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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 Square
S^2
Pir^2h
The distance from one point on the circle to another point on the circle.
Ac+ad+bc+bd
2. How do you find the sum of a geometric sequence?
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
T1 * r^(n-1)/(r-1)
Total distance/total time
3. Define the formula for calculating slope.
Equal
Middle term
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Bh
4. What is the formula for the diagonal of any square?
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.
1/2 h (b1 + b2)
S*v2
(a+b)(a-b)
5. Area of Triangle
(a+b)(a²-ab+b²)
Lw
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.
1/2bh
6. Define a factorial of a number - and how it is written.
x² + 2xy + y²
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.
4pir^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.
7. Explain the difference between a digit and a number.
8. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
N x M
S*v2
x²-y²
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
9. How do you multiply and divide square roots?
(x1+x2)/2 - (y1+y2)/2
Probability A * Probability B
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
10. The length of one side of any triangle is ____ than the sum of the other two sides.
(pi)r^2(h)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
Less
11. What is the unfactored version of x²-y² ?
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.
(y2-y1)/(x2-x1)
(x+y)(x-y)
S*v2
12. a²-2ab+b²
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.
2(pi)r
b±[vb²-4ac]/2a
(a-b)²
13. Perimeter of rectangle
(n degrees/360) * 2(pi)r
(x+y)²
2l+2w
Middle term
14. What is the average speed?
1/3Bh
Lw
2x2x2x5x5
Total distance/total time
15. How do you find the sum of an arithmetic sequence?
2pi*r
(n-2)180
A=bh
(n/2) * (t1+tn)
16. Circumference Formula
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.
A=?r2
C =?d
(x-y)²
17. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
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.
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.
T1 * r^(n-1)/(r-1)
18. What is directly proportional?
A segment connecting the center of a circle to any point on the circle
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.
y = kx
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.
19. What must be true before a quadratic equation can be solved?
20. In a parabola - if the first term is negative - the parabola ________.
Between 0 and 1.
The average - mean - median - or mode.
Last term
Opens down
21. Area of a triangle
½(base x height) [or (base x height)÷2]
4pir^2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Negative
22. Perimeter of a rectangle
Number of desired outcomes/number of total outcomes
2Length + 2width [or (length + width) x 2]
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.
2(pi)r(r+h)
23. a²-b²
The distance from one point on the circle to another point on the circle.
1/3Bh
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.
(a-b)(a+b)
24. Area of a square
S² - where s = length of a side
(a+b)(a²-ab+b²)
Less
(a-b)(a²+ab+b²)
25. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
(x+y)²
2l+2w
Bh
26. length of a sector
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.
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.
x°/360 times (2 pi r) - where x is the degrees in the angle
Less
27. Define the 'Third side' rule for triangles
28. How do you find the slope?
(a-b)²
N x M
y2-y1/x2-x1
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.
29. How do you calculate the percentage of change?
Percentage Change = Difference/Original * 100
S^2
Probability A + Probability B
Not necessarily. This is a trick question - because x could be either positive or negative.
30. What is the area of a sector?
S^2
(n degrees/360) * (pi)r^2
N x M
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.
31. Perimeter of polygon
T1 * r^(n-1)/(r-1)
Sum of the lengths of the sides
Between 0 and 1.
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
32. Define the range of a set of numbers.
2x2x2x5x5
Sum of the lengths of the sides
(a-b)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.
33. Rough est. of v2 =
1.4
S^2
(n-2)180
4s (where s = length of a side)
34. What is the volume of a cylinder?
(pi)r^2(h)
Sum of the lengths of the sides
The average - mean - median - or mode.
(x-y)²
35. What is an 'equilateral' triangle?
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
2(pi)r(r+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.
2(lw+wh+lh)
36. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
x°/360 times (?r²) - where x is the degrees in the angle
Part of a circle connecting two points on the circle.
Probability A * Probability B
37. What is the factored version of x² + 2xy + y² ?
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.
Total distance/total time
(x+y)²
Ac+ad+bc+bd
38. What is the average?
y = kx
(a-b)(a+b)
Sum of terms/number of terms
1/2bh
39. What is the side ratio for a 30:60:90 triangle?
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(x+y)²
40. Does order matter for a permutation? How about for a combination?
Sum of terms/number of terms
(n degrees/360) * 2(pi)r
Order does matter for a permutation - but does not matter for a combination.
?d OR 2?r
41. How do you solve a permutation?
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.
4pir^2
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
(a+b)²
42. If something is possible but not certain - what is the numeric range of probability of it happening?
Number of desired outcomes/number of total outcomes
2pi*r
Between 0 and 1.
Lwh
43. How do you calculate a diagonal inside a 3-dimensional rectangular box?
1/2 h (b1 + b2)
2x2x2x5x5
2pir^2 + 2pir*h
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
44. Area of Trapezoid
Lw
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
1/2 h (b1 + b2)
45. Chord
Part of a circle connecting two points on the circle.
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 distance from one point on the circle to another point on the circle.
x² -2xy + y²
46. What is the equation of a line?
47. Central Angle
x°/360 times (?r²) - where x is the degrees in the angle
Ac+ad+bc+bd
An ange whose vertex is the center of the circle
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.
48. Volume of prism
2 pi r
Bh
(0 -0)
2lw+2lh+2wh
49. Area of Rectangle
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.
(pi)r^2(h)
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.
50. Circle
2 pi r
The set of points which are all the same distance (the radius) from a certain point (the center).
?d OR 2?r
4/3pir^3