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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'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
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2. (a+b)(c+d)
Ac+ad+bc+bd
(y2-y1)/(x2-x1)
1/2 h (b1 + b2)
Pi*r^2
3. What must be true before a quadratic equation can be solved?
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4. When you reverse FOIL - the term that needs to add out is the _____
Total distance/total time
T1 + (n-1)d
Middle term
(n-2)180
5. What is the 'distributive law'?
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.
Opens up
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.
x²-y²
6. Circumference of cirlce using diameter
Pi*d
Lw
Opens up
2(lw+wh+lh)
7. Circumference of a circle using radius
2(lw+wh+lh)
2pi*r
The four big angles are equal and the four small angles are equal
(a+b)(a-b)
8. What is the prime factorization of 200?
Pi*r^2
(a-b)²
?r²
2x2x2x5x5
9. Surface Area of Cylinder
2pir^2 + 2pir*h
y2-y1/x2-x1
b±[vb²-4ac]/2a
Sum of the lengths of the sides
10. 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.
Bh
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
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.
11. Define the mode of a set of numbers.
Less
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.
T1 * r^(n-1)/(r-1)
Not necessarily. This is a trick question - because x could be either positive or negative.
12. What is the factored version of x² -2xy + y² ?
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
(0 -0)
(x-y)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.
13. Volume of sphere
4/3pir^3
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.
(x1+x2)/2 - (y1+y2)/2
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
14. Quadratic Formula
2pi*r
(n/2) * (t1+tn)
b±[vb²-4ac]/2a
2lw+2lh+2wh
15. Volume of Cylinder
Pir^2h
A²-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
x²-y²
16. How do you find the nth term of an arithmetic sequence?
T1 + (n-1)d
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
(n/2) * (t1+tn)
Order does matter for a permutation - but does not matter for a combination.
17. Area of Circle
(x-y)²
Pi*r^2
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Opens down
18. How do you get rid of the fraction in this equation: 5x + 3/2 = 7x
Opens down
y = kx
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.
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.
19. Rough est. of v3 =
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.
2Length + 2width [or (length + width) x 2]
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.
1.7
20. Define 'proportionate' values
2l+2w
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'.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
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.
21. a³-b³
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
(a-b)(a²+ab+b²)
Opens down
y2-y1/x2-x1
22. What is the point-slope form?
(y-y1)=m(x-x1)
?d OR 2?r
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
1
23. How do you multiply and divide square roots?
Opens down
Part of a circle connecting two points on the circle.
(a-b)(a²+ab+b²)
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
24. What is the average?
Middle term
2(pi)r
Sum of terms/number of terms
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.
25. Explain the special properties of zero.
Ac+ad+bc+bd
Bh
1.4
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.
26. What'S the most important thing to remember about charts you'll see on the GRE?
1/x^a
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.
2Length + 2width [or (length + width) x 2]
The set of points which are all the same distance (the radius) from a certain point (the center).
27. What is inversely proportional?
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.
y = k/x
T1 * r^(n-1)
An ange whose vertex is the center of the circle
28. Rough est. of v2 =
1.4
Order does matter for a permutation - but does not matter for a combination.
Last term
Equal
29. What is the unfactored version of (x-y)² ?
½(base x height) [or (base x height)÷2]
x² -2xy + y²
Groups - teams - or committees.
Bh
30. The probability of an event happening and the probability of an event NOT happening must add up to what number?
y = k/x
x² + 2xy + y²
1. Given event A: A + notA = 1.
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.
31. In a parabola - if the first term is positive - the parabola ________.
(a+b)(a-b)
Number of desired outcomes/number of total outcomes
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Opens up
32. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
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
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.
(x+y)²
Ac+ad+bc+bd
33. What is a '30:60:90' triangle?
1/2bh
2x2x2x5x5
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
?r²
34. Define a factorial of a number - and how it is written.
The average - mean - median - or mode.
Less
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.
35. Rough est. of v1 =
1
Sum of terms/number of terms
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.
Bh
36. If something is possible but not certain - what is the numeric range of probability of it happening?
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.
y = k/x
Between 0 and 1.
(y-y1)=m(x-x1)
37. Perimeter of polygon
Between 0 and 1.
(x1+x2)/2 - (y1+y2)/2
Sum of the lengths of the sides
(pi)r^2(h)
38. How do you calculate the surface area of a rectangular box?
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.
(x1+x2)/2 - (y1+y2)/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.
Sum of terms/number of terms
39. How do you find the sum of a geometric sequence?
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.
Lwh
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
T1 * r^(n-1)/(r-1)
40. What is the probability?
Negative
(a-b)(a²+ab+b²)
Number of desired outcomes/number of total outcomes
Lwh
41. In a coordinate system - what is the origin?
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.
Order does matter for a permutation - but does not matter for a combination.
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.
(0 -0)
42. Perimeter (circumference) of a circle
y2-y1/x2-x1
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
2 pi r
The distance across the circle through the center of the circle.The diameter is twice the radius.
43. Perimeter of a square
1. Given event A: A + notA = 1.
Between 0 and 1.
4s (where s = length of a side)
Pi*r^2
44. How do you solve a permutation?
Groups - teams - or committees.
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
Less
Between 0 and 1.
45. Slope
(y2-y1)/(x2-x1)
The average - mean - median - or mode.
(x+y)²
?r²
46. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
Part of a circle connecting two points on 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.
2pi*r
47. What is the area of a cylinder?
2pi*r
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(pi)r(r+h)
Probability A * Probability B
48. x^a * x^b = x^__
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.
Opens down
A+b
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
49. What is the volume of a cylinder?
Pir^2h
(pi)r^2(h)
(n degrees/360) * (pi)r^2
b±[vb²-4ac]/2a
50. What is the side ratio for a 30:60:90 triangle?
1.4
Bh
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x²-y²