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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. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
360°
M = (y2 - y1)/(x2 - x1)
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

2. Law of exponents 2
B^m*b^n = b^m+n
A = bh
B^m/b^n = b^m-n
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

3. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Set y = 0 - and solve.
V = lwh
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

4. What are the median and the mode of a set of data?
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.
Their sum is 90°.
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 every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

5. What is the formula for the area of a triangle?
A = [(s^2*v3)/4]
[(x1 + x2)/2] -[(y1 + y2)/2]
A = (1/2)bh.
The two pairs of opposite angles formed are equal to each other.

6. What is true about the measures of the three angles in a triangle?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Is a right triangle with a ratio of sides x:xv3:2x.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Their sum is 180°.

7. Properties of one 2
For any integer n: 1^n = 1.
Write the percent as a decimal - and multiply.
Equal slopes.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

8. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
M = (y2 - y1)/(x2 - x1)
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A fraction whose denominator is 100 i.e. 17% = 17/100

9. What is p?
Set x = 0 - and solve.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
(Circumference/diameter) of a circle - or approximately 3.14.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

10. Properties of square roots
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any number b: b = -b if and only if b = 0.

11. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
[(x1 + x2)/2] -[(y1 + y2)/2]
(Circumference/diameter) of a circle - or approximately 3.14.
(b^m)^n = b^mn

12. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
A = 6(l^2)
Write the percent over 100 and reduce.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

13. What is the probability of an event that cannot occur? That must occur?
Cannot is 0 - must is 1 - all others are in between.
Avg = sum of n numbers/n
Shifted right 2 units.
A = pr^2

14. How do you find the x-intercept of a graph?
Corresponding sides of similar triangles are in proportion.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Set y = 0 - and solve.
At least one of the factors is 0.

15. Properties of one 4
The two pairs of opposite angles formed are equal to each other.
For any number b: b = -b if and only if b = 0.
1 is the smallest positive odd integer.
B^m*b^n = b^m+n

16. If the product of two or more numbers is 0 - what do you know about the numbers?
Avg = sum of n numbers/n
At least one of the factors is 0.
Shifted right 2 units.
Cannot is 0 - must is 1 - all others are in between.

17. What is a prime number?
1 is the smallest positive odd integer.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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 - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

18. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(x + y)(x - y) = x^2 - y^2
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 integer greater than one that is not prime.

19. What is an exterior angle of a polygon?
A = bh
Shifted left 2 units.
An angle formed by extending the side of the polygon.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

20. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
B^m*b^n = b^m+n
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
0 is the only number that is neither positive nor negative.

21. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Set x = 0 - and solve.
For any number n: x^-n means 1/x^n.

22. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
Set x = 0 - and solve.
(Circumference/diameter) of a circle - or approximately 3.14.
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.

23. Properties of zero 3
0 is a multiple of every integer.
360°
Even numbers are divisible by 2 and odd numbers are not.
360°

24. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Shifted left 2 units.
Shifted down 2 units.
(b^m)^n = b^mn

25. What is the volume of a cube?
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.
B^m*b^n = b^m+n
V = l^3
0 is the only number that is neither positive nor negative.

26. 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.
A fraction whose denominator is 100 i.e. 17% = 17/100
C = p2r

27. In a circle of radius r - what is the formula for the diameter?
Shifted down 2 units.
0 is a multiple of every integer.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
D = 2r

28. In a circle of radius r - what is the formula for the area?
An integer greater than one that is not prime.
A = 6(l^2)
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = pr^2

29. Important binomial 3
Write the percent as a decimal - and multiply.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The ratio of corresponding sides of similar triangles.
360°

30. Properties of zero 2
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Shifted right 2 units.
V = pr^2h
If a is negative and b is positive - then a < 0 < b.

31. What is a composite number?
An integer greater than one that is not prime.
Set x = 0 - and solve.
For any number n: x^-n means 1/x^n.
A = 2(lw + lh + hw)

32. Properties of zero 4
A = lw
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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.

33. What are the quotient and the remainder?

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34. What does it mean if y is directly proportional to x?
Then the quotient y/x is a constant.
At least one of the factors is 0.
0 is a multiple of every integer.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

35. For what values of a function is the function undefined?
Avg = sum of n numbers/n
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.
(x + y)(x - y) = x^2 - y^2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

36. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
Divide - then multiply by 100.
(Circumference/diameter) of a circle - or approximately 3.14.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

37. What formula is used for an average?
[(x1 + x2)/2] -[(y1 + y2)/2]
Avg = sum of n numbers/n
For any number n: x^-n means 1/x^n.
For any integer n: 1^n = 1.

38. What is the distance formula?
Area = (x°/360)(pr^2) where x is the central angle.
Even numbers are divisible by 2 and odd numbers are not.
A = pr^2
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

39. What is the Pythagorean theorem?
Set x = 0 - and solve.
Then the product xy is a constant.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any right triangle - a^2 + b^2 = c^2.

40. What is an exponent?
[(x1 + x2)/2] -[(y1 + y2)/2]
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
In the expression x^b - x is the base and b is the exponent.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

41. How you convert a fraction or a decimal to a percent?
No matter how many angles there are - the sum around the point is 360°.
Divide - then multiply by 100.
Write the percent over 100 and reduce.
The set of all ordered pairs (x -y) such that y = f(x).

42. What is an exterior angle of a triangle?
An integer greater than one that is not prime.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(x + y)(x - y) = x^2 - y^2

43. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
[(x1 + x2)/2] -[(y1 + y2)/2]

44. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
At least one of the factors is 0.
Avg = sum of n numbers/n

45. Law of exponents 1
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Is a right triangle with a ratio of sides x:xv3:2x.
B^m*b^n = b^m+n

46. What is true about the measures of the four angles formed by two intersecting lines?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
The two pairs of opposite angles formed are equal to each other.
Divide - then multiply by 100.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

47. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
A = [(s^2*v3)/4]
Shifted up 2 units.
Is a right triangle with a ratio of sides x:xv3:2x.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

48. What is the distributive law?
They are both the same. A divisor or factor of an integer leaves no remainder.
Arc = (x°/360)(2pr) where x is the central angle.
V = l^3
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

49. What is the formula for the surface area of a rectangular solid?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = 2(lw + lh + hw)
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°.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

50. What is the sum of the measures of the four angles in a quadrilateral?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
360°
For any integer n: 1^n = 1.

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