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GRE Math: Facts

Subjects : gre, math

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Answer 50 questions in 15 minutes.
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Match each statement with the correct term.
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1. Important binomial 2
A = 2(lw + lh + hw)
A^m*b^m = (ab)^m
1 is a divisor (or factor) of every integer.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

2. What is true about the measures of the three angles in a triangle?
Their sum is 90°.
A fraction whose denominator is 100 i.e. 17% = 17/100
Their sum is 180°.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

3. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
An equation that states that two ratios are equivalent. 4/6 = 10/15
0 is a multiple of every integer.

4. 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.
Shifted right 2 units.
C = p2r
1 is the smallest positive odd integer.

5. Law of exponents 1
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
1 is a divisor (or factor) of every integer.
B^m*b^n = b^m+n
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°.

6. What is a divisor and a factor of an integer?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For any integer n: 1^n = 1.
They are both the same. A divisor or factor of an integer leaves no remainder.
Divide - then multiply by 100.

7. What is the formula for the volume of a cylinder?
A = bh
V = pr^2h
Set y = 0 - and solve.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

8. What is the sum of the measures of the n angles of a polygon with n sides?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
If a is negative and b is positive - then a < 0 < b.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
(n - 2)(180°)

9. What is true about the measures of the four angles formed by two intersecting lines?
A^m*b^m = (ab)^m
A = s^2 or A =d^2/2 where d is the diagonal
The two pairs of opposite angles formed are equal to each other.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

10. Important binomial 1
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Even numbers are divisible by 2 and odd numbers are not.
(x + y)(x - y) = x^2 - y^2
A^m*b^m = (ab)^m

11. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Write the percent over 100 and reduce.
The two pairs of opposite angles formed are equal to each other.
Shifted down 2 units.

12. What does it mean if y is directly proportional to x?
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.
They are both the same. A divisor or factor of an integer leaves no remainder.
Then the quotient y/x is a constant.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

13. What is the sum of the measures of the four angles in a quadrilateral?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
M = (y2 - y1)/(x2 - x1)
B^m*b^n = b^m+n
360°

14. Properties of one 3
Cannot is 0 - must is 1 - all others are in between.
Equal slopes.
Shifted down 2 units.
1 is a divisor (or factor) of every integer.

15. What is the measure of a straight angle?
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 as a decimal - and multiply.
180°. If two or more angles form a straight angle - their sum is 180°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

16. What are the quotient and the remainder?

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17. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
0 is the only number that is neither positive nor negative.
360°
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.
No matter how many angles there are - the sum around the point is 360°.

18. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
A = lw

19. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
(Circumference/diameter) of a circle - or approximately 3.14.
For any number a: a * 1 = a and a / 1 = a.
A^m*b^m = (ab)^m

20. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Equal slopes.
Even numbers are divisible by 2 and odd numbers are not.
Shifted left 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

21. How do you calculate a weighted average?
Arc = (x°/360)(2pr) where x is the central angle.
A = 2(lw + lh + hw)
Shifted up 2 units.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

22. Law of exponents 5
If a is negative and b is positive - then a < 0 < b.
A = [(s^2*v3)/4]
A^m/b^m = (a/b)^m
Shifted right 2 units.

23. What are the properties of a square?
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.
V = lwh
Area = (x°/360)(pr^2) where x is the central angle.
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.

24. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
1 is a divisor (or factor) of every integer.
0 is a multiple of every integer.
(Circumference/diameter) of a circle - or approximately 3.14.

25. What do we mean by the slope of the line?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
How steep the line is. Horizontal line = 0 - vertical has no slope.
0 is the only number that is neither positive nor negative.
0 is a multiple of every integer.

26. Law of exponents 4
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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 = pr^2
A^m*b^m = (ab)^m

27. What is the formula for the surface area of a cube?
No matter how many angles there are - the sum around the point is 360°.
A = 6(l^2)
Arc = (x°/360)(2pr) where x is the central angle.
An integer greater than one that is not prime.

28. What is the Pythagorean theorem?
1 is the smallest positive odd integer.
A = lw
An integer greater than one that is not prime.
For any right triangle - a^2 + b^2 = c^2.

29. What is the midpoint formula?
1 is a divisor (or factor) of every integer.
C = p2r
[(x1 + x2)/2] -[(y1 + y2)/2]
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

30. What is a negative exponent?
1 is the smallest positive odd integer.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any number n: x^-n means 1/x^n.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

31. What is true about the slopes of parallel lines?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Equal slopes.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
D = 2r

32. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
A^m*b^m = (ab)^m
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.
B^m*b^n = b^m+n

33. Properties of zero 5
A = pr^2
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.
0 is the only number that is neither positive nor negative.
For any number b: b = -b if and only if b = 0.

34. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
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.
The product of their slopes is -1 (negative reciprocal).

35. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
(b^m)^n = b^mn
Shifted up 2 units.
The product of their slopes is -1 (negative reciprocal).
A = lw

36. How do you find the probability that an event will occur?
(Circumference/diameter) of a circle - or approximately 3.14.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A = bh
(b^m)^n = b^mn

37. What is a percent?
360°
A fraction whose denominator is 100 i.e. 17% = 17/100
All positive and negative whole numbers - and zero.
180°. If two or more angles form a straight angle - their sum is 180°.

38. What is the distance formula?
D = 2r
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°.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

39. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
M = (y2 - y1)/(x2 - x1)
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.
360°

40. In a circle of radius r - what is the formula for the circumference?
No matter how many angles there are - the sum around the point is 360°.
Cannot is 0 - must is 1 - all others are in between.
C = p2r
A = 2(lw + lh + hw)

41. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
A = pr^2
All positive and negative whole numbers - and zero.
They are both the same. A divisor or factor of an integer leaves no remainder.

42. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
(Circumference/diameter) of a circle - or approximately 3.14.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
An equation that states that two ratios are equivalent. 4/6 = 10/15

43. Properties of zero 1
A^m*b^m = (ab)^m
180°. If two or more angles form a straight angle - their sum is 180°.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
0 is the only number that is neither positive nor negative.

44. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
The set of all ordered pairs (x -y) such that y = f(x).
Avg = sum of n numbers/n
An integer greater than one that is not prime.

45. What is a multiple of an integer?
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.
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.
A = bh
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

46. If you were given the graph of y = f(x) - what does f(a) represent?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Corresponding sides of similar triangles are in proportion.

47. What is the triangle inequality?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Cannot is 0 - must is 1 - all others are in between.
The sum of the length of any two sides of the triangle is greater than the length of the third side i.e. x + y > z - x + z > y - & y + z > x.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

48. What is an integer?
The product of their slopes is -1 (negative reciprocal).
All positive and negative whole numbers - and zero.
V = pr^2h
(Circumference/diameter) of a circle - or approximately 3.14.

49. How do you find the x-intercept of a graph?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Shifted right 2 units.
Set y = 0 - and solve.
B^m*b^n = b^m+n

50. What is the volume of a cube?
A^m*b^m = (ab)^m
Corresponding sides of similar triangles are in proportion.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
V = l^3

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