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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 formula for the diagonal of any square?
1/x^a
Groups - teams - or committees.
S*v2
(n-2)180
2. Point-Slope form
y-y1=m(x-x1)
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'.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(n/2) * (t1+tn)
3. Surface Area of rectangular prism
C =?d
1/3Bh
2lw+2lh+2wh
(pi)r^2
4. Surface Area of Sphere
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
(x-y)²
Probability A + Probability B
4pir^2
5. x^-a =
The set of points which are all the same distance (the radius) from a certain point (the center).
1/x^a
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
6. What is the factored version of x² -2xy + y² ?
Sum of terms/number of terms
Groups - teams - or committees.
S*v2
(x-y)²
7. In a parabola - if the first term is positive - the parabola ________.
Opens up
b±[vb²-4ac]/2a
T1 + (n-1)d
2 pi r
8. What is an 'equilateral' 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.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(pi)r^2
?r²
9. In a coordinate system - identify the quadrants and describe their location.
1/x^a
Sum of terms/number of terms
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
y = kx
10. What is the 'Third side' rule for triangles?
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.
Groups - teams - or committees.
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.
1. Given event A: A + notA = 1.
11. Area of Parallelogram
1/x^a
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.
Bh
4/3pir^3
12. length of a sector
x°/360 times (2 pi r) - where x is the degrees in the angle
(a-b)(a²+ab+b²)
(a-b)(a+b)
C =?d
13. 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
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.
Part of a circle connecting two points on the circle.
14. What are the side ratios 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.
4s (where s = length of a side)
1. Given event A: A + notA = 1.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
15. Circumference of cirlce using diameter
(n degrees/360) * (pi)r^2
(x-y)²
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.
Pi*d
16. What is the area of a solid rectangle?
Opens down
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
2(lw+wh+lh)
(a+b)(a²-ab+b²)
17. Define the mode of a set of numbers.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
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.
18. What is the average speed?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Order does matter for a permutation - but does not matter for a combination.
Last term
Total distance/total time
19. What is the probability?
2 pi r
Number of desired outcomes/number of total outcomes
Less
(a-b)²
20. What'S the most important thing to remember about charts you'll see on the GRE?
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.
Sqr( x2 -x1) + (y2- y1)
x² + 2xy + y²
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.
21. In a coordinate system - what is the origin?
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.
T1 + (n-1)d
(0 -0)
Less
22. What is the length of an arc?
Percentage Change = Difference/Original * 100
(n degrees/360) * 2(pi)r
1/3pir^2*h
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.
23. What is the area of a triangle?
Total distance/total time
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
(y-y1)=m(x-x1)
1/2bh
24. Sector
Arrangements - orders - schedules - or lists.
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.
Bh
Last term
25. Chord
The four big angles are equal and the four small angles are equal
N x M
2x2x2x5x5
The distance from one point on the circle to another point on the circle.
26. How do you calculate the percentage of change?
Lwh
Percentage Change = Difference/Original * 100
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
y = kx
27. What is the unfactored version of (x+y)² ?
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1/3pir^2*h
x² + 2xy + y²
(x-y)²
28. Volume of sphere
Lw
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.
C =?d
4/3pir^3
29. Arc
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
2pi*r
Part of a circle connecting two points on the circle.
1. Given event A: A + notA = 1.
30. How do you find the nth term of a geometric sequence?
T1 * r^(n-1)
Middle term
Lw
x² -2xy + y²
31. Area of a sector
?d OR 2?r
S² - where s = length of a side
x² + 2xy + y²
x°/360 times (?r²) - where x is the degrees in the angle
32. (a+b)(a-b)=
A²-b²
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.
Negative
A segment connecting the center of a circle to any point on the circle
33. In intersecting lines - opposite angles are _____.
(pi)r^2
Equal
Pi*d
(x1+x2)/2 - (y1+y2)/2
34. a²-b²
Groups - teams - or committees.
Arrangements - orders - schedules - or lists.
Less
(a-b)(a+b)
35. What is the sum of the inside angles of an n-sided polygon?
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
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(a-b)(a²+ab+b²)
(n-2)180
36. Rough est. of v2 =
4pir^2
1.4
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Equal
37. What do combination problems usually ask for?
Groups - teams - or committees.
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.
Probability A * Probability B
2(pi)r(r+h)
38. Area of rectangle - square - parallelogram
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.
y = k/x
A=bh
(n degrees/360) * (pi)r^2
39. Perimeter of a square
The set of points which are all the same distance (the radius) from a certain point (the center).
(y-y1)=m(x-x1)
4s (where s = length of a side)
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.
40. Area of Trapezoid
(x+y)(x-y)
Between 0 and 1.
x² + 2xy + y²
1/2 h (b1 + b2)
41. a²-2ab+b²
(x+y)(x-y)
(a-b)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.
4s (where s = length of a side)
42. What is the circumference of a circle?
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
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
43. Perimeter of a rectangle
T1 + (n-1)d
S^2
1/2 h (b1 + b2)
2Length + 2width [or (length + width) x 2]
44. Area of a circle
(a-b)(a²+ab+b²)
2x2x2x5x5
?r²
(a+b)(a²-ab+b²)
45. What is the factored version of (x+y)(x-y) ?
T1 * r^(n-1)
S*v2
(a-b)²
x²-y²
46. If something is possible but not certain - what is the numeric range of probability of it happening?
2(pi)r(r+h)
Between 0 and 1.
The four big angles are equal and the four small angles are equal
A+b
47. How do you find the nth term of an arithmetic sequence?
(y2-y1)/(x2-x1)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2l+2w
T1 + (n-1)d
48. How do you calculate the surface area of a rectangular box?
(a+b)²
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.
Lw
4s (where s = length of a side)
49. Perimeter of rectangle
2(pi)r(r+h)
(n degrees/360) * (pi)r^2
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.
2l+2w
50. Perimeter of polygon
Sum of the lengths of the sides
2(pi)r
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.
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.