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GRE Math: Facts

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
Match each statement with the correct term.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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?
Write the percent as a decimal - and multiply.
V = lwh
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Area = (x°/360)(pr^2) where x is the central angle.

2. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
If a is negative and b is positive - then a < 0 < b.
Even numbers are divisible by 2 and odd numbers are not.
360°

3. Properties of zero 1
Shifted up 2 units.
At least one of the factors is 0.
The set of all ordered pairs (x -y) such that y = f(x).
0 is the only number that is neither positive nor negative.

4. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
V = l^3
Shifted left 2 units.
They are both the same. A divisor or factor of an integer leaves no remainder.
Equal slopes.

5. What are the properties of a rectangle?
Then the quotient y/x is a constant.
C = p2r
The set of all ordered pairs (x -y) such that y = f(x).
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

6. What is the graph of a function?
Then the product xy is a constant.
B^m*b^n = b^m+n
Corresponding sides of similar triangles are in proportion.
The set of all ordered pairs (x -y) such that y = f(x).

7. Properties of zero 5
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Shifted up 2 units.
Set y = 0 - and solve.
For any number b: b = -b if and only if b = 0.

8. What is a proportion?
A^m/b^m = (a/b)^m
All positive and negative whole numbers - and zero.
(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

9. Law of exponents 2
B^m/b^n = b^m-n
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(b^m)^n = b^mn
A^m/b^m = (a/b)^m

10. What is the sum of the measures of the four angles in a quadrilateral?
360°
Then the product xy is a constant.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
V = l^3

11. What is p?
360°
(Circumference/diameter) of a circle - or approximately 3.14.
For any number a: a * 1 = a and a / 1 = a.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

12. What is an exterior angle of a polygon?
B^m*b^n = b^m+n
For any number n: x^-n means 1/x^n.
Set x = 0 - and solve.
An angle formed by extending the side of the polygon.

13. How you convert a fraction or a decimal to a percent?
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 = s^2 or A =d^2/2 where d is the diagonal
Divide - then multiply by 100.
[(x1 + x2)/2] -[(y1 + y2)/2]

14. In a circle of radius r - what is the formula for the diameter?
For any number a: a * 1 = a and a / 1 = a.
D = 2r
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

15. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
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 greater than one that is not prime.
B^m*b^n = b^m+n

16. What is the ratio of similitude?
Their sum is 180°.
How steep the line is. Horizontal line = 0 - vertical has no slope.
The ratio of corresponding sides of similar triangles.
360°

17. What is a divisor and a factor of an integer?
They are both the same. A divisor or factor of an integer leaves no remainder.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Shifted right 2 units.
The set of all ordered pairs (x -y) such that y = f(x).

18. What is the relationship between a radius of a circle and a line that is tangent to the circle?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
If a is negative and b is positive - then a < 0 < b.

19. What is an even and an odd number?
Write the percent over 100 and reduce.
A^m/b^m = (a/b)^m
Even numbers are divisible by 2 and odd numbers are not.
Shifted left 2 units.

20. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
Their sum is 90°.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
At least one of the factors is 0.

21. What are the sum - difference - products - and quotient of two numbers?
The product of their slopes is -1 (negative reciprocal).
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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.

22. What is the square root of a number?
Then the quotient y/x is a constant.
If a is negative and b is positive - then a < 0 < b.
A^m*b^m = (ab)^m
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

23. What is the formula for the area of a parallelogram?
A = s^2 or A =d^2/2 where d is the diagonal
(b^m)^n = b^mn
In the expression x^b - x is the base and b is the exponent.
A = bh

24. What is true about the slopes of parallel lines?
Then the product xy is a constant.
The set of all ordered pairs (x -y) such that y = f(x).
Is a right triangle with a ratio of sides x:xv3:2x.
Equal slopes.

25. What is the Pythagorean theorem?
(x + y)(x - y) = x^2 - y^2
For any right triangle - a^2 + b^2 = c^2.
Cannot is 0 - must is 1 - all others are in between.
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.

