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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 area of a solid rectangle?
1/x^a
2(lw+wh+lh)
(pi)r^2(h)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2. a²-2ab+b²
(a-b)²
4pir^2
1/2 h (b1 + b2)
2pir^2 + 2pir*h
3. Point-Slope form
1/3Bh
Opens up
y-y1=m(x-x1)
2(pi)r
4. Area of Square
S^2
1
2lw+2lh+2wh
1.4
5. What is the unfactored version of (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.
x² + 2xy + 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.
(a+b)²
6. What is the probability?
?r²
Number of desired outcomes/number of total outcomes
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'.
Lwh
7. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.
8. a³-b³
A=?r2
½(base x height) [or (base x height)÷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.
(a-b)(a²+ab+b²)
9. What are the side ratios for a 30:60:90 triangle?
(a-b)²
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Total distance/total time
10. In a parabola - if the first term is negative - the parabola ________.
1
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
Between 0 and 1.
Opens down
11. a²+2ab+b²
(a+b)²
The distance across the circle through the center of the circle.The diameter is twice the radius.
Number of desired outcomes/number of total outcomes
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.
12. (a+b)(a-b)=
A²-b²
2 pi r
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.
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.
13. Perimeter of polygon
(a+b)²
Between 0 and 1.
2(lw+wh+lh)
Sum of the lengths of the sides
14. What is a 'Right isosceles' triangle?
1/1
½(b1 +b2) x h [or (b1 +b2) x h÷2]
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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.
15. Area of Trapezoid
An ange whose vertex is the center of the circle
C =?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.
1/2 h (b1 + b2)
16. 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.
A²-b²
Opens down
S*v2
17. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
The four big angles are equal and the four small angles are equal
(y2-y1)/(x2-x1)
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.
Arrangements - orders - schedules - or lists.
18. What do permutation problems often ask for?
A segment connecting the center of a circle to any point on the circle
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.
2(pi)r
Arrangements - orders - schedules - or lists.
19. Surface Area of rectangular prism
2lw+2lh+2wh
(n degrees/360) * (pi)r^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.
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.
20. Define a factorial of a number - and how it is written.
Pi*d
1. Given event A: A + notA = 1.
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.
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.
21. What is directly proportional?
(n degrees/360) * 2(pi)r
(a+b)²
y = kx
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.
22. What do combination problems usually ask for?
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.
Groups - teams - or committees.
Between 0 and 1.
4s (where s = length of a side)
23. In intersecting lines - opposite angles are _____.
x² + 2xy + y²
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.
Equal
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
24. Slope
(y2-y1)/(x2-x1)
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2(pi)r(r+h)
(n degrees/360) * 2(pi)r
25. Volume of prism
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
The average - mean - median - or mode.
Bh
26. Volume of sphere
Less
y = kx
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.
4/3pir^3
27. When you reverse FOIL - the term that needs to add out is the _____
Pi*d
1. Given event A: A + notA = 1.
Middle term
T1 * r^(n-1)
28. What is the side ratio for a 30:60:90 triangle?
Opens down
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
x²-y²
29. What is inversely proportional?
1/2bh
y = k/x
2(lw+wh+lh)
A segment connecting the center of a circle to any point on the circle
30. Define the 'Third side' rule for triangles
31. Lines reflected over the x or y axis have ____ slopes.
The total # of possible outcomes.
Negative
4pir^2
2(pi)r(r+h)
32. What is the unfactored version of x²-y² ?
Probability A * Probability B
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
(x+y)(x-y)
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.
33. Area of Circles
Middle term
?d OR 2?r
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=?r2
34. Surface Area of Cylinder
The distance from one point on the circle to another point on the circle.
S^2
(x+y)²
2pir^2 + 2pir*h
35. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
(pi)r^2
A²-b²
Equal
36. If x² = 144 - does v144 = x?
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.
Not necessarily. This is a trick question - because x could be either positive or negative.
?d OR 2?r
37. Area of Rectangle
1. Given event A: A + notA = 1.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Lw
38. Circumference of cirlce using diameter
y = kx
Pi*d
4pir^2
4s (where s = length of a side)
39. What is the factored version of x² -2xy + y² ?
1/3pir^2*h
(x-y)²
Sqr( x2 -x1) + (y2- y1)
A=?r2
40. Volume of Cone
T1 * r^(n-1)/(r-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.
1/3pir^2*h
The total # of possible outcomes.
41. What is the average speed?
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.
T1 * r^(n-1)
Last term
Total distance/total time
42. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the angle
S*v2
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Sqr( x2 -x1) + (y2- y1)
43. What is the circumference of a circle?
Probability A + Probability B
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2(pi)r
A+b
44. What is a '30:60:90' triangle?
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.
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.
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
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
45. What is 'absolute value' - and how is it represented?
46. To divide powers with the same base...
C =?d
Equal
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/3Bh
47. Rough est. of v2 =
(a-b)(a²+ab+b²)
2l+2w
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
48. Define the formula for calculating slope.
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
N x M
49. What'S the most important thing to remember about charts you'll see on the GRE?
(a+b)(a²-ab+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.
2l+2w
2lw+2lh+2wh
50. Explain the special properties of zero.
y-y1=m(x-x1)
Pi*r^2
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.
The total # of possible outcomes.