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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. Perimeter of rectangle
2l+2w
1/2bh
1/x^a
1/3pir^2*h
2. What is the area of a triangle?
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.
1/3Bh
y-y1=m(x-x1)
1/2bh
3. Volume of sphere
4/3pir^3
Lwh
2(pi)r
The average - mean - median - or mode.
4. What is the circumference of a circle?
2(pi)r
1/x^a
(a+b)(a-b)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
5. What is the unfactored version of x²-y² ?
2(pi)r(r+h)
(x+y)(x-y)
2(lw+wh+lh)
A=?r2
6. If something is possible but not certain - what is the numeric range of probability of it happening?
1.7
Last term
Between 0 and 1.
2 pi r
7. Perimeter of polygon
Sum of the lengths of the sides
T1 * r^(n-1)
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Sum of terms/number of terms
8. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
Sum of terms/number of terms
1.4
2(lw+wh+lh)
9. What is 'absolute value' - and how is it represented?
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10. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.
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11. What is the area of a sector?
(a-b)²
(n degrees/360) * (pi)r^2
S*v2
Probability A * Probability B
12. Slope
(a-b)(a²+ab+b²)
?d OR 2?r
(y2-y1)/(x2-x1)
Order does matter for a permutation - but does not matter for a combination.
13. a³-b³
(a-b)(a²+ab+b²)
Lw
y = k/x
?d OR 2?r
14. Area of a trapezoid
1/2 h (b1 + b2)
Arrangements - orders - schedules - or lists.
½(b1 +b2) x h [or (b1 +b2) x h÷2]
Equal
15. Chord
The distance from one point on the circle to another point on the circle.
Sum of terms/number of terms
1/2 h (b1 + b2)
2 pi r
16. Area of a sector
Less
x°/360 times (?r²) - where x is the degrees in the angle
x²-y²
1/x^a
17. Perimeter of a rectangle
Probability A + Probability B
Order does matter for a permutation - but does not matter for a combination.
(x1+x2)/2 - (y1+y2)/2
2Length + 2width [or (length + width) x 2]
18. How do you multiply powers with the same base?
(x+y)(x-y)
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
x°/360 times (2 pi r) - where x is the degrees in the angle
1/3pir^2*h
19. Define the range of a set of numbers.
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. Given event A: A + notA = 1.
1.7
4s (where s = length of a side)
20. What is the side ratio 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.
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.
y-y1=m(x-x1)
x² + 2xy + y²
21. Define the 'Third side' rule for triangles
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22. What do combination problems usually ask for?
Negative
4s (where s = length of a side)
Groups - teams - or committees.
S^2
23. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
4s (where s = length of a side)
Bh
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
Last term
24. When you reverse FOIL - the term that needs to multiply out is the _____
Last term
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.
(y2-y1)/(x2-x1)
Bh
25. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
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.
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.
Bh
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
26. Define a factorial of a number - and how it is written.
(n-2)180
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 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.
4pir^2
27. Define the mode of a set of numbers.
1/3pir^2*h
1.7
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.
(a+b)(a-b)
28. a³+b³
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.
(a+b)(a²-ab+b²)
y-y1=m(x-x1)
4s
29. Area of Rectangle
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
2(lw+wh+lh)
Lw
30. In a coordinate system - identify the quadrants and describe their location.
Lw
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.
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
A=?r2
31. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
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32. Volume of Cone
Sqr( x2 -x1) + (y2- y1)
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/1
1/3pir^2*h
33. How do you calculate the surface area of a rectangular box?
b±[vb²-4ac]/2a
1/3pir^2*h
Bh
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.
34. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
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.
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.
Middle term
4/3pir^3
35. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
1/3Bh
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.
1/2bh
2(pi)r(r+h)
36. Point-Slope form
1.7
y-y1=m(x-x1)
Sqr( x2 -x1) + (y2- y1)
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.
37. What is the side ratio for a Right Isosceles triangle?
½(b1 +b2) x h [or (b1 +b2) x h÷2]
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2l+2w
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
38. Explain the special properties of zero.
Probability A * Probability B
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.
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.
Groups - teams - or committees.
39. What is an 'equilateral' triangle?
Lwh
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
Pir^2h
?d OR 2?r
40. Perimeter of a square
4s (where s = length of a side)
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
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
Groups - teams - or committees.
41. Arc
Part of a circle connecting two points on the circle.
4s
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
x°/360 times (2 pi r) - where x is the degrees in the angle
42. Radius (Radii)
A segment connecting the center of a circle to any point on the circle
(a+b)²
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
1/3Bh
43. In a parabola - if the first term is positive - the parabola ________.
1/3pir^2*h
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.
Total distance/total time
Opens up
44. Volume of pyramid
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
1/3Bh
The distance across the circle through the center of the circle.The diameter is twice the radius.
45. How do you find the midpoint?
(x1+x2)/2 - (y1+y2)/2
y-y1=m(x-x1)
(a+b)(a²-ab+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.
46. Central Angle
The average - mean - median - or mode.
An ange whose vertex is the center of the circle
4/3pir^3
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.
47. Circle
A segment connecting the center of a circle to any point on the circle
2(pi)r
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 set of points which are all the same distance (the radius) from a certain point (the center).
48. In a parabola - if the first term is negative - the parabola ________.
4s
(a+b)(a²-ab+b²)
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.
Opens down
49. To divide powers with the same base...
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1/x^a
½(b1 +b2) x h [or (b1 +b2) x h÷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.
50. Sector
(a+b)²
(x+y)²
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.
1/2bh