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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 sector?
x°/360 times (?r²) - where x is the degrees in the angle
(pi)r^2
½(base x height) [or (base x height)÷2]
(n degrees/360) * (pi)r^2
2. What must be true before a quadratic equation can be solved?
3. Rough est. of v1 =
1
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(x+y)(x-y)
x°/360 times (?r²) - where x is the degrees in the angle
4. Perimeter of a rectangle
(n/2) * (t1+tn)
4/3pir^3
2Length + 2width [or (length + width) x 2]
(a+b)(a²-ab+b²)
5. How do you calculate the probability of two events in a row? (Probability of A and B)
Probability A * Probability B
(x1+x2)/2 - (y1+y2)/2
Pir^2h
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.
6. How do you calculate the surface area of a rectangular box?
1/1
½(b1 +b2) x h [or (b1 +b2) x h÷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.
(y2-y1)/(x2-x1)
7. What is inversely proportional?
(x+y)²
Number of desired outcomes/number of total outcomes
y = k/x
(n degrees/360) * 2(pi)r
8. In intersecting lines - opposite angles are _____.
Equal
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1/2bh
The average - mean - median - or mode.
9. How do you find the midpoint?
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+b
y2-y1/x2-x1
(x1+x2)/2 - (y1+y2)/2
10. What is the factored version of (x+y)(x-y) ?
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.
Pir^2h
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
11. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
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.
1.4
(x1+x2)/2 - (y1+y2)/2
12. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Pi*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.
Probability A * Probability B
13. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
Ac+ad+bc+bd
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.
The average - mean - median - or mode.
14. (a+b)(c+d)
Order does matter for a permutation - but does not matter for a combination.
2x2x2x5x5
Ac+ad+bc+bd
The average - mean - median - or mode.
15. If x² = 144 - does v144 = x?
Opens up
Total distance/total time
Bh
Not necessarily. This is a trick question - because x could be either positive or negative.
16. What is the area of a solid rectangle?
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(lw+wh+lh)
Part of a circle connecting two points on the circle.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
17. How do you find the nth term of a geometric sequence?
y = k/x
T1 * r^(n-1)
Opens down
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
18. length of a sector
T1 * r^(n-1)/(r-1)
x°/360 times (2 pi r) - where x is the degrees in the angle
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*v2
19. a³-b³
(a-b)(a²+ab+b²)
(n degrees/360) * (pi)r^2
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.
Between 0 and 1.
20. What is the 'Third side' rule for triangles?
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.
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. 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
Between 0 and 1.
21. How do you multiply and divide square roots?
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2pir^2 + 2pir*h
2lw+2lh+2wh
Equal
22. Define 'proportionate' values
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Groups - teams - or committees.
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 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.
23. Volume of pyramid
1/3Bh
Opens up
2(pi)r
A=bh
24. a² - b² is equal to
(a+b)(a-b)
?d OR 2?r
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
Lw
25. Define the 'Third side' rule for triangles
26. Area of Trapezoid
Equal
1/2 h (b1 + b2)
b±[vb²-4ac]/2a
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
27. Area of a sector
2l+2w
x°/360 times (?r²) - where x is the degrees in the angle
T1 * r^(n-1)
1/x^a
28. What is the sum of the inside angles of an n-sided polygon?
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.
1/x^a
The set of points which are all the same distance (the radius) from a certain point (the center).
(n-2)180
29. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.
30. Diameter
Groups - teams - or committees.
Bh
The distance across the circle through the center of the circle.The diameter is twice the radius.
2(pi)r
31. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.
32. The probability of an event happening and the probability of an event NOT happening must add up to what number?
?d OR 2?r
2(pi)r
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1. Given event A: A + notA = 1.
33. In a parabola - if the first term is negative - the parabola ________.
Opens down
(0 -0)
Opens up
S^2
34. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
35. Area of Rectangle
Lw
T1 + (n-1)d
2x2x2x5x5
Percentage Change = Difference/Original * 100
36. What is the average speed?
Total distance/total time
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
4pir^2
Number of desired outcomes/number of total outcomes
37. Does order matter for a permutation? How about for a combination?
x²-y²
Order does matter for a permutation - but does not matter for a combination.
Opens up
Percentage Change = Difference/Original * 100
38. What is the unfactored version of (x-y)² ?
The distance across the circle through the center of the circle.The diameter is twice the radius.
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.
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
x² -2xy + y²
39. What is the unfactored version of x²-y² ?
4s
(x+y)(x-y)
(x+y)²
N x M
40. Circumference of a circle
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.
N x M
?d OR 2?r
The distance from one point on the circle to another point on the circle.
41. What is a '30:60:90' triangle?
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
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.
T1 * r^(n-1)/(r-1)
(x+y)²
42. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
Probability A + Probability B
1/1
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'.
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.
43. How do you solve a permutation?
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
T1 * r^(n-1)
Lwh
(n degrees/360) * 2(pi)r
44. Volume of Cylinder
Between 0 and 1.
1.4
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.
Pir^2h
45. When you reverse FOIL - the term that needs to multiply out is the _____
(n degrees/360) * (pi)r^2
Pi*r^2
Last term
(a+b)(a²-ab+b²)
46. Surface Area of Sphere
1
1/x^a
b±[vb²-4ac]/2a
4pir^2
47. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
A+b
(n degrees/360) * 2(pi)r
N x M
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
48. Define a factorial of a number - and how it is written.
(x-y)²
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.
Opens down
Middle term
49. What is the factored version of x² -2xy + y² ?
Pi*d
(a-b)²
(x-y)²
Pi*r^2
50. Area of a triangle
½(base x height) [or (base x height)÷2]
2 pi r
2(pi)r(r+h)
(x1+x2)/2 - (y1+y2)/2