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GRE Math: Facts

Subjects : gre, math

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Answer 50 questions in 15 minutes.
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1. What important property do similar triangles have?
All positive and negative whole numbers - and zero.
360°
Corresponding sides of similar triangles are in proportion.
Their sum is 180°.

2. What is the volume of a cube?
For any number a: a * 1 = a and a / 1 = a.
V = l^3
Their sum is 90°.
A^m*b^m = (ab)^m

3. What is true about the measures of the four angles formed by two intersecting lines?
For any number a: a * 1 = a and a / 1 = a.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Even numbers are divisible by 2 and odd numbers are not.
The two pairs of opposite angles formed are equal to each other.

4. What is special formula for the area of an equilateral triangle?
An angle formed by extending the side of the polygon.
Shifted left 2 units.
A = [(s^2*v3)/4]
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

5. What is the distance formula?
Set y = 0 - and solve.
Shifted left 2 units.
In the expression x^b - x is the base and b is the exponent.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

6. In a circle of radius r - what is the formula for the circumference?
C = p2r
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
B^m*b^n = b^m+n

7. What is a composite number?
An integer greater than one that is not prime.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
1 is a divisor (or factor) of every integer.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

8. What is a prime number?
(b^m)^n = b^mn
A = lw
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

9. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
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.
Shifted right 2 units.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

10. What is a multiple of an integer?
Avg = sum of n numbers/n
A = s^2 or A =d^2/2 where d is the diagonal
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15

11. 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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
No matter how many angles there are - the sum around the point is 360°.
For any integer n: 1^n = 1.

12. What is a ratio?

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13. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Equal slopes.
The ratio of corresponding sides of similar triangles.

14. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
(Circumference/diameter) of a circle - or approximately 3.14.
Even numbers are divisible by 2 and odd numbers are not.
Divide - then multiply by 100.
360°

15. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
360°
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Shifted up 2 units.
The ratio of corresponding sides of similar triangles.

16. 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.
Write the percent as a decimal - and multiply.
(x + y)(x - y) = x^2 - y^2
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.

17. What is a percent?
Shifted up 2 units.
All positive and negative whole numbers - and zero.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A fraction whose denominator is 100 i.e. 17% = 17/100

18. What is an exterior angle of a polygon?
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.
How steep the line is. Horizontal line = 0 - vertical has no slope.
An angle formed by extending the side of the polygon.
Avg = sum of n numbers/n

19. Important binomial 3
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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.
Then the product xy is a constant.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

20. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
A = bh
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°.
All positive and negative whole numbers - and zero.
Shifted left 2 units.

21. How do you find the probability that an event will occur?
A = bh
P(e) = (# of favorable outcomes)/(# of possible outcomes)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

22. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted up 2 units.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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°.

23. Law of exponents 1
B^m*b^n = b^m+n
Then the quotient y/x is a constant.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Their sum is 180°.

24. What is the sum of the measures of the n angles of a polygon with n sides?
A^m/b^m = (a/b)^m
(n - 2)(180°)
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Divide - then multiply by 100.

25. How do you find the y-intercept of a graph?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Set x = 0 - and solve.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
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.

26. What are the quotient and the remainder?

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27. What does it mean if y is directly proportional to x?
If a is negative and b is positive - then a < 0 < b.
Their sum is 90°.
Then the quotient y/x is a constant.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

28. What is true about the slopes of perpendicular lines?
For any number b: b = -b if and only if b = 0.
Corresponding sides of similar triangles are in proportion.
The product of their slopes is -1 (negative reciprocal).
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

29. What is an even and an odd number?
A = 6(l^2)
Even numbers are divisible by 2 and odd numbers are not.
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.
They are both the same. A divisor or factor of an integer leaves no remainder.

30. What is the area of a square?
Divide - then multiply by 100.
(b^m)^n = b^mn
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = s^2 or A =d^2/2 where d is the diagonal

31. Properties of zero 5
Write the percent as a decimal - and multiply.
For any number b: b = -b if and only if b = 0.
An integer greater than one that is not prime.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

32. What are the important properties of 30-60-90 triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Then the quotient y/x is a constant.
The two pairs of opposite angles formed are equal to each other.
Is a right triangle with a ratio of sides x:xv3:2x.

33. What is a fractional exponent?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.
Their sum is 90°.

34. What is the formula for the surface area of a cube?
A = 6(l^2)
1 is the smallest positive odd integer.
A fraction whose denominator is 100 i.e. 17% = 17/100
Write the percent over 100 and reduce.

35. How do you calculate a weighted average?
A = 2(lw + lh + hw)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
The two pairs of opposite angles formed are equal to each other.

36. What is the triangle inequality?
The two pairs of opposite angles formed are equal to each other.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any number a: a * 1 = a and a / 1 = a.
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.

37. What is the probability of an event that cannot occur? That must occur?
Write the percent as a decimal - and multiply.
Cannot is 0 - must is 1 - all others are in between.
M = (y2 - y1)/(x2 - x1)
P(e) = (# of favorable outcomes)/(# of possible outcomes)

38. What is the measure of a straight angle?
The set of all ordered pairs (x -y) such that y = f(x).
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
180°. If two or more angles form a straight angle - their sum is 180°.
0 is a multiple of every integer.

39. What are the properties of a rectangle?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
(x + y)(x - y) = x^2 - y^2

40. What is an integer?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
All positive and negative whole numbers - and zero.
An integer greater than one that is not prime.
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.

41. What is the formula for the volume of a cylinder?
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 median is the middle number (for odd total) or average of two middle numbers (for even total). The mode is the number that appears most often.
V = pr^2h
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

42. Properties of one 2
A = (1/2)bh.
360°
For any integer n: 1^n = 1.
A fraction whose denominator is 100 i.e. 17% = 17/100

43. What is true about the slopes of parallel lines?
(b^m)^n = b^mn
1 is the smallest positive odd integer.
Equal slopes.
A = lw

44. What are the median and the mode of a set of data?
The median is the middle number (for odd total) or average of two middle numbers (for even total). The mode is the number that appears most often.
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 over 100 and reduce.
V = lwh

45. What is the Pythagorean theorem?
The two pairs of opposite angles formed are equal to each other.
A = 2(lw + lh + hw)
For any right triangle - a^2 + b^2 = c^2.
Arc = (x°/360)(2pr) where x is the central angle.

46. Law of exponents 3
The median is the middle number (for odd total) or average of two middle numbers (for even total). The mode is the number that appears most often.
For any number a: a * 1 = a and a / 1 = a.
(b^m)^n = b^mn
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.

47. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
A fraction whose denominator is 100 i.e. 17% = 17/100
Is a right triangle with a ratio of sides x:xv3:2x.
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.
360°

48. What are similar triangles?
No matter how many angles there are - the sum around the point is 360°.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = s^2 or A =d^2/2 where d is the diagonal
A^m/b^m = (a/b)^m

49. What are the sum - difference - products - and quotient of two numbers?
No matter how many angles there are - the sum around the point is 360°.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
The set of all ordered pairs (x -y) such that y = f(x).

50. What is p?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(Circumference/diameter) of a circle - or approximately 3.14.
A = bh
A = 2(lw + lh + hw)

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