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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 do permutation problems often ask for?
Arrangements - orders - schedules - or lists.
Last term
y2-y1/x2-x1
x°/360 times (2 pi r) - where x is the degrees in the angle
2. Area of Rectangle
Opens down
2(pi)r
Lw
S*v2
3. The length of one side of any triangle is ____ than the sum of the other two sides.
Pi*d
Less
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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.
4. What must be true before a quadratic equation can be solved?
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5. What is inversely proportional?
Middle term
Probability A + Probability B
y = k/x
The distance from one point on the circle to another point on the circle.
6. What is the prime factorization of 200?
2x2x2x5x5
Sqr( x2 -x1) + (y2- y1)
Part of a circle connecting two points on the circle.
x² -2xy + y²
7. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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
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.
(n degrees/360) * (pi)r^2
?r²
8. How do you find the nth term of a geometric sequence?
1.7
T1 * r^(n-1)
An ange whose vertex is the center of the circle
Bh
9. How do you calculate the surface area of a rectangular box?
Sqr( x2 -x1) + (y2- y1)
2Length + 2width [or (length + width) x 2]
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 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.
10. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
(n degrees/360) * 2(pi)r
S*v2
A segment connecting the center of a circle to any point on the circle
11. Area of Circles
A=?r2
y = kx
Total distance/total time
(n degrees/360) * (pi)r^2
12. What is the 'distributive law'?
x°/360 times (?r²) - where x is the degrees in the angle
Sum of the lengths of the sides
Number of desired outcomes/number of total outcomes
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.
13. Sector
2(pi)r(r+h)
?r²
The four big angles are equal and the four small angles are equal
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.
14. What is directly proportional?
1/2 h (b1 + b2)
y = kx
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.
1.7
15. In a coordinate system - what is the origin?
4/3pir^3
(0 -0)
?r²
(n-2)180
16. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
1
2x2x2x5x5
Ac+ad+bc+bd
17. perimeter of square
(y2-y1)/(x2-x1)
Last term
2pir^2 + 2pir*h
4s
18. What is the area of a circle?
(pi)r^2
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
19. 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.
Sum of terms/number of terms
Pi*r^2
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
20. Surface Area of Cylinder
2pir^2 + 2pir*h
y2-y1/x2-x1
1/2 h (b1 + b2)
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
21. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
Between 0 and 1.
1/2bh
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.
22. x^-a =
1/x^a
Bh
C =?d
4pir^2
23. Lines reflected over the x or y axis have ____ slopes.
Negative
The total # of possible outcomes.
The distance from one point on the circle to another point on the circle.
(a+b)(a²-ab+b²)
24. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
S^2
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.
25. Quadratic Formula
A=?r2
b±[vb²-4ac]/2a
2lw+2lh+2wh
T1 + (n-1)d
26. How do you calculate a diagonal inside a 3-dimensional rectangular box?
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
x°/360 times (2 pi r) - where x is the degrees in the angle
2pir^2 + 2pir*h
(a-b)²
27. To divide powers with the same base...
(a-b)²
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
28. Area of a square
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.
y-y1=m(x-x1)
Pir^2h
S² - where s = length of a side
29. Area of a circle
Opens up
(n/2) * (t1+tn)
?r²
(x1+x2)/2 - (y1+y2)/2
30. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.
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31. a²+2ab+b²
(a+b)²
(x+y)(x-y)
(x+y)²
2pir^2 + 2pir*h
32. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
T1 + (n-1)d
(n/2) * (t1+tn)
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'.
33. What is the volume of a cylinder?
(pi)r^2(h)
(n-2)180
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.
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.
34. (a+b)(c+d)
(x1+x2)/2 - (y1+y2)/2
2x2x2x5x5
Pir^2h
Ac+ad+bc+bd
35. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Pir^2h
Probability A + Probability B
2 pi r
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
36. What is the average speed?
C =?d
4s (where s = length of a side)
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.
Total distance/total time
37. What is the length of an arc?
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.
1/3Bh
(n degrees/360) * 2(pi)r
1/1
38. Perimeter of a square
4s (where s = length of a side)
(0 -0)
2l+2w
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.
39. What is the equation of a line?
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40. In a coordinate system - identify the quadrants and describe their location.
Negative
S*v2
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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
41. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
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
y = k/x
The average - mean - median - or mode.
42. Volume of sphere
A=?r2
4/3pir^3
Middle term
4s
43. What is the area of a triangle?
The average - mean - median - or mode.
y = kx
Bh
1/2bh
44. In a parabola - if the first term is negative - the parabola ________.
2pi*r
Opens down
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-b)²
45. a²-b²
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'.
Groups - teams - or committees.
(a-b)(a+b)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
46. a³+b³
2lw+2lh+2wh
(n-2)180
2x2x2x5x5
(a+b)(a²-ab+b²)
47. Volume of pyramid
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.
Less
The total # of possible outcomes.
1/3Bh
48. What is the average?
(pi)r^2
Sum of terms/number of terms
y = k/x
Arrangements - orders - schedules - or lists.
49. Area of Parallelogram
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Bh
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
S*v2
50. Area of a trapezoid
N x M
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
x²-y²