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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 side ratio for 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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(x+y)²
Sum of terms/number of terms
2. Define the 'Third side' rule for triangles
3. What is the probability?
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Number of desired outcomes/number of total outcomes
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.
x°/360 times (2 pi r) - where x is the degrees in the angle
4. If x² = 144 - does v144 = x?
2(pi)r(r+h)
Total distance/total time
Not necessarily. This is a trick question - because x could be either positive or negative.
2pi*r
5. Define the range of a set of numbers.
1/x^a
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
Opens up
6. What is the unfactored version of (x+y)² ?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
x² + 2xy + y²
A=?r2
The average - mean - median - or mode.
7. What is the area of a cylinder?
Equal
x°/360 times (2 pi r) - where x is the degrees in the angle
(x+y)²
2(pi)r(r+h)
8. In intersecting lines - opposite angles are _____.
4s
Less
Equal
1
9. a³-b³
1
Sum of the lengths of the sides
x°/360 times (?r²) - where x is the degrees in the angle
(a-b)(a²+ab+b²)
10. a²-b²
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)
Probability A * Probability B
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.
11. Explain the difference between a digit and a number.
12. How do you find the slope?
y2-y1/x2-x1
(0 -0)
2l+2w
Equal
13. (a+b)(c+d)
Ac+ad+bc+bd
Arrangements - orders - schedules - or lists.
S² - where s = length of a side
Opens up
14. In a coordinate system - what is the origin?
S*v2
(0 -0)
?d OR 2?r
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
15. Area of Triangle
2(pi)r
4/3pir^3
Lw
1/2bh
16. Define the mode of a set of numbers.
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 average - mean - median - or mode.
1/2bh
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.
17. Area of Circle
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.
Arrangements - orders - schedules - or lists.
Pi*r^2
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
18. What must be true before a quadratic equation can be solved?
19. Perimeter of a square
(n/2) * (t1+tn)
4s (where s = length of a side)
1. Given event A: A + notA = 1.
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.
20. Circumference of cirlce using diameter
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.
N x M
Pi*d
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.
21. What is the factored version of x² -2xy + y² ?
Pi*d
4/3pir^3
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.
(x-y)²
22. Area of a triangle
4s (where s = length of a side)
1/2bh
½(base x height) [or (base x height)÷2]
Groups - teams - or committees.
23. Area of Trapezoid
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.
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.
Bh
1/2 h (b1 + b2)
24. Area of a trapezoid
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.
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
25. Volume of Cylinder
Pir^2h
Ac+ad+bc+bd
2(lw+wh+lh)
x°/360 times (2 pi r) - where x is the degrees in the angle
26. When you reverse FOIL - the term that needs to multiply out is the _____
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.
Last term
2(lw+wh+lh)
Sum of the lengths of the sides
27. Define a factorial of a number - and how it is written.
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.
S² - where s = length of a side
1.4
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.
28. What is 'absolute value' - and how is it represented?
29. Area of a square
The distance from one point on the circle to another point on the circle.
S² - where s = length of a side
4s
(pi)r^2
30. What is a '30:60:90' triangle?
The total # of possible outcomes.
(a+b)²
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
2pi*r
31. How do you calculate the surface area of a rectangular box?
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.
Opens down
Number of desired outcomes/number of total outcomes
(a+b)(a-b)
32. What is the average?
Sum of terms/number of terms
Groups - teams - or committees.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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.
33. Volume of pyramid
1/3Bh
2x2x2x5x5
Bh
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.
34. What is a 'Right isosceles' triangle?
2(pi)r(r+h)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
A+b
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.
35. Surface Area of Cylinder
2pir^2 + 2pir*h
(0 -0)
(x+y)(x-y)
x² -2xy + y²
36. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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) * 2(pi)r
Bh
x² -2xy + y²
37. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.
38. What is the distance formula?
(n degrees/360) * 2(pi)r
Probability A + Probability B
Sqr( x2 -x1) + (y2- y1)
2(lw+wh+lh)
39. Surface Area of rectangular prism
A²-b²
2lw+2lh+2wh
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(a-b)²
40. a³+b³
Order does matter for a permutation - but does not matter for a combination.
(a+b)(a²-ab+b²)
4s
Part of a circle connecting two points on the circle.
41. Diameter
1/x^a
The distance across the circle through the center of the circle.The diameter is twice the radius.
2(lw+wh+lh)
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
42. The length of one side of any triangle is ____ than the sum of the other two sides.
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
Sum of the lengths of the sides
Less
43. Area of a circle
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.
?r²
1/3Bh
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
44. How do you find the sum of an arithmetic sequence?
(n/2) * (t1+tn)
Lwh
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.
45. a² - b² is equal to
x²-y²
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.
T1 + (n-1)d
(a+b)(a-b)
46. What is the unfactored version of x²-y² ?
(x+y)(x-y)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
A segment connecting the center of a circle to any point on the circle
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
47. What is the unfactored version of (x-y)² ?
Order does matter for a permutation - but does not matter for a combination.
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
1.4
x² -2xy + y²
48. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
A=?r2
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Negative
49. Rough est. of v2 =
The distance from one point on the circle to another point on the circle.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1.4
(pi)r^2
50. What is the prime factorization of 200?
(n/2) * (t1+tn)
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.
2x2x2x5x5
(a-b)²