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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 special formula for the area of an equilateral triangle?
An angle formed by extending the side of the polygon.
A = [(s^2*v3)/4]
V = l^3
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

2. What is true about the slopes of perpendicular lines?
A^m/b^m = (a/b)^m
(b^m)^n = b^mn
The product of their slopes is -1 (negative reciprocal).
If a is negative and b is positive - then a < 0 < b.

3. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180)
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
[(x1 + x2)/2] -[(y1 + y2)/2]
D = 2r

4. How you convert a fraction or a decimal to a percent?
An integer greater than one that is not prime.
For any integer n: 1^n = 1.
Divide - then multiply by 100.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

5. What is true about the slopes of parallel lines?
Equal slopes.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
D = 2r
A = s^2 or A =d^2/2 where d is the diagonal

6. How do you find the length of an arc of a circle?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(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
Arc = (x/360)(2pr) where x is the central angle.

7. What is the volume of a cube?
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.
No matter how many angles there are - the sum around the point is 360.
V = l^3

8. What is the probability of an event that cannot occur? That must occur?
A = (1/2)bh.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Cannot is 0 - must is 1 - all others are in between.
V = lwh

9. What is a proportion?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
An equation that states that two ratios are equivalent. 4/6 = 10/15
360

10. What are the important properties of 30-60-90 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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Is a right triangle with a ratio of sides x:xv3:2x.
Shifted down 2 units.

11. What is true about the measures of the four angles formed by two intersecting lines?
V = l^3
For any integer n: 1^n = 1.
The two pairs of opposite angles formed are equal to each other.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

12. How do you find the area of a sector of a circle?
(b^m)^n = b^mn
[(x1 + x2)/2] -[(y1 + y2)/2]
B^m*b^n = b^m+n
Area = (x/360)(pr^2) where x is the central angle.

13. How do you find the x-intercept of a graph?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Set y = 0 - and solve.
Then the quotient y/x is a constant.
At least one of the factors is 0.

14. What is an integer?
(Circumference/diameter) of a circle - or approximately 3.14.
All positive and negative whole numbers - and zero.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A = s^2 or A =d^2/2 where d is the diagonal

15. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
1 is the smallest positive odd integer.
Shifted left 2 units.
C = p2r
Area = (x/360)(pr^2) where x is the central angle.

16. If the product of two or more numbers is 0 - what do you know about the numbers?
They are both the same. A divisor or factor of an integer leaves no remainder.
For any number n: x^-n means 1/x^n.
At least one of the factors is 0.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

17. What is a function?
The two pairs of opposite angles formed are equal to each other.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Area = (x/360)(pr^2) where x is the central angle.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

18. In a circle of radius r - what is the formula for the circumference?
(Circumference/diameter) of a circle - or approximately 3.14.
They are both the same. A divisor or factor of an integer leaves no remainder.
C = p2r
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

19. What is the triangle inequality?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180 - and the diagonals bisect.
The set of all ordered pairs (x -y) such that y = f(x).
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.
0 is the only number that is neither positive nor negative.

20. What is the graph of a function?
Their sum is 90.
The set of all ordered pairs (x -y) such that y = f(x).
B^m/b^n = b^m-n
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.

21. Properties of zero 5
For any number b: b = -b if and only if b = 0.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Then the quotient y/x is a constant.
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.

22. Properties of zero 3
Set x = 0 - and solve.
0 is a multiple of every integer.
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.
All positive and negative whole numbers - and zero.

23. Law of exponents 4
For any number a: a * 1 = a and a / 1 = a.
(b^m)^n = b^mn
A^m*b^m = (ab)^m
The set of all ordered pairs (x -y) such that y = f(x).

24. What is the formula for the area of a parallelogram?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A fraction whose denominator is 100 i.e. 17% = 17/100
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = bh

25. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Shifted up 2 units.
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.
A fraction whose denominator is 100 i.e. 17% = 17/100

26. How do you convert a percent to a fraction or a decimal?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Set y = 0 - and solve.
Write the percent over 100 and reduce.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

27. What is the distance formula?
For any number b: b = -b if and only if b = 0.
Avg = sum of n numbers/n
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

28. What is true about the areas of similar triangles?
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.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
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.
Shifted right 2 units.

29. What is the ratio of similitude?
An angle formed by extending the side of the polygon.
Then the product xy is a constant.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
The ratio of corresponding sides of similar triangles.

30. What is a negative exponent?
For any number n: x^-n means 1/x^n.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
If a is negative and b is positive - then a < 0 < b.
A = lw

31. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
Area = (x/360)(pr^2) where x is the central angle.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A = pr^2

32. What does it mean if y is directly proportional to x?
At least one of the factors is 0.
Then the quotient y/x is a constant.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
(b^m)^n = b^mn

33. 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.
360
If a is negative and b is positive - then a < 0 < b.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

34. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 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.
An angle formed by extending the side of the polygon.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

35. What is an exterior angle of a polygon?
A = bh
An angle formed by extending the side of the polygon.
(b^m)^n = b^mn
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

36. How do you find a percent of a number?
Then the quotient y/x is a constant.
Equal slopes.
Write the percent as a decimal - and multiply.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180 - and the diagonals bisect.

37. In a circle of radius r - what is the formula for the diameter?
A = [(s^2*v3)/4]
M = (y2 - y1)/(x2 - x1)
D = 2r
Equal slopes.

38. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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.
For any number n: x^-n means 1/x^n.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

39. What is a prime number?
For any number b: b = -b if and only if b = 0.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(Circumference/diameter) of a circle - or approximately 3.14.
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.

40. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
An angle formed by extending the side of the polygon.
A^m*b^m = (ab)^m
B^m/b^n = b^m-n

41. For what values of a function is the function undefined?
A^m/b^m = (a/b)^m
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

42. What is a divisor and a factor of an integer?
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.
They are both the same. A divisor or factor of an integer leaves no remainder.
0 is a multiple of every integer.
M = (y2 - y1)/(x2 - x1)

43. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
In the expression x^b - x is the base and b is the exponent.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
C = p2r

44. What are the important properties of a 45-45 - 90 triangle?
A = 6(l^2)
Write the percent over 100 and reduce.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

45. What is the formula for the volume of a rectangular solid?
V = lwh
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.
At least one of the factors is 0.
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.

46. What is a percent?
An angle formed by extending the side of the polygon.
Avg = sum of n numbers/n
A fraction whose denominator is 100 i.e. 17% = 17/100
All positive and negative whole numbers - and zero.

47. What is a multiple of an integer?
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.
1 is a divisor (or factor) of every integer.
A = bh
P(e) = (# of favorable outcomes)/(# of possible outcomes)

48. What formula is used for an average?
Avg = sum of n numbers/n
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
B^m/b^n = b^m-n
Set y = 0 - and solve.

49. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A^m*b^m = (ab)^m
(n - 2)(180)

50. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Shifted left 2 units.
A = (1/2)bh.
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]

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