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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. What is the volume of a solid rectangle?
The distance from one point on the circle to another point on the circle.
Lwh
1/2 h (b1 + b2)
x²-y²
2. What do permutation problems often ask for?
(x1+x2)/2 - (y1+y2)/2
Arrangements - orders - schedules - or lists.
Groups - teams - or committees.
1/3Bh
3. Arc
(n/2) * (t1+tn)
2 pi r
Part of a circle connecting two points on the circle.
A segment connecting the center of a circle to any point on the circle
4. Perimeter of a rectangle
2Length + 2width [or (length + width) x 2]
y-y1=m(x-x1)
y = kx
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
5. What is the area of a triangle?
1/2bh
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
Opens down
Groups - teams - or committees.
6. Area of a sector
2(pi)r(r+h)
x°/360 times (?r²) - where x is the degrees in the angle
Sum of terms/number of terms
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
7. Area of a circle
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
?r²
Between 0 and 1.
N x M
8. What is the factored version of x² + 2xy + y² ?
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.
Order does matter for a permutation - but does not matter for a combination.
4s
(x+y)²
9. Area of Circles
A+b
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
A=?r2
10. What is the 'Third side' rule for triangles?
Less
?d OR 2?r
(x1+x2)/2 - (y1+y2)/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.
11. Lines reflected over the x or y axis have ____ slopes.
Negative
2l+2w
Ac+ad+bc+bd
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.
12. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Lw
Probability A + Probability B
2Length + 2width [or (length + width) x 2]
Middle term
13. What are the side ratios for a 30:60:90 triangle?
Middle term
x°/360 times (?r²) - where x is the degrees in the angle
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Sum of terms/number of terms
14. In a coordinate system - identify the quadrants and describe their location.
1/3pir^2*h
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
(n degrees/360) * 2(pi)r
Sqr( x2 -x1) + (y2- y1)
15. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
Not necessarily. This is a trick question - because x could be either positive or negative.
Negative
Arrangements - orders - schedules - or lists.
16. a²+2ab+b²
4s
(a+b)²
?r²
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.
17. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Pir^2h
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
2(pi)r(r+h)
18. 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.
Bh
Opens down
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
19. Perimeter of a square
Pir^2h
4s (where s = length of a side)
1.7
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
20. To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Groups - teams - or committees.
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.
Pir^2h
21. Volume of pyramid
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
x°/360 times (?r²) - where x is the degrees in the angle
(pi)r^2
22. What is the unfactored version of (x-y)² ?
x² -2xy + y²
Opens down
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'.
(n degrees/360) * 2(pi)r
23. What is the unfactored version of x²-y² ?
The distance from one point on the circle to another point on the circle.
(x+y)(x-y)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
24. The length of one side of any triangle is ____ than the sum of the other two sides.
Arrangements - orders - schedules - or lists.
(0 -0)
Less
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.
25. a² - b² is equal to
?r²
Middle term
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(a+b)(a-b)
26. How do you calculate the probability of two events in a row? (Probability of A and B)
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
Probability A + Probability B
Pi*d
27. What is the area of a solid rectangle?
2(lw+wh+lh)
(y2-y1)/(x2-x1)
1/x^a
x² + 2xy + y²
28. In a parabola - if the first term is positive - the parabola ________.
x² + 2xy + y²
Opens up
C =?d
1
29. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.
30. perimeter of square
4pir^2
The set of points which are all the same distance (the radius) from a certain point (the center).
4s
x°/360 times (2 pi r) - where x is the degrees in the angle
31. Quadratic Formula
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x² + 2xy + y²
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.
b±[vb²-4ac]/2a
32. Rough est. of v1 =
1
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.
2 pi r
33. Radius (Radii)
(a+b)(a-b)
A segment connecting the center of a circle to any point on the circle
Part of a circle connecting two points on the circle.
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.
34. What is the probability?
Number of desired outcomes/number of total outcomes
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.
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.
4pir^2
35. (a+b)(c+d)
Opens up
Ac+ad+bc+bd
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
The distance across the circle through the center of the circle.The diameter is twice the radius.
36. Area of rectangle - square - parallelogram
Ac+ad+bc+bd
The four big angles are equal and the four small angles are equal
A=bh
Equal
37. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
4/3pir^3
A segment connecting the center of a circle to any point on the circle
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.
38. How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
1/3pir^2*h
2(pi)r
x² -2xy + y²
39. How do you solve a permutation?
2Length + 2width [or (length + width) x 2]
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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
?r²
40. How do you calculate a diagonal inside a 3-dimensional rectangular box?
Pir^2h
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
41. What is the 'distributive law'?
1/3Bh
2 pi r
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.
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.
42. Diameter
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a+b)(a-b)
The distance across the circle through the center of the circle.The diameter is twice the radius.
1/2bh
43. What is inversely proportional?
Lwh
An ange whose vertex is the center of the circle
y = k/x
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
44. How do you find the nth term of a geometric sequence?
Pi*d
T1 * r^(n-1)
Sum of terms/number of terms
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.
45. How do you find the sum of a geometric sequence?
(0 -0)
b±[vb²-4ac]/2a
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
T1 * r^(n-1)/(r-1)
46. Area of Square
Sum of terms/number of terms
S^2
Part of a circle connecting two points on the circle.
(x-y)²
47. Rough est. of v3 =
T1 * r^(n-1)/(r-1)
Order does matter for a permutation - but does not matter for a combination.
Total distance/total time
1.7
48. What is directly proportional?
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
y = kx
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
49. In a coordinate system - what is the origin?
The distance across the circle through the center of the circle.The diameter is twice the radius.
(0 -0)
y = k/x
(a-b)(a²+ab+b²)
50. Explain the difference between a digit and a number.