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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.
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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 a function?
1 is a divisor (or factor) of every integer.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A^m*b^m = (ab)^m
The set of all ordered pairs (x -y) such that y = f(x).

2. How do you find a percent of a number?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
360°
Write the percent as a decimal - and multiply.

3. What is a negative exponent?
If a is negative and b is positive - then a < 0 < b.
A^m/b^m = (a/b)^m
No matter how many angles there are - the sum around the point is 360°.
For any number n: x^-n means 1/x^n.

4. How do you calculate percent increases and decreases?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Their sum is 180°.
For any right triangle - a^2 + b^2 = c^2.

5. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
No matter how many angles there are - the sum around the point is 360°.
(Circumference/diameter) of a circle - or approximately 3.14.

6. If you were given the graph of y = f(x) - what does f(a) represent?
Avg = sum of n numbers/n
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.
(b^m)^n = b^mn
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

7. What is the formula for the area of a parallelogram?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Is a right triangle with a ratio of sides x:xv3:2x.
A = bh
1 is a divisor (or factor) of every integer.

8. What is the distributive law?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
For any integer n: 1^n = 1.
180°. If two or more angles form a straight angle - their sum is 180°.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

9. What is a ratio?

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10. How do we write the equation of a line?
The set of all ordered pairs (x -y) such that y = f(x).
Divide - then multiply by 100.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A^m*b^m = (ab)^m

11. What are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
V = pr^2h
Equal slopes.
Divide - then multiply by 100.

12. What are the quotient and the remainder?

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13. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180°)
For any number n: x^-n means 1/x^n.
Write the percent as a decimal - and multiply.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

14. What is true about the measures of the four angles formed by two intersecting lines?
All positive and negative whole numbers - and zero.
The two pairs of opposite angles formed are equal to each other.
Their sum is 90°.
B^m*b^n = b^m+n

15. What is the square root of a number?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
An integer greater than one that is not prime.
Arc = (x°/360)(2pr) where x is the central angle.

16. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
Is a right triangle with a ratio of sides x:xv3:2x.
V = l^3
Shifted right 2 units.

17. Properties of zero 1
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.
0 is the only number that is neither positive nor negative.
360°
For any number a: a * 1 = a and a / 1 = a.

18. What is a composite number?
1 is the smallest positive odd integer.
An equation that states that two ratios are equivalent. 4/6 = 10/15
A = pr^2
An integer greater than one that is not prime.

19. In a circle of radius r - what is the formula for the circumference?
M = (y2 - y1)/(x2 - x1)
For any integer n: 1^n = 1.
C = p2r
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

20. What is a proportion?
A^m/b^m = (a/b)^m
In the expression x^b - x is the base and b is the exponent.
Then the quotient y/x is a constant.
An equation that states that two ratios are equivalent. 4/6 = 10/15

21. What is a prime number?
0 is a multiple of every integer.
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 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.
An equation that states that two ratios are equivalent. 4/6 = 10/15

22. How do you convert a percent to a fraction or a decimal?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Write the percent over 100 and reduce.
Equal slopes.
Set y = 0 - and solve.

23. In a circle of radius r - what is the formula for the area?
0 is the only number that is neither positive nor negative.
A = pr^2
An integer greater than one that is not prime.
How steep the line is. Horizontal line = 0 - vertical has no slope.

24. What is true about the measures of the three angles in a triangle?
Even numbers are divisible by 2 and odd numbers are not.
Their sum is 180°.
1 is the smallest positive odd integer.
Then the product xy is a constant.

25. What is the formula for the area of a triangle?
The set of all ordered pairs (x -y) such that y = f(x).
An angle formed by extending the side of the polygon.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = (1/2)bh.

26. Properties of one 2
For any integer n: 1^n = 1.
A = [(s^2*v3)/4]
D = 2r
If a is negative and b is positive - then a < 0 < b.

27. What does it mean if y is inversely proportional to x?
If a is negative and b is positive - then a < 0 < b.
The ratio of corresponding sides of similar triangles.
Then the product xy is a constant.
Shifted left 2 units.

28. In a circle of radius r - what is the formula for the diameter?
Write the percent as a decimal - and multiply.
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.
D = 2r
An integer greater than one that is not prime.

29. What is a divisor and a factor of an integer?
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.
Shifted down 2 units.
They are both the same. A divisor or factor of an integer leaves no remainder.

30. What is true about the areas of similar triangles?
An integer greater than one that is not prime.
B^m/b^n = b^m-n
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Area = (x°/360)(pr^2) where x is the central angle.

31. What is true about the measures of the two acute angles in a right triangle?
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.
1 is the smallest positive odd integer.
1 is a divisor (or factor) of every integer.
Their sum is 90°.

32. What is the sum of the measures of all angles around a point?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
No matter how many angles there are - the sum around the point is 360°.
1 is a divisor (or factor) of every integer.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

33. Law of exponents 4
Shifted up 2 units.
All positive and negative whole numbers - and zero.
A^m*b^m = (ab)^m
If a is negative and b is positive - then a < 0 < b.

34. How you convert a fraction or a decimal to a percent?
If a is negative and b is positive - then a < 0 < b.
Divide - then multiply by 100.
(x + y)(x - y) = x^2 - y^2
Cannot is 0 - must is 1 - all others are in between.

35. How do you calculate a weighted average?
For any number b: b = -b if and only if b = 0.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
0 is the only number that is neither positive nor negative.
Then the quotient y/x is a constant.

36. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
At least one of the factors is 0.
Shifted right 2 units.
(Circumference/diameter) of a circle - or approximately 3.14.

37. What is the formula for the surface area of a cube?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Write the percent as a decimal - and multiply.
A^m/b^m = (a/b)^m
A = 6(l^2)

38. What is an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
Avg = sum of n numbers/n
If a is negative and b is positive - then a < 0 < b.
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.

39. What is an even and an odd number?
For any integer n: 1^n = 1.
Even numbers are divisible by 2 and odd numbers are not.
0 is the only number that is neither positive nor negative.
A = 6(l^2)

40. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = bh

41. What are the median and the mode of a set of data?
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°.
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.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
0 is the only number that is neither positive nor negative.

42. Law of exponents 5
1 is the smallest positive odd integer.
A^m/b^m = (a/b)^m
Cannot is 0 - must is 1 - all others are in between.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

43. What is a multiple of an integer?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Avg = sum of n numbers/n
Corresponding sides of similar triangles are in proportion.
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.

44. What is the sum of the measures of the four angles in a quadrilateral?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
360°
1 is a divisor (or factor) of every integer.
A^m/b^m = (a/b)^m

45. 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.
A^m*b^m = (ab)^m
Shifted right 2 units.
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.

46. Law of exponents 1
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
B^m*b^n = b^m+n
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

47. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Divide - then multiply by 100.

48. Law of exponents 3
(b^m)^n = b^mn
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Set x = 0 - and solve.

49. What formula is used for an average?
Avg = sum of n numbers/n
Then the quotient y/x is a constant.
Write the percent as a decimal - and multiply.
Cannot is 0 - must is 1 - all others are in between.

50. What is an exterior angle of a triangle?
The product of their slopes is -1 (negative reciprocal).
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

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