GRE Math 2

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. Define the 'Third side' rule for triangles

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2. When you reverse FOIL - the term that needs to add out is the _____
(n degrees/360) * 2(pi)r
Last term
2(pi)r(r+h)
Middle term


3. What is the probability?
Total distance/total time
y = kx
Number of desired outcomes/number of total outcomes
T1 * r^(n-1)/(r-1)


4. What is the average?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(x+y)²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Sum of terms/number of terms


5. Circumference Formula
4s
The average - mean - median - or mode.
C =?d
1


6. What is the volume of a cylinder?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(x+y)(x-y)
(pi)r^2(h)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.


7. Surface Area of Cylinder
b±[vb²-4ac]/2a
2pir^2 + 2pir*h
(x-y)²
A²-b²


8. Define 'proportionate' values
Lw
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
The average - mean - median - or mode.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


9. x^-a =
1/x^a
(0 -0)
Pi*r^2
The average - mean - median - or mode.


10. To divide powers with the same base...
4/3pir^3
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
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
1/3Bh


11. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
Order does matter for a permutation - but does not matter for a combination.
Total distance/total time
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.


12. When a line crosses two parallel lines - ________.
2lw+2lh+2wh
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
(pi)r^2(h)
The four big angles are equal and the four small angles are equal


13. Volume of sphere
4/3pir^3
Last term
Total distance/total time
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.


14. What is the area of a triangle?
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
1/2bh
Sum of terms/number of terms
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


15. What is the surface area of a cylinder?
(a+b)(a²-ab+b²)
2(pi)r(r+h)
Pi*d
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


16. What is the circumference of a circle?
(a-b)²
1/3pir^2*h
2(pi)r
(y2-y1)/(x2-x1)


17. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
Arrangements - orders - schedules - or lists.
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
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.


18. Define the range of a set of numbers.
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.
Bh
Middle term
Total distance/total time


19. What is the formula for the diagonal of any square?
An ange whose vertex is the center of the circle
Not necessarily. This is a trick question - because x could be either positive or negative.
S*v2
(a-b)²


20. Explain the difference between a digit and a number.

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21. Perimeter of polygon
(a+b)(a²-ab+b²)
Sum of the lengths of the sides
(a-b)²
A circle'S perimeter is roughly 3x its diameter (the formula is pd).


22. Area of a trapezoid
Probability A * Probability 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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
x°/360 times (?r²) - where x is the degrees in the angle


23. Lines reflected over the x or y axis have ____ slopes.
Sum of terms/number of terms
Negative
(n degrees/360) * (pi)r^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.


24. What is the sum of the inside angles of an n-sided polygon?
S*v2
The distance from one point on the circle to another point on the circle.
A+b
(n-2)180


25. a²+2ab+b²
T1 * r^(n-1)
(a+b)²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(pi)r^2(h)


26. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
Pi*r^2
Between 0 and 1.
S^2


27. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?

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28. If x² = 144 - does v144 = x?
(a+b)(a-b)
Number of desired outcomes/number of total outcomes
2pi*r
Not necessarily. This is a trick question - because x could be either positive or negative.


29. Area of rectangle - square - parallelogram
(n-2)180
Opens up
A=bh
2(pi)r


30. What is the side ratio for a Right Isosceles triangle?
4pir^2
1/3pir^2*h
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
Pi*r^2


31. The probability of an event happening and the probability of an event NOT happening must add up to what number?
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.
1. Given event A: A + notA = 1.
(y-y1)=m(x-x1)
½(b1 +b2) x h [or (b1 +b2) x h÷2]


32. How do you find the nth term of an arithmetic sequence?
Ac+ad+bc+bd
x² -2xy + y²
T1 + (n-1)d
?d OR 2?r


33. 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
y = k/x
(y2-y1)/(x2-x1)
Less


34. How do you find the nth term of a geometric sequence?
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'.
T1 * r^(n-1)
(y2-y1)/(x2-x1)
The distance from one point on the circle to another point on the circle.


35. 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.
2lw+2lh+2wh
T1 * r^(n-1)
2(pi)r


36. Volume of pyramid
1/3Bh
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.
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.
T1 + (n-1)d


37. Diameter
2(lw+wh+lh)
x°/360 times (2 pi r) - where x is the degrees in the angle
The distance across the circle through the center of the circle.The diameter is twice the radius.
½(base x height) [or (base x height)÷2]


38. What must be true before a quadratic equation can be solved?

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39. Circumference of a circle
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
A²-b²
C =?d


40. Rough est. of v3 =
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.
1/3Bh
1.7
A²-b²


41. Circle
y2-y1/x2-x1
1/2bh
The set of points which are all the same distance (the radius) from a certain point (the center).
S² - where s = length of a side


42. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.

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43. When you reverse FOIL - the term that needs to multiply out is the _____
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Last term
The set of points which are all the same distance (the radius) from a certain point (the center).
2 pi r


44. What are the side ratios for a 30:60:90 triangle?
Less
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Probability A * Probability B


45. What is the 'distributive law'?
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.
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+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.
C =?d


46. What do combination problems usually ask for?
Sqr( x2 -x1) + (y2- y1)
A=?r2
Groups - teams - or committees.
Percentage Change = Difference/Original * 100


47. In a coordinate system - identify the quadrants and describe their location.
2(lw+wh+lh)
A+b
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Middle term


48. What is a '30:60:90' triangle?
1.4
x²-y²
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
2Length + 2width [or (length + width) x 2]


49. Area of Trapezoid
2(pi)r(r+h)
2(pi)r(r+h)
1/2 h (b1 + b2)
A segment connecting the center of a circle to any point on the circle


50. What'S the most important thing to remember about charts you'll see on the GRE?
The distance from one point on the circle to another point on the circle.
(n-2)180
x°/360 times (2 pi r) - where x is the degrees in the angle
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.