2width [or (length + width) x 2]
C =?d
(y2-y1)/(x2-x1)
A+b
50. a³+b³
4s
Last term
(a+b)(a²-ab+b²)
The distance from one point on the circle to another point on the circle.