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GRE Math 2

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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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. When a line crosses two parallel lines - ________.
2Length + 2width [or (length + width) x 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
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
The four big angles are equal and the four small angles are equal

2. Surface Area of Cylinder
S^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.
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.
2pir^2 + 2pir*h

3. If x² = 144 - does v144 = x?
Not necessarily. This is a trick question - because x could be either positive or negative.
The ratio of sides is x:x:xv2 - where xv2 is the hypotenuse.
2lw+2lh+2wh
(y-y1)=m(x-x1)

4. x^-a =
A=bh
1/x^a
(y2-y1)/(x2-x1)
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'.

5. In a parabola - if the first term is negative - the parabola ________.
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
1.4
Opens down

6. Lines reflected over the x or y axis have ____ slopes.
1/3pir^2*h
Negative
Sum of the lengths of the sides
2(lw+wh+lh)

7. How do you find the sum of an arithmetic sequence?
(n/2) * (t1+tn)
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.
Sum of terms/number of terms
(pi)r^2(h)

8. Area of a sector
x°/360 times (?r²) - where x is the degrees in the angle
Percentage Change = Difference/Original * 100
2 pi r
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.

9. How do you multiply powers with the same base?
T1 * r^(n-1)/(r-1)
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.
Ratio of sides is x : xv3 : 2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Add the exponents - retain the base. for example - x² + x5 = x²+5 = x7

10. length of a sector
Total distance/total time
Pir^2h
1/2bh
x°/360 times (2 pi r) - where x is the degrees in the angle

11. Circumference of a circle
?d OR 2?r
Equal
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.
2lw+2lh+2wh

12. What is 'absolute value' - and how is it represented?

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13. Describe and define three expressions of quadratic equations - in both factored and unfactored forms. Know these cold.
1/2bh
(a-b)²
1/2bh
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

14. Surface Area of rectangular prism
½(b1 +b2) x h [or (b1 +b2) x h÷2]
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.
2lw+2lh+2wh
2l+2w

15. Quadratic Formula
(x+y)²
b±[vb²-4ac]/2a
?r²
Sum of terms/number of terms

16. What kind of triangle is this: has two sides of equal length - and a 90 degree angle?
The average - mean - median - or mode.
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.
A=bh
(pi)r^2(h)

17. If an event can happen N ways - and another can happen M ways - then both events together can happen in ____ ways.
S² - where s = length of a side
(y-y1)=m(x-x1)
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
N x M

18. How do you find the nth term of an arithmetic sequence?
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
x°/360 times (?r²) - where x is the degrees in the angle
T1 + (n-1)d
y = kx

19. Volume of pyramid
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.
1/3Bh
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.
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.

20. In a coordinate system - identify the quadrants and describe their location.
2lw+2lh+2wh
(x-y)²
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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

21. perimeter of square
T1 + (n-1)d
2(pi)r
x² -2xy + y²
4s

22. What number goes on the bottom of a probability fraction?
The total # of possible outcomes.
Ratio of sides is x:xv3:2x - where x is the base - xv3 is the height - and 2x is the hypotenuse.
Bh
The set of points which are all the same distance (the radius) from a certain point (the center).

23. Circumference of a circle using radius
?r²
Probability A * Probability B
½(b1 +b2) x h [or (b1 +b2) x h÷2]
2pi*r

24. Circle
2(pi)r
The set of points which are all the same distance (the radius) from a certain point (the center).
4pir^2
An ange whose vertex is the center of the circle

25. Perimeter of a square
4s (where s = length of a side)
(a-b)²
(y-y1)=m(x-x1)
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.

26. What is the sum of the inside angles of an n-sided polygon?
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.
(n-2)180
A²-b²
2Length + 2width [or (length + width) x 2]

27. What is the factored version of x² -2xy + y² ?
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.
S^2
(x-y)²
(x+y)(x-y)

28. Diameter
Negative
The distance across the circle through the center of the circle.The diameter is twice the radius.
(n degrees/360) * 2(pi)r
x°/360 times (2 pi r) - where x is the degrees in the angle

29. What'S the most important thing to remember about charts you'll see on the GRE?
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.
The average - mean - median - or mode.
Sum of terms/number of terms
An ange whose vertex is the center of the circle

30. What is the 'Third side' rule for triangles?
2(pi)r(r+h)
Last term
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.
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.

31. How do you find the sum of a geometric sequence?
4s (where s = length of a side)
?r²
T1 * r^(n-1)/(r-1)
y2-y1/x2-x1

32. What is the area of a triangle?
1/2bh
1/2 h (b1 + b2)
2l+2w
Equal

33. Rough est. of v2 =
Pi*d
2Length + 2width [or (length + width) x 2]
1.4
(y2-y1)/(x2-x1)

34. Define the formula for calculating slope.
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
1.7
½(base x height) [or (base x height)÷2]
1/1

35. Chord
(x1+x2)/2 - (y1+y2)/2
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
The distance from one point on the circle to another point on the circle.
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

36. When you reverse FOIL - the term that needs to multiply out is the _____
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'.
4s (where s = length of a side)
Last term
C =?d

37. Area of a triangle
Like any other number. For example - v3*v12 = v36 = 6 For example - v(16/4) = v16/v4 = 4/2 = 2
Part of a circle connecting two points on the circle.
Sum of the lengths of the sides
½(base x height) [or (base x height)÷2]

38. Perimeter (circumference) of a circle
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.
2 pi r
Groups - teams - or committees.

39. Perimeter of polygon
Probability A * Probability B
1/1
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Sum of the lengths of the sides

40. Area of a square
T1 * r^(n-1)/(r-1)
b±[vb²-4ac]/2a
T1 * r^(n-1)
S² - where s = length of a side

41. a² - b² is equal to
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.
(a+b)(a-b)
(0 -0)
(pi)r^2

42. What is the prime factorization of 200?
(x+y)(x-y)
(a-b)(a²+ab+b²)
2x2x2x5x5
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.

43. Area of Rectangle
4pir^2
Number of desired outcomes/number of total outcomes
The formula is a² + b² + c² = d² where a - b - c are the dimensions of the figure and d is the diagonal.
Lw

44. In a parabola - if the first term is positive - the parabola ________.
(a-b)(a²+ab+b²)
(a-b)²
Opens up
T1 * r^(n-1)

45. What is the area of a sector?
b±[vb²-4ac]/2a
(y-y1)=m(x-x1)
(n degrees/360) * (pi)r^2
Sum of terms/number of terms

46. What is the distance formula?
Slope = rise/run. Find the change in y-coordinates (rise) and the change in x-coordinates (run) to calculate.
Sqr( x2 -x1) + (y2- y1)
S² - where s = length of a side
A=bh

47. Area of Trapezoid
1/2 h (b1 + b2)
Quadrant 1 is top right. Q 2 is top left. Q 3 is bottom left. Q 4 is bottom right.
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.
Pi*r^2

48. What is the average?
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.
Sum of terms/number of terms
(a-b)(a²+ab+b²)
2l+2w

49. What is inversely proportional?
y = k/x
Probability A * Probability B
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.
(x-y)²

50. Explain the special properties of zero.
2l+2w
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 = kx
x²-y²

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GRE Math 2

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