26. How do you find the probability that an event will occur?
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.
C = p2r
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Area = (x°/360)(pr^2) where x is the central angle.

27. In a circle of radius r - what is the formula for the area?
For any number a: a * 1 = a and a / 1 = a.
Cannot is 0 - must is 1 - all others are in between.
360°
A = pr^2

28. What is a percent?
A = [(s^2*v3)/4]
How steep the line is. Horizontal line = 0 - vertical has no slope.
No matter how many angles there are - the sum around the point is 360°.
A fraction whose denominator is 100 i.e. 17% = 17/100

29. What is the formula for the surface area of a cube?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = 6(l^2)
A = pr^2
V = l^3

30. What is the measure of a straight angle?
For any number n: x^-n means 1/x^n.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
180°. If two or more angles form a straight angle - their sum is 180°.

31. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Equal slopes.
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.

32. What is the midpoint formula?
No matter how many angles there are - the sum around the point is 360°.
Area = (x°/360)(pr^2) where x is the central angle.
A^m/b^m = (a/b)^m
[(x1 + x2)/2] -[(y1 + y2)/2]

33. How do you find the x-intercept of a graph?
Area = (x°/360)(pr^2) where x is the central angle.
1 is a divisor (or factor) of every integer.
Set y = 0 - and solve.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

34. What is a multiple of an integer?
0 is the only number that is neither positive nor negative.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Shifted left 2 units.
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.

35. How do you find the length of an arc of a circle?
For any number b: b = -b if and only if b = 0.
Then the quotient y/x is a constant.
Arc = (x°/360)(2pr) where x is the central angle.
180°. If two or more angles form a straight angle - their sum is 180°.

36. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Even numbers are divisible by 2 and odd numbers are not.

37. In a circle of radius r - what is the formula for the circumference?
All positive and negative whole numbers - and zero.
(Circumference/diameter) of a circle - or approximately 3.14.
Write the percent as a decimal - and multiply.
C = p2r

38. How do you find a percent of a number?
A = s^2 or A =d^2/2 where d is the diagonal
Shifted right 2 units.
Write the percent as a decimal - and multiply.
They are both the same. A divisor or factor of an integer leaves no remainder.

39. What is an integer?
All positive and negative whole numbers - and zero.
B^m/b^n = b^m-n
For any number n: x^-n means 1/x^n.
Write the percent as a decimal - and multiply.

40. If you were given the graph of y = f(x) - what does f(a) represent?
B^m/b^n = b^m-n
(Circumference/diameter) of a circle - or approximately 3.14.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

41. Law of exponents 3
An angle formed by extending the side of the polygon.
C = p2r
(b^m)^n = b^mn
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.

42. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
For any number a: a * 1 = a and a / 1 = a.
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.
Is a right triangle with a ratio of sides x:xv3:2x.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

43. What is the formula for the area of a triangle?
A = (1/2)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°.
A = pr^2
An equation that states that two ratios are equivalent. 4/6 = 10/15

44. Law of exponents 1
B^m*b^n = b^m+n
A = 6(l^2)
For any integer n: 1^n = 1.
They are both the same. A divisor or factor of an integer leaves no remainder.

45. What is the formula for the volume of a rectangular solid?
V = lwh
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
A fraction whose denominator is 100 i.e. 17% = 17/100
Then the quotient y/x is a constant.

46. Law of exponents 5
Corresponding sides of similar triangles are in proportion.
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.
A^m/b^m = (a/b)^m

47. What are the median and the mode of a set of data?
Set x = 0 - and solve.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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.

48. What is true about the measures of the three angles in a triangle?
Their sum is 180°.
Cannot is 0 - must is 1 - all others are in between.
Avg = sum of n numbers/n
1 is the smallest positive odd integer.

49. What is a composite number?
An integer greater than one that is not prime.
Is a right triangle with a ratio of sides x:xv3:2x.
360°
Arc = (x°/360)(2pr) where x is the central angle.

50. How do you calculate a weighted average?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
They are both the same. A divisor or factor of an integer leaves no remainder.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.