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GRE Math: Facts

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
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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 sum of the measures of the four angles in a quadrilateral?
360°
Divide - then multiply by 100.
M = (y2 - y1)/(x2 - x1)
Shifted right 2 units.

2. Properties of zero 4
A = [(s^2*v3)/4]
For any number b: b = -b if and only if b = 0.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Avg = sum of n numbers/n

3. What is a prime number?
An integer greater than one that is not prime.
The two pairs of opposite angles formed are equal to each other.
An integer divisible by only one and itself. 1 is not - 2 is the only even - and 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and 29 are the 10 smallest.
A = s^2 or A =d^2/2 where d is the diagonal

4. What are the properties of a parallelogram?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
V = l^3

5. What is a ratio?

6. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
An angle formed by extending the side of the polygon.
Write the percent over 100 and reduce.
Then the product xy is a constant.

7. What are the properties of a square?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For any number a: a * 1 = a and a / 1 = a.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Same as a parallelogram and a rectangle - as well as all four sides are the same length - the diagonals are perpendicular - and each diagonal divides the square into a 45-45-90 isosceles right triangle.

8. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
(x + y)(x - y) = x^2 - y^2
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
M = (y2 - y1)/(x2 - x1)

9. What does it mean if y is inversely proportional to x?
If the line is not perpendicular - all four acute angles have the same measure - all four obtuse have the same measure - and the sum of any one acute and one obtuse angle is 180°.
An angle formed by extending the side of the polygon.
Shifted left 2 units.
Then the product xy is a constant.

10. Properties of zero 1
For any number b: b = -b if and only if b = 0.
0 is the only number that is neither positive nor negative.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Avg = sum of n numbers/n

11. How do you find the length of an arc of a circle?
B^m/b^n = b^m-n
Arc = (x°/360)(2pr) where x is the central angle.
In the expression x^b - x is the base and b is the exponent.
How steep the line is. Horizontal line = 0 - vertical has no slope.

12. What is a proportion?
No matter how many angles there are - the sum around the point is 360°.
0 is a multiple of every integer.
For any number a: a * 1 = a and a / 1 = a.
An equation that states that two ratios are equivalent. 4/6 = 10/15

13. Properties of one 3
1 is a divisor (or factor) of every integer.
Arc = (x°/360)(2pr) where x is the central angle.
Avg = sum of n numbers/n
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

14. What is the formula for the surface area of a rectangular solid?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
The product of their slopes is -1 (negative reciprocal).
A = 2(lw + lh + hw)

15. What is the midpoint formula?
An integer greater than one that is not prime.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
[(x1 + x2)/2] -[(y1 + y2)/2]
A = [(s^2*v3)/4]

16. What is a function?
Corresponding sides of similar triangles are in proportion.
0 is a multiple of every integer.
A = 2(lw + lh + hw)
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

17. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Then the quotient y/x is a constant.

18. What is the measure of a straight angle?
M = (y2 - y1)/(x2 - x1)
A = lw
Shifted right 2 units.
180°. If two or more angles form a straight angle - their sum is 180°.

19. What is the formula for the volume of a cylinder?
V = pr^2h
360°
Their sum is 90°.
Shifted down 2 units.

20. Properties of one 2
(n - 2)(180°)
For any integer n: 1^n = 1.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

21. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
Set y = 0 - and solve.
360°
A = pr^2

22. What is true about the measures of the four angles formed by two intersecting lines?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A multiple of an integer - n - is any integer that is a product of n and another integer i.e. 12 is a multiple of 3 and 3 is a divisor of 12.
The two pairs of opposite angles formed are equal to each other.
All positive and negative whole numbers - and zero.

23. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
D = 2r
A = [(s^2*v3)/4]
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

24. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Avg = sum of n numbers/n
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Write the percent over 100 and reduce.

25. What are the properties of a rectangle?
A = s^2 or A =d^2/2 where d is the diagonal
Avg = sum of n numbers/n
(b^m)^n = b^mn
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

26. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
Area = (x°/360)(pr^2) where x is the central angle.
M = (y2 - y1)/(x2 - x1)
If the line is not perpendicular - all four acute angles have the same measure - all four obtuse have the same measure - and the sum of any one acute and one obtuse angle is 180°.

27. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
If the line is not perpendicular - all four acute angles have the same measure - all four obtuse have the same measure - and the sum of any one acute and one obtuse angle is 180°.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For any number n: x^-n means 1/x^n.

