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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. Surface Area of rectangular prism
2lw+2lh+2wh
Between 0 and 1.
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.
Opens up
2. Volume of sphere
4/3pir^3
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1.7
(a+b)(a²-ab+b²)
3. What is the formula for the diagonal of any square?
Ac+ad+bc+bd
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
S*v2
A=?r2
4. Volume of Cone
y = k/x
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
1/3pir^2*h
5. 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.
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.
(0 -0)
1/2bh
6. Define the formula for calculating slope.
1.4
1/2 h (b1 + b2)
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.
7. What is the probability?
2lw+2lh+2wh
Number of desired outcomes/number of total outcomes
The set of points which are all the same distance (the radius) from a certain point (the center).
2x2x2x5x5
8. Volume of pyramid
(n/2) * (t1+tn)
x² + 2xy + y²
1/3Bh
(a+b)²
9. In a parabola - if the first term is positive - the parabola ________.
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'.
Opens up
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
10. Define the 'Third side' rule for triangles
11. Area of a trapezoid
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
12. Define the mode of a set of numbers.
(pi)r^2
x²-y²
2lw+2lh+2wh
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.
13. Area of a circle
?r²
2l+2w
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.
½(base x height) [or (base x height)÷2]
14. List two odd behaviors of exponents
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.
(n degrees/360) * 2(pi)r
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
Groups - teams - or committees.
15. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
1.7
A median is the middle value of a set of numbers. For an odd number of values - it'S simply the middle number. For an even number of values - take the average of the center two values.
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.
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.
16. How do you find the nth term of a geometric sequence?
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
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.
An ange whose vertex is the center of the circle
T1 * r^(n-1)
17. In a coordinate system - what is the origin?
T1 * r^(n-1)/(r-1)
(0 -0)
2Length + 2width [or (length + width) x 2]
(a+b)(a-b)
18. What is the area of a sector?
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.
Part of a circle connecting two points on the circle.
1.4
(n degrees/360) * (pi)r^2
19. How do you calculate the probability of two events in a row? (Probability of A and B)
The total # of possible outcomes.
Probability A * Probability B
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Negative
20. Circumference of a circle using radius
The four big angles are equal and the four small angles are equal
1/1
(n-2)180
2pi*r
21. Explain the special properties of zero.
½(base x height) [or (base x height)÷2]
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.
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.
(x-y)²
22. What is 'absolute value' - and how is it represented?
23. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.
24. a²+2ab+b²
?d OR 2?r
(n/2) * (t1+tn)
T1 * r^(n-1)/(r-1)
(a+b)²
25. If x² = 144 - does v144 = x?
Pir^2h
A segment connecting the center of a circle to any point on the circle
Not necessarily. This is a trick question - because x could be either positive or negative.
The average - mean - median - or mode.
26. Explain the difference between a digit and a number.
27. Rough est. of v3 =
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.
1.7
x² + 2xy + y²
Arrangements - orders - schedules - or lists.
28. What is the side ratio for a 30:60:90 triangle?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2x2x2x5x5
Percentage Change = Difference/Original * 100
?d OR 2?r
29. What is directly proportional?
2pir^2 + 2pir*h
y = kx
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.
A segment connecting the center of a circle to any point on the circle
30. What is the area of a circle?
1. Given event A: A + notA = 1.
(n degrees/360) * (pi)r^2
Groups - teams - or committees.
(pi)r^2
31. How do you calculate the percentage of change?
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.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Sum of the lengths of the sides
Percentage Change = Difference/Original * 100
32. a³+b³
2pir^2 + 2pir*h
Lwh
(a+b)(a²-ab+b²)
Opens up
33. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
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.
Lwh
(pi)r^2(h)
34. What is a '30:60:90' triangle?
1/1
(x+y)(x-y)
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
(a-b)(a²+ab+b²)
35. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
Probability A * Probability B
T1 * r^(n-1)/(r-1)
Less
36. What is a 'Right isosceles' triangle?
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
2(pi)r
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
37. Rough est. of v2 =
(a-b)(a²+ab+b²)
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1.4
The set of points which are all the same distance (the radius) from a certain point (the center).
38. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
(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.
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.
39. Area of Triangle
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.
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.
1/2bh
Equal
40. If something is possible but not certain - what is the numeric range of probability of it happening?
Between 0 and 1.
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.
1/1
2(lw+wh+lh)
41. Area of rectangle - square - parallelogram
Number of desired outcomes/number of total outcomes
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.
2(lw+wh+lh)
A=bh
42. Area of Trapezoid
1/2 h (b1 + b2)
Between 0 and 1.
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.
1.7
43. (a+b)(c+d)
Ac+ad+bc+bd
y2-y1/x2-x1
?d OR 2?r
(x-y)²
44. What is the 'distributive law'?
A=bh
1/x^a
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
45. What is the side ratio for a Right Isosceles triangle?
Probability A + Probability B
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
(pi)r^2(h)
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.
46. What is the factored version of x² + 2xy + y² ?
(x+y)²
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.
4s (where s = length of a side)
47. How do you find the slope?
4pir^2
y2-y1/x2-x1
2x2x2x5x5
(y-y1)=m(x-x1)
48. Area of Square
1/2 h (b1 + b2)
1.4
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
S^2
49. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
50. How do you calculate the surface area of a rectangular box?
(pi)r^2
The average - mean - median - or mode.
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.
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.