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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 is the average?
x°/360 times (?r²) - where x is the degrees in the angle
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
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.
Sum of terms/number of terms
2. If x² = 144 - does v144 = x?
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.
(a-b)(a+b)
Equal
Not necessarily. This is a trick question - because x could be either positive or negative.
3. Radius (Radii)
(a+b)(a-b)
x² -2xy + y²
A segment connecting the center of a circle to any point on the circle
y = k/x
4. What is one misleading characteristic of quadratic equations that will be exploited on the GRE?
2l+2w
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
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.
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.
5. What is the circumference of a circle?
1/1
2(pi)r
The total # of possible outcomes.
T1 + (n-1)d
6. 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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7. Quadratic Formula
y = k/x
b±[vb²-4ac]/2a
N x M
x² -2xy + y²
8. Area of Rectangle
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.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
(a-b)²
9. What is the distance formula?
Sqr( x2 -x1) + (y2- y1)
The distance across the circle through the center of the circle.The diameter is twice the radius.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
y2-y1/x2-x1
10. The probability of an event happening and the probability of an event NOT happening must add up to what number?
C =?d
1. Given event A: A + notA = 1.
?d OR 2?r
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.
11. Explain a method for quickly comparing fractions with different denominators - to determine which is larger.
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12. What is the volume of a solid rectangle?
Total distance/total time
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
2(lw+wh+lh)
Lwh
13. What is the prime factorization of 200?
?r²
2x2x2x5x5
(x+y)(x-y)
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.
14. a³+b³
Lwh
(a+b)(a²-ab+b²)
(a-b)(a²+ab+b²)
½(base x height) [or (base x height)÷2]
15. To divide powers with the same base...
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.
Subtract the exponents - retain the base For example - x? ÷ x4 = x?-4 = x5
Sqr( x2 -x1) + (y2- y1)
A²-b²
16. Volume of Cylinder
?r²
Pir^2h
1.4
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'.
17. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
Probability A + Probability B
(n/2) * (t1+tn)
y = k/x
18. What is the unfactored version of x²-y² ?
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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)(x-y)
Ac+ad+bc+bd
19. What are the side ratios for a 30:60:90 triangle?
Less
Pir^2h
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
2Length + 2width [or (length + width) x 2]
20. a²+2ab+b²
(x+y)²
S^2
Lwh
(a+b)²
21. Point-Slope form
y-y1=m(x-x1)
Sum of terms/number of terms
4pir^2
A=bh
22. What is the probability?
1.4
T1 * r^(n-1)
Number of desired outcomes/number of total outcomes
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
23. What is the formula for the diagonal of any square?
S*v2
Order does matter for a permutation - but does not matter for a combination.
1/3Bh
2pi*r
24. What is the factored version of x² -2xy + y² ?
½(base x height) [or (base x height)÷2]
(x-y)²
Pir^2h
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
25. In a parabola - if the first term is negative - the parabola ________.
(y2-y1)/(x2-x1)
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.
Opens down
?d OR 2?r
26. Perimeter of a square
4s (where s = length of a side)
(a+b)(a²-ab+b²)
(a-b)(a²+ab+b²)
2(pi)r(r+h)
27. What is an 'equilateral' triangle?
1/2bh
4s
2pi*r
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
28. Define 'proportionate' values
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.
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
(0 -0)
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.
29. Area of a triangle
The distance across the circle through the center of the circle.The diameter is twice the radius.
½(base x height) [or (base x height)÷2]
The total # of possible outcomes.
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
30. Area of a circle
An ange whose vertex is the center of the circle
?r²
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
1/x^a
31. How do you multiply powers with the same base?
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.
4s
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
2lw+2lh+2wh
32. How do you find the nth term of a geometric sequence?
T1 * r^(n-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.
Opens up
2lw+2lh+2wh
33. How do you find the sum of an arithmetic sequence?
Lw
(n/2) * (t1+tn)
(y2-y1)/(x2-x1)
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.
34. What'S a handy rough estimate for a circle'S perimeter - if you know it'S diameter?
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35. What is the area of a sector?
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
(n degrees/360) * (pi)r^2
Probability A * Probability B
(pi)r^2
36. For a bell curve - what three terms might be used to describe the number in the middle?
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.
The average - mean - median - or mode.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
37. When you reverse FOIL - the term that needs to add out is the _____
(a-b)²
Proportionate values are equivalent. Example: 1/2 and 4/8 are proportionate - but 1/2 and 2/3 are not.
Middle term
(x1+x2)/2 - (y1+y2)/2
38. Surface Area of Cylinder
(a+b)(a-b)
Percentage Change = Difference/Original * 100
(n degrees/360) * (pi)r^2
2pir^2 + 2pir*h
39. What is the surface area of a cylinder?
Between 0 and 1.
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'.
2(pi)r(r+h)
4s
40. Volume of prism
Bh
(pi)r^2
Opens down
y = k/x
41. Area of a trapezoid
2x2x2x5x5
Interior angles are equal: 60:60:60 degrees each. All sides are equal length.
4s
½(b1 +b2) x h [or (b1 +b2) x h÷2]
42. Does order matter for a permutation? How about for a combination?
Order does matter for a permutation - but does not matter for a combination.
Groups - teams - or committees.
T1 * r^(n-1)
(n/2) * (t1+tn)
43. What is directly proportional?
Less
y = kx
Probability A + Probability B
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.
44. What is the unfactored version of (x-y)² ?
4pir^2
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.
Last term
x² -2xy + y²
45. List two odd behaviors of exponents
1/3Bh
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
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.
46. How do you find the sum of a geometric sequence?
T1 * r^(n-1)/(r-1)
Opens down
(x+y)²
1/3pir^2*h
47. If something is certain to happen - how is the probability of this event expressed mathematically?
1/1
Probability A + Probability B
Sum of terms/number of terms
1/3Bh
48. How do you multiply and divide square roots?
Percentage Change = Difference/Original * 100
1/1
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
The four big angles are equal and the four small angles are equal
49. What is the 'distributive law'?
2(pi)r(r+h)
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.
2(pi)r
x²-y²
50. a²-2ab+b²
(a-b)²
1/2 h (b1 + b2)
1/2bh
(a-b)(a+b)