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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. Area of a circle
2(lw+wh+lh)
?r²
A²-b²
Equal
2. What is the factored version of (x+y)(x-y) ?
2lw+2lh+2wh
Between 0 and 1.
Pi*r^2
x²-y²
3. What is the area of a triangle?
Last term
T1 * r^(n-1)
Order does matter for a permutation - but does not matter for a combination.
1/2bh
4. perimeter of square
4s
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.
2pir^2 + 2pir*h
Not necessarily. This is a trick question - because x could be either positive or negative.
5. Rough est. of v2 =
A=bh
Less
1.4
y2-y1/x2-x1
6. Rough est. of v3 =
1.7
Total distance/total time
4pir^2
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
7. The length of one side of any triangle is ____ than the sum of the other two sides.
?r²
x² + 2xy + y²
Less
A=bh
8. Perimeter of rectangle
½(base x height) [or (base x height)÷2]
y = k/x
2l+2w
1.4
9. What is the side ratio for a Right Isosceles triangle?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
2pi*r
(a-b)(a²+ab+b²)
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
10. Diameter
The distance across the circle through the center of the circle.The diameter is twice the radius.
1/3pir^2*h
Part of a circle connecting two points on the circle.
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.
11. 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.
Bh
Pi*d
Opens down
12. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
2pi*r
(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 ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
13. What is the 'Third side' rule for triangles?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Negative
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 - and greater than the difference between the other two sides.
14. What is directly proportional?
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.
2pi*r
Number of desired outcomes/number of total outcomes
y = kx
15. In a parabola - if the first term is positive - the parabola ________.
(x1+x2)/2 - (y1+y2)/2
4/3pir^3
Opens up
2(pi)r(r+h)
16. What is the distance formula?
y = kx
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
(y-y1)=m(x-x1)
Sqr( x2 -x1) + (y2- y1)
17. Volume of prism
Bh
Last term
Probability A + Probability B
1/x^a
18. Define the median of a set of numbers - and how to find it for an odd and even number of values in a set.
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19. How do you calculate the probability of two events in a row? (Probability of A and B)
Opens up
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
1/1
Probability A * Probability B
20. What must be true before a quadratic equation can be solved?
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21. What is an 'equilateral' triangle?
Less
?d OR 2?r
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2pi*r
22. What is the area of a circle?
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 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.
(pi)r^2
1.4
23. What is the formula for the diagonal of any square?
T1 + (n-1)d
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.
(0 -0)
S*v2
24. Area of Trapezoid
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
2Length + 2width [or (length + width) x 2]
1/2 h (b1 + b2)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
25. a²-b²
(a-b)(a²+ab+b²)
2(pi)r(r+h)
Opens down
(a-b)(a+b)
26. What is the side ratio for a 30:60:90 triangle?
A segment connecting the center of a circle to any point on the circle
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Number of desired outcomes/number of total outcomes
27. x^-a =
1/x^a
(a+b)²
The total # of possible outcomes.
Lwh
28. a²+2ab+b²
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.
Probability A + Probability B
(a+b)²
x² -2xy + y²
29. 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
Opens up
Between 0 and 1.
30. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
Total distance/total time
1/2 h (b1 + b2)
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
(0 -0)
31. Area of a trapezoid
½(b1 +b2) x h [or (b1 +b2) x h÷2]
1/2bh
Middle term
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.
32. If something is possible but not certain - what is the numeric range of probability of it happening?
Lw
T1 + (n-1)d
Between 0 and 1.
A²-b²
33. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
1/x^a
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.
x² + 2xy + y²
Sum of the lengths of the sides
34. Area of Circles
A=?r2
x² -2xy + y²
½(base x height) [or (base x height)÷2]
(n degrees/360) * (pi)r^2
35. Define 'proportionate' values
Negative
C =?d
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
36. Area of Triangle
1/2bh
(x+y)(x-y)
1/3pir^2*h
2Length + 2width [or (length + width) x 2]
37. Perimeter of a rectangle
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.
x²-y²
(a+b)(a-b)
2Length + 2width [or (length + width) x 2]
38. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
2(pi)r
N x M
2 pi r
Ac+ad+bc+bd
39. Area of a triangle
½(base x height) [or (base x height)÷2]
?d OR 2?r
y = kx
T1 * r^(n-1)/(r-1)
40. In a coordinate system - identify the quadrants and describe their location.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
x²-y²
(a-b)(a²+ab+b²)
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.
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
Not necessarily. This is a trick question - because x could be either positive or negative.
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'.
2l+2w
42. In intersecting lines - opposite angles are _____.
(a+b)²
Equal
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
T1 * r^(n-1)/(r-1)
43. x^a * x^b = x^__
2(pi)r
2lw+2lh+2wh
A+b
Pir^2h
44. Volume of Cone
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
1/3pir^2*h
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.
S² - where s = length of a side
45. What is the point-slope form?
(x+y)²
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
(y-y1)=m(x-x1)
46. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
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47. Does order matter for a permutation? How about for a combination?
C =?d
(n-2)180
Order does matter for a permutation - but does not matter for a combination.
(pi)r^2(h)
48. Surface Area of rectangular prism
2lw+2lh+2wh
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Bh
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
49. Surface Area of Cylinder
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
2pir^2 + 2pir*h
50. How do you calculate the surface area of a rectangular box?
x² + 2xy + y²
The distance from one point on the circle to another point on the circle.
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.
Middle term