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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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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 true about the slopes of perpendicular lines?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Then the product xy is a constant.
The product of their slopes is -1 (negative reciprocal).
Shifted up 2 units.

2. What is the sum of the measures of the n angles of a polygon with n sides?
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.
No matter how many angles there are - the sum around the point is 360°.
Corresponding sides of similar triangles are in proportion.
(n - 2)(180°)

3. Important binomial 3
A^m*b^m = (ab)^m
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Even numbers are divisible by 2 and odd numbers are not.
No matter how many angles there are - the sum around the point is 360°.

4. What is the formula for the volume of a cylinder?
A^m/b^m = (a/b)^m
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Write the percent as a decimal - and multiply.
V = pr^2h

5. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The two pairs of opposite angles formed are equal to each other.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(x + y)(x - y) = x^2 - y^2

6. What is the triangle inequality?
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.
An angle formed by extending the side of the polygon.
Then the product xy is a constant.
Then the quotient y/x is a constant.

7. What is a fractional exponent?
A^m/b^m = (a/b)^m
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
All positive and negative whole numbers - and zero.
Set y = 0 - and solve.

8. In a circle of radius r - what is the formula for the area?
For any number n: x^-n means 1/x^n.
A = 6(l^2)
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = pr^2

9. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

10. What is the formula for the surface area of a rectangular solid?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
D = 2r
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A = 2(lw + lh + hw)

11. What is the relationship between the graph of f(x) the graph of y = f(x - 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.
Shifted up 2 units.
C = p2r
Shifted right 2 units.

12. Law of exponents 2
At least one of the factors is 0.
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
Divide - then multiply by 100.

13. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Corresponding sides of similar triangles are in proportion.
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted up 2 units.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

14. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
180°. If two or more angles form a straight angle - their sum is 180°.
Shifted up 2 units.
Their sum is 90°.

15. What are the sum - difference - products - and quotient of two numbers?
They are both the same. A divisor or factor of an integer leaves no remainder.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
C = p2r
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

16. What is the sum of the measures of the four angles in a quadrilateral?
360°
For any number n: x^-n means 1/x^n.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Their sum is 90°.

17. What is special formula for the area of an equilateral triangle?
They are both the same. A divisor or factor of an integer leaves no remainder.
A = [(s^2*v3)/4]
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

18. What formula is used for an average?
At least one of the factors is 0.
Shifted down 2 units.
Avg = sum of n numbers/n
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

19. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
For any number b: b = -b if and only if b = 0.
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.
A^m*b^m = (ab)^m

20. What is the formula for the area of a rectangle?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = lw
1 is a divisor (or factor) of every integer.

21. What is true about the areas of similar triangles?
The ratio of corresponding sides of similar triangles.
If a is negative and b is positive - then a < 0 < b.
A = lw
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

22. What is the sum of the measures of all angles around a point?
Even numbers are divisible by 2 and odd numbers are not.
No matter how many angles there are - the sum around the point is 360°.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

23. How do you find the slope of a line?
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.
M = (y2 - y1)/(x2 - x1)
A = lw

24. How do you find the y-intercept of a graph?
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Even numbers are divisible by 2 and odd numbers are not.
Set x = 0 - and solve.

25. What are the properties of a square?
No matter how many angles there are - the sum around the point is 360°.
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.
Even numbers are divisible by 2 and odd numbers are not.
B^m/b^n = b^m-n

26. Law of exponents 5
At least one of the factors is 0.
C = p2r
A^m/b^m = (a/b)^m
An integer greater than one that is not prime.

27. What are the properties of a rectangle?
V = lwh
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A = lw

28. What is the formula for the area of a triangle?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Even numbers are divisible by 2 and odd numbers are not.
A = (1/2)bh.
Divide - then multiply by 100.

29. What is a Venn diagram?
180°. If two or more angles form a straight angle - their sum is 180°.
For any number b: b = -b if and only if b = 0.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Shifted left 2 units.

30. How do you find the area of a sector of a circle?
Write the percent over 100 and reduce.
M = (y2 - y1)/(x2 - x1)
Area = (x°/360)(pr^2) where x is the central angle.
For any right triangle - a^2 + b^2 = c^2.

31. What are the important properties of a 45-45 - 90 triangle?
Even numbers are divisible by 2 and odd numbers are not.
They are both the same. A divisor or factor of an integer leaves no remainder.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

32. What is the ratio of similitude?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Shifted down 2 units.
The ratio of corresponding sides of similar triangles.
0 is the only number that is neither positive nor negative.

33. What is the probability of an event that cannot occur? That must occur?
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.
A = 6(l^2)
Cannot is 0 - must is 1 - all others are in between.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

34. If the product of two or more numbers is 0 - what do you know about the numbers?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
360°
At least one of the factors is 0.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

35. What does it mean if y is inversely proportional to x?
Cannot is 0 - must is 1 - all others are in between.
B^m*b^n = b^m+n
Then the product xy is a constant.
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.

36. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(n - 2)(180°)
For any integer n: 1^n = 1.

37. What is a function?
In the expression x^b - x is the base and b is the exponent.
If a is negative and b is positive - then a < 0 < b.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
M = (y2 - y1)/(x2 - x1)

38. Properties of zero 4
1 is a divisor (or factor) of every integer.
Shifted left 2 units.
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.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

39. What are the properties of a parallelogram?
[(x1 + x2)/2] -[(y1 + y2)/2]
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

40. How do you convert a percent to a fraction or a decimal?
Their sum is 90°.
Write the percent over 100 and reduce.
V = l^3
P(e) = (# of favorable outcomes)/(# of possible outcomes)

41. What is an integer?
A fraction whose denominator is 100 i.e. 17% = 17/100
All positive and negative whole numbers - and zero.
Shifted down 2 units.
Write the percent as a decimal - and multiply.

42. What is the formula for the area of a parallelogram?
Write the percent over 100 and reduce.
V = lwh
A = bh
If a is negative and b is positive - then a < 0 < b.

43. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The ratio of corresponding sides of similar triangles.
A^m*b^m = (ab)^m

44. Properties of zero 3
Write the percent as a decimal - and multiply.
Arc = (x°/360)(2pr) where x is the central angle.
0 is a multiple of every integer.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

45. How do you find a percent of a number?
Their sum is 90°.
Write the percent over 100 and reduce.
A^m*b^m = (ab)^m
Write the percent as a decimal - and multiply.

46. What is true about the measures of the three angles in a triangle?
Write the percent over 100 and reduce.
Their sum is 180°.
M = (y2 - y1)/(x2 - x1)
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

47. What is the square root of a number?
An equation that states that two ratios are equivalent. 4/6 = 10/15
(n - 2)(180°)
Shifted right 2 units.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

48. Law of exponents 4
Avg = sum of n numbers/n
A^m*b^m = (ab)^m
A^m/b^m = (a/b)^m
(b^m)^n = b^mn

49. How do we write the equation of a line?
Arc = (x°/360)(2pr) where x is the central angle.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.
Then the quotient y/x is a constant.

50. Properties of zero 1
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = s^2 or A =d^2/2 where d is the diagonal
0 is the only number that is neither positive nor negative.
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.

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