28. What is the formula for the surface area of a cube?
Same as a parallelogram and a rectangle - as well as all four sides are the same length - the diagonals are perpendicular - and each diagonal divides the square into a 45-45-90 isosceles right triangle.
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = 6(l^2)
A multiple of an integer - n - is any integer that is a product of n and another integer i.e. 12 is a multiple of 3 and 3 is a divisor of 12.

29. Law of exponents 5
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A^m/b^m = (a/b)^m
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

30. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
A^m/b^m = (a/b)^m
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
V = pr^2h

31. What is the probability of an event that cannot occur? That must occur?
If the line is not perpendicular - all four acute angles have the same measure - all four obtuse have the same measure - and the sum of any one acute and one obtuse angle is 180°.
Cannot is 0 - must is 1 - all others are in between.
V = pr^2h
Then the product xy is a constant.

32. What is special formula for the area of an equilateral triangle?
180°. If two or more angles form a straight angle - their sum is 180°.
The ratio of corresponding sides of similar triangles.
A = [(s^2*v3)/4]
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

33. For what values of a function is the function undefined?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
M = (y2 - y1)/(x2 - x1)
0 is a multiple of every integer.
(b^m)^n = b^mn

34. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
Area = (x°/360)(pr^2) where x is the central angle.
Set y = 0 - and solve.
Set x = 0 - and solve.

35. Law of exponents 3
In the expression x^b - x is the base and b is the exponent.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
(b^m)^n = b^mn
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

36. If you were given the graph of y = f(x) - what does f(a) represent?
A = (1/2)bh.
A = s^2 or A =d^2/2 where d is the diagonal
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Arc = (x°/360)(2pr) where x is the central angle.

37. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
The longest side is opposite the largest angle - the shortest side is opposite the smallest angle - and same length sides are opposite same measure angles.
Write the percent as a decimal - and multiply.

38. Law of exponents 2
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
B^m/b^n = b^m-n
Then the product xy is a constant.
Even numbers are divisible by 2 and odd numbers are not.

39. What is the sum of the measures of the n angles of a polygon with n sides?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
If a is negative and b is positive - then a < 0 < b.
(n - 2)(180°)
Is a right triangle with a ratio of sides x:xv3:2x.

40. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
The product of their slopes is -1 (negative reciprocal).
Is a right triangle with a ratio of sides x:xv3:2x.

41. What is true about the measures of the three angles in a triangle?
A fraction whose denominator is 100 i.e. 17% = 17/100
Their sum is 180°.
V = lwh
D = 2r

42. How do you find a percent of a number?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Write the percent as a decimal - and multiply.
V = pr^2h
An integer greater than one that is not prime.

43. If the product of two or more numbers is 0 - what do you know about the numbers?
The set of all ordered pairs (x -y) such that y = f(x).
An integer divisible by only one and itself. 1 is not - 2 is the only even - and 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and 29 are the 10 smallest.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
At least one of the factors is 0.

44. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
For any number b: b = -b if and only if b = 0.
B^m/b^n = b^m-n
(Circumference/diameter) of a circle - or approximately 3.14.

45. How do you find the y-intercept of a graph?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Set x = 0 - and solve.
The longest side is opposite the largest angle - the shortest side is opposite the smallest angle - and same length sides are opposite same measure angles.
(n - 2)(180°)

46. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
The longest side is opposite the largest angle - the shortest side is opposite the smallest angle - and same length sides are opposite same measure angles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

47. What is a Venn diagram?
Shifted up 2 units.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
The two pairs of opposite angles formed are equal to each other.
A = pr^2

48. How do you calculate a weighted average?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Cannot is 0 - must is 1 - all others are in between.

49. How do you find the slope of a line?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A^m*b^m = (ab)^m
An integer divisible by only one and itself. 1 is not - 2 is the only even - and 3 - 5 - 7 - 11 - 13 - 17 - 19 - 23 - and 29 are the 10 smallest.
M = (y2 - y1)/(x2 - x1)

50. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
They are both the same. A divisor or factor of an integer leaves no remainder.
A multiple of an integer - n - is any integer that is a product of n and another integer i.e. 12 is a multiple of 3 and 3 is a divisor of 12.
For any number n: x^-n means 1/x^n.
Shifted down 2 units.