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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.
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 the sum of the measures of the n angles of a polygon with n sides?
If a is negative and b is positive - then a < 0 < b.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Write the percent over 100 and reduce.
(n - 2)(180°)

2. What is the distance formula?
Avg = sum of n numbers/n
1 is a divisor (or factor) of every integer.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
V = lwh

3. What important property do similar triangles have?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Corresponding sides of similar triangles are in proportion.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Set y = 0 - and solve.

4. What is the ratio of similitude?
For any number n: x^-n means 1/x^n.
The ratio of corresponding sides of similar triangles.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Equal slopes.

5. What is the Pythagorean theorem?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = (1/2)bh.
For any right triangle - a^2 + b^2 = c^2.
1 is the smallest positive odd integer.

6. What are similar triangles?
Their sum is 180°.
[(x1 + x2)/2] -[(y1 + y2)/2]
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The product of their slopes is -1 (negative reciprocal).

7. How do you calculate percent increases and decreases?
A = s^2 or A =d^2/2 where d is the diagonal
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted down 2 units.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

8. What is an integer?
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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
All positive and negative whole numbers - and zero.
Shifted down 2 units.

9. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Shifted left 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Avg = sum of n numbers/n

10. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Set y = 0 - and solve.
A^m/b^m = (a/b)^m
No matter how many angles there are - the sum around the point is 360°.

11. What is true about the areas of similar triangles?
Write the percent as a decimal - and multiply.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
For any number b: b = -b if and only if b = 0.
If a is negative and b is positive - then a < 0 < b.

12. How do you find the x-intercept of a graph?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Write the percent as a decimal - and multiply.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Set y = 0 - and solve.

13. How do you find the slope of a line?
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.
[(x1 + x2)/2] -[(y1 + y2)/2]
For any number b: b = -b if and only if b = 0.
M = (y2 - y1)/(x2 - x1)

14. Law of exponents 5
[(x1 + x2)/2] -[(y1 + y2)/2]
Their sum is 90°.
A^m/b^m = (a/b)^m
In the expression x^b - x is the base and b is the exponent.

15. Properties of one 2
For any integer n: 1^n = 1.
Shifted left 2 units.
Write the percent over 100 and reduce.
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.

16. How do you find the length of an arc of a circle?
In the expression x^b - x is the base and b is the exponent.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Arc = (x°/360)(2pr) where x is the central angle.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

17. What is p?
Shifted up 2 units.
A fraction whose denominator is 100 i.e. 17% = 17/100
Write the percent over 100 and reduce.
(Circumference/diameter) of a circle - or approximately 3.14.

18. Properties of zero 3
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
0 is a multiple of every integer.
(x + y)(x - y) = x^2 - y^2
A = bh

19. What is the triangle inequality?
For any number a: a * 1 = a and a / 1 = a.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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 fraction whose denominator is 100 i.e. 17% = 17/100

20. For what values of a function is the function undefined?
Equal slopes.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
V = lwh
A = [(s^2*v3)/4]

21. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For any number n: x^-n means 1/x^n.
360°
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

22. What is the midpoint formula?
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
[(x1 + x2)/2] -[(y1 + y2)/2]
For any number b: b = -b if and only if b = 0.

23. What is the formula for the volume of a cylinder?
Divide - then multiply by 100.
V = pr^2h
180°. If two or more angles form a straight angle - their sum is 180°.
(n - 2)(180°)

24. Properties of one 3
P(e) = (# of favorable outcomes)/(# of possible outcomes)
180°. If two or more angles form a straight angle - their sum is 180°.
1 is a divisor (or factor) of every integer.
B^m/b^n = b^m-n

25. If the product of two or more numbers is 0 - what do you know about the numbers?
A = s^2 or A =d^2/2 where d is the diagonal
Arc = (x°/360)(2pr) where x is the central angle.
At least one of the factors is 0.
The ratio of corresponding sides of similar triangles.

26. What is the sum of the measures of the four angles in a quadrilateral?
360°
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = s^2 or A =d^2/2 where d is the diagonal

27. 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.
Corresponding sides of similar triangles are in proportion.
1 is a divisor (or factor) of every integer.
180°. If two or more angles form a straight angle - their sum is 180°.

28. What is true about the slopes of parallel lines?
A = 2(lw + lh + hw)
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
B^m*b^n = b^m+n
Equal slopes.

29. How do you convert a percent to a fraction or a decimal?
In the expression x^b - x is the base and b is the exponent.
Write the percent over 100 and reduce.
Then the quotient y/x is a constant.
Then the product xy is a constant.

30. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
(n - 2)(180°)
If a is negative and b is positive - then a < 0 < b.
Write the percent as a decimal - and multiply.

31. What is a prime number?
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.
C = p2r
Shifted up 2 units.
In the expression x^b - x is the base and b is the exponent.

32. How do you find the area of a sector of a circle?
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°
For any number b: b = -b if and only if b = 0.
Area = (x°/360)(pr^2) where x is the central angle.

33. Law of exponents 3
[(x1 + x2)/2] -[(y1 + y2)/2]
B^m/b^n = b^m-n
(b^m)^n = b^mn
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.

34. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
The product of their slopes is -1 (negative reciprocal).
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°.
Set y = 0 - and solve.
All positive and negative whole numbers - and zero.

35. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
Corresponding sides of similar triangles are in proportion.
V = l^3
A = s^2 or A =d^2/2 where d is the diagonal

36. What is an exterior angle of a polygon?
A^m/b^m = (a/b)^m
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°.
For any number b: b = -b if and only if b = 0.
An angle formed by extending the side of the polygon.

37. What is a function?
A = [(s^2*v3)/4]
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

38. What is the formula for the surface area of a cube?
A = 6(l^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°.
Divide - then multiply by 100.
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.

39. What is an exponent?
360°
In the expression x^b - x is the base and b is the exponent.
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

40. What is the formula for the area of a rectangle?
A = lw
Then the quotient y/x is a constant.
An equation that states that two ratios are equivalent. 4/6 = 10/15
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

41. 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.
V = pr^2h
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

42. What is a proportion?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Then the quotient y/x is a constant.

43. What is the volume of a cube?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(b^m)^n = b^mn
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
V = l^3

44. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Then the quotient y/x is a constant.
A = pr^2
Shifted up 2 units.

45. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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.
Write the percent over 100 and reduce.

46. What does it mean if y is directly proportional to x?
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.
Then the quotient y/x is a constant.
A = s^2 or A =d^2/2 where d is the diagonal

47. What do we mean by the slope of the line?
How steep the line is. Horizontal line = 0 - vertical has no slope.
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.
Then the product xy is a constant.

48. In a circle of radius r - what is the formula for the diameter?
Write the percent over 100 and reduce.
A = s^2 or A =d^2/2 where d is the diagonal
D = 2r
For any right triangle - a^2 + b^2 = c^2.

49. What is the area of a square?
[(x1 + x2)/2] -[(y1 + y2)/2]
For any right triangle - a^2 + b^2 = c^2.
Set x = 0 - and solve.
A = s^2 or A =d^2/2 where d is the diagonal

50. Properties of one 1
V = lwh
For any number a: a * 1 = a and a / 1 = a.
The two pairs of opposite angles formed are equal to each other.
No matter how many angles there are - the sum around the point is 360°.