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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. Rough est. of v2 =
(a-b)(a²+ab+b²)
Opens up
1.4
1
2. 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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3. What is the area of a circle?
1/x^a
Ac+ad+bc+bd
1/1
(pi)r^2
4. Area of Circle
N x M
A segment connecting the center of a circle to any point on the circle
Pi*r^2
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.
5. 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.
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.
Pi*r^2
1.4
6. What is the factored version of (x+y)(x-y) ?
(x1+x2)/2 - (y1+y2)/2
½(b1 +b2) x h [or (b1 +b2) x h÷2]
A=?r2
x²-y²
7. Explain the special properties of zero.
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.
x²-y²
Equal
A segment connecting the center of a circle to any point on the circle
8. Surface Area of rectangular prism
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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.
Order does matter for a permutation - but does not matter for a combination.
2lw+2lh+2wh
9. The probability of an event happening and the probability of an event NOT happening must add up to what number?
S*v2
1. Given event A: A + notA = 1.
(n degrees/360) * 2(pi)r
The set of points which are all the same distance (the radius) from a certain point (the center).
10. Area of a circle
4s
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.
?d OR 2?r
?r²
11. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.
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12. Area of rectangle - square - parallelogram
A=bh
?d OR 2?r
(x+y)²
An ange whose vertex is the center of the circle
13. Area of Square
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
S^2
x°/360 times (?r²) - where x is the degrees in the angle
A=?r2
14. Circle
The set of points which are all the same distance (the radius) from a certain point (the center).
A segment connecting the center of a circle to any point on the circle
y2-y1/x2-x1
½(base x height) [or (base x height)÷2]
15. Perimeter of rectangle
2Length + 2width [or (length + width) x 2]
2l+2w
1/3Bh
Probability A * Probability B
16. 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.
1/1
2(lw+wh+lh)
(a+b)(a²-ab+b²)
17. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
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18. Perimeter of polygon
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.
Part of a circle connecting two points on the circle.
Sum of the lengths of the sides
1/2 h (b1 + b2)
19. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
T1 + (n-1)d
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.
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.
20. How do you multiply and divide square roots?
The average - mean - median - or mode.
The four big angles are equal and the four small angles are equal
y-y1=m(x-x1)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
21. Area of Rectangle
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.
Groups - teams - or committees.
4s (where s = length of a side)
Lw
22. How do you solve a permutation?
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.
(a+b)²
Part of a circle connecting two points on the 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
23. (a+b)(c+d)
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1.7
Ac+ad+bc+bd
24. Circumference of a circle
(y-y1)=m(x-x1)
4/3pir^3
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
?d OR 2?r
25. perimeter of square
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2(pi)r
Pi*d
4s
26. Rough est. of v1 =
Pi*r^2
A segment connecting the center of a circle to any point on the circle
1
y2-y1/x2-x1
27. What is the volume of a cylinder?
(pi)r^2(h)
2(pi)r(r+h)
Sum of the lengths of the sides
N x M
28. Explain the difference between a digit and a number.
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29. How do you find the slope?
T1 * r^(n-1)/(r-1)
2(pi)r
y2-y1/x2-x1
Not necessarily. This is a trick question - because x could be either positive or negative.
30. What is the unfactored version of (x+y)² ?
x² + 2xy + y²
(0 -0)
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.
Pir^2h
31. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
(x+y)²
S² - 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.
2(lw+wh+lh)
32. If something is possible but not certain - what is the numeric range of probability of it happening?
Sqr( x2 -x1) + (y2- y1)
Between 0 and 1.
2(lw+wh+lh)
(pi)r^2
33. What is the distance formula?
Sqr( x2 -x1) + (y2- y1)
?d OR 2?r
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.
Middle term
34. How do you calculate the percentage of change?
½(base x height) [or (base x height)÷2]
2pi*r
Between 0 and 1.
Percentage Change = Difference/Original * 100
35. What is the point-slope form?
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.
Pi*r^2
(y-y1)=m(x-x1)
Between 0 and 1.
36. What do permutation problems often ask for?
(a-b)(a+b)
1/1
Arrangements - orders - schedules - or lists.
1.4
37. a²+2ab+b²
1
Not necessarily. This is a trick question - because x could be either positive or negative.
(a+b)²
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
38. What is the prime factorization of 200?
2x2x2x5x5
Middle term
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 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.
39. What is the length of an arc?
1
1/3Bh
1/1
(n degrees/360) * 2(pi)r
40. Arc
The total # of possible outcomes.
C =?d
(0 -0)
Part of a circle connecting two points on the circle.
41. In a coordinate system - what is the origin?
(0 -0)
T1 + (n-1)d
Arrangements - orders - schedules - or lists.
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.
42. What is 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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
4s (where s = length of a side)
The total # of possible outcomes.
43. a³-b³
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(a-b)(a²+ab+b²)
A²-b²
(pi)r^2(h)
44. What is an 'equilateral' triangle?
2(lw+wh+lh)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2x2x2x5x5
Equal
45. When a line crosses two parallel lines - ________.
Number of desired outcomes/number of total outcomes
x² -2xy + y²
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
The four big angles are equal and the four small angles are equal
46. Lines reflected over the x or y axis have ____ slopes.
Bh
Negative
1
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.
47. How do you calculate a diagonal inside a 3-dimensional rectangular box?
N x M
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2pi*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.
48. Perimeter of a rectangle
2 pi r
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.
2Length + 2width [or (length + width) x 2]
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.
49. (a+b)(a-b)=
Probability A * Probability B
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.
4s (where s = length of a side)
A²-b²
50. How do you calculate the probability of two events in a row? (Probability of A and B)
1
y-y1=m(x-x1)
(a+b)(a²-ab+b²)
Probability A * Probability B