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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. Circumference of a circle
y2-y1/x2-x1
?d OR 2?r
T1 * r^(n-1)/(r-1)
Middle term
2. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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'.
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.
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
3. What is the area of a circle?
Negative
(pi)r^2
x°/360 times (?r²) - where x is the degrees in the angle
(x+y)(x-y)
4. x^-a =
1/x^a
(a+b)(a²-ab+b²)
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.
Sum of the lengths of the sides
5. What is 'absolute value' - and how is it represented?
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6. Lines reflected over the x or y axis have ____ slopes.
2lw+2lh+2wh
Negative
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2l+2w
7. Define 'proportionate' values
1/x^a
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
2(pi)r(r+h)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
8. Define the 'Third side' rule for triangles
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9. Quadratic Formula
A=bh
The average - mean - median - or mode.
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.
b±[vb²-4ac]/2a
10. Rough est. of v3 =
(x+y)(x-y)
Pi*r^2
1.7
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.
11. (a+b)(a-b)=
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.
A²-b²
x² -2xy + y²
A circle'S perimeter is roughly 3x its diameter (the formula is pd).
12. Define a factorial of a number - and how it is written.
Pir^2h
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.
(x1+x2)/2 - (y1+y2)/2
Order does matter for a permutation - but does not matter for a combination.
13. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
1/x^a
1/2bh
(a-b)²
14. What is a 'Right isosceles' triangle?
2Length + 2width [or (length + width) x 2]
1/3pir^2*h
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.
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. a²+2ab+b²
2pir^2 + 2pir*h
2(pi)r
Not necessarily. This is a trick question - because x could be either positive or negative.
(a+b)²
16. What is the 'Third side' rule for triangles?
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 circle'S perimeter is roughly 3x its diameter (the formula is pd).
Percentage Change = Difference/Original * 100
2pi*r
17. Define the mode of a set of numbers.
Between 0 and 1.
The set of points which are all the same distance (the radius) from a certain point (the center).
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
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. Area of Trapezoid
2(pi)r(r+h)
(a-b)(a²+ab+b²)
Groups - teams - or committees.
1/2 h (b1 + b2)
19. The probability of an event happening and the probability of an event NOT happening must add up to what number?
(a-b)(a²+ab+b²)
1. Given event A: A + notA = 1.
The set of points which are all the same distance (the radius) from a certain point (the center).
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.
20. Sector
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.
Probability A + Probability B
?d OR 2?r
2pir^2 + 2pir*h
21. What is the unfactored version of (x-y)² ?
1/2bh
A=?r2
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
22. Point-Slope form
y-y1=m(x-x1)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
4s (where s = length of a side)
23. When you reverse FOIL - the term that needs to add out is the _____
An ange whose vertex is the center of the circle
Middle term
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
½(b1 +b2) x h [or (b1 +b2) x h÷2]
24. Area of Circle
x°/360 times (?r²) - where x is the degrees in the angle
Pi*r^2
Pi*d
(a-b)(a+b)
25. In a coordinate system - identify the quadrants and describe their location.
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.
Lwh
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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
26. Circumference of a circle using radius
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'.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
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.
2pi*r
27. Area of Circles
A=?r2
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Part of a circle connecting two points on the circle.
An ange whose vertex is the center of the circle
28. If something is certain to happen - how is the probability of this event expressed mathematically?
Probability A + Probability B
x² + 2xy + y²
1/1
1. Given event A: A + notA = 1.
29. In a coordinate system - what is the origin?
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.
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.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
(0 -0)
30. How do you calculate the probability of EITHER one event OR another event happening? (Probability of A or B)
1/2bh
Equal
?d OR 2?r
Probability A + Probability B
31. For a bell curve - what three terms might be used to describe the number in the middle?
(a+b)(a²-ab+b²)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
The average - mean - median - or mode.
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.
32. Area of Rectangle
Groups - teams - or committees.
Lw
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(x-y)²
33. What is the equation of a line?
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34. When a line crosses two parallel lines - ________.
Not necessarily. This is a trick question - because x could be either positive or negative.
Probability A * Probability B
The four big angles are equal and the four small angles are equal
Arrangements - orders - schedules - or lists.
35. Circumference of cirlce using diameter
Pi*d
Last term
Number of desired outcomes/number of total outcomes
4s (where s = length of a side)
36. a³-b³
T1 * r^(n-1)/(r-1)
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)
(a+b)(a²-ab+b²)
37. What is the unfactored version of (x+y)² ?
x² + 2xy + y²
Lw
b±[vb²-4ac]/2a
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.
38. List two odd behaviors of exponents
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.
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.
1/2bh
39. What is the 'distributive law'?
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.
(0 -0)
2 pi r
Sqr( x2 -x1) + (y2- y1)
40. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
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)
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
41. What is the side ratio for a 30:60:90 triangle?
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.
Pi*r^2
1/2 h (b1 + b2)
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
42. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
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43. How do you find the sum of a geometric sequence?
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
1/3pir^2*h
T1 * r^(n-1)/(r-1)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
44. Define the formula for calculating slope.
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.
(a+b)(a-b)
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(n-2)180
45. In a parabola - if the first term is negative - the parabola ________.
(a-b)²
Order does matter for a permutation - but does not matter for a combination.
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.
Opens down
46. Area of Triangle
(a+b)²
Order does matter for a permutation - but does not matter for a combination.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1/2bh
47. (a+b)(c+d)
Ac+ad+bc+bd
Total distance/total time
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1
48. Volume of sphere
4/3pir^3
1/2bh
?d OR 2?r
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.
49. What do permutation problems often ask for?
Between 0 and 1.
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.
Arrangements - orders - schedules - or lists.
2x2x2x5x5
50. How do you calculate the percentage of change?
(pi)r^2
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.
Percentage Change = Difference/Original * 100
(n degrees/360) * 2(pi)r