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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. Circumference Formula
?r²
Percentage Change = Difference/Original * 100
C =?d
(pi)r^2
2. Surface Area of rectangular prism
2lw+2lh+2wh
Part of a circle connecting two points on the circle.
4s (where s = length of a side)
Middle term
3. How do you multiply and divide square roots?
2pi*r
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Lwh
Probability A + Probability B
4. Radius (Radii)
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.
Lw
Lwh
A segment connecting the center of a circle to any point on the circle
5. Rough est. of v2 =
1.4
A=?r2
4s (where s = length of a side)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
6. Volume of pyramid
4pir^2
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/3Bh
7. How do you multiply powers with the same base?
Equal
Part of a circle connecting two points on the circle.
y = k/x
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
8. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.
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9. Point-Slope form
2(lw+wh+lh)
y-y1=m(x-x1)
1. Given event A: A + notA = 1.
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
10. What is the sum of the inside angles of an n-sided polygon?
The set of points which are all the same distance (the radius) from a certain point (the center).
(n-2)180
The distance from one point on the circle to another point on the circle.
2(pi)r(r+h)
11. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
(pi)r^2(h)
(n/2) * (t1+tn)
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
12. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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. 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
2(pi)r(r+h)
13. Surface Area of Sphere
4pir^2
1/2 h (b1 + b2)
(x+y)²
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.
14. Lines reflected over the x or y axis have ____ slopes.
2(pi)r(r+h)
Negative
The distance across the circle through the center of the circle.The diameter is twice the radius.
4pir^2
15. perimeter of square
Less
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
4s
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.
16. What is the prime factorization of 200?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
4/3pir^3
(pi)r^2(h)
2x2x2x5x5
17. What is the factored version of x² + 2xy + y² ?
(x+y)²
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.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
18. x^a * x^b = x^__
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
A+b
(pi)r^2
(a+b)(a-b)
19. Perimeter (circumference) of a circle
2(pi)r(r+h)
2 pi r
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.
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 is a 'Right isosceles' triangle?
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.
(pi)r^2(h)
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.
The distance across the circle through the center of the circle.The diameter is twice the radius.
21. Perimeter of a square
4s (where s = length of a side)
(x-y)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.
Lwh
22. In a parabola - if the first term is negative - the parabola ________.
Opens down
(x-y)²
(n degrees/360) * (pi)r^2
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
23. Sector
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.
x°/360 times (2 pi r) - where x is the degrees in the angle
2pir^2 + 2pir*h
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
24. a³+b³
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.
Total distance/total time
(a+b)(a²-ab+b²)
T1 * r^(n-1)/(r-1)
25. Volume of Cylinder
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.
y = kx
Pir^2h
Opens down
26. When you reverse FOIL - the term that needs to multiply out is the _____
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
4s
N x M
Last term
27. a²-b²
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.
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 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.
28. To divide powers with the same base...
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(n-2)180
2(lw+wh+lh)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
29. What must be true before a quadratic equation can be solved?
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30. What is the factored version of (x+y)(x-y) ?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
A+b
Pir^2h
x²-y²
31. a³-b³
(a-b)(a²+ab+b²)
Middle term
4s (where s = length of a side)
Probability A * Probability B
32. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Groups - teams - or committees.
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.
2(lw+wh+lh)
33. x^-a =
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/x^a
4s (where s = length of a side)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
34. Circle
Opens up
The set of points which are all the same distance (the radius) from a certain point (the center).
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.
(x-y)²
35. What is the 'Third side' rule for triangles?
(x+y)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.
Percentage Change = Difference/Original * 100
1. Given event A: A + notA = 1.
36. What do permutation problems often ask for?
Negative
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.
Sum of terms/number of terms
Arrangements - orders - schedules - or lists.
37. Area of rectangle - square - parallelogram
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.
S² - where s = length of a side
A=bh
2(pi)r(r+h)
38. Arc
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.
Part of a circle connecting two points on the circle.
(x-y)²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
39. What is the surface area of a cylinder?
2(pi)r(r+h)
(a+b)²
Between 0 and 1.
x°/360 times (2 pi r) - where x is the degrees in the angle
40. How do you find the sum of a geometric sequence?
S*v2
T1 * r^(n-1)/(r-1)
(x-y)²
Opens up
41. What is the formula for the diagonal of any square?
Pi*r^2
1/2bh
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.
S*v2
42. Define 'proportionate' values
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.
2(pi)r
The distance across the circle through the center of the circle.The diameter is twice the radius.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
43. What is the length of an arc?
Last term
2lw+2lh+2wh
x°/360 times (?r²) - where x is the degrees in the angle
(n degrees/360) * 2(pi)r
44. For a bell curve - what three terms might be used to describe the number in the middle?
C =?d
4s
S² - where s = length of a side
The average - mean - median - or mode.
45. a² - b² is equal to
T1 * r^(n-1)/(r-1)
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)(a-b)
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.
46. What is the volume of a cylinder?
(pi)r^2(h)
x² -2xy + y²
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.
½(base x height) [or (base x height)÷2]
47. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
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48. What is the unfactored version of (x-y)² ?
x² -2xy + y²
A+b
A=bh
Opens down
49. What is the unfactored version of x²-y² ?
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+b)(a²-ab+b²)
(x+y)(x-y)
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.
50. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Arrangements - orders - schedules - or lists.
x°/360 times (2 pi r) - where x is the degrees in the angle
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.
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.