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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. What formula is used for an average?
Avg = sum of n numbers/n
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
C = p2r

2. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Is a right triangle with a ratio of sides x:xv3:2x.
They are both the same. A divisor or factor of an integer leaves no remainder.
C = p2r
360°

3. What is p?
Divide - then multiply by 100.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
(Circumference/diameter) of a circle - or approximately 3.14.
No matter how many angles there are - the sum around the point is 360°.

4. What are similar triangles?
360°
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Write the percent as a decimal - and multiply.
Cannot is 0 - must is 1 - all others are in between.

5. How do you find the length of an arc of a circle?
The ratio of corresponding sides of similar triangles.
360°
Arc = (x°/360)(2pr) where x is the central angle.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

6. What is true about the measures of the three angles in a triangle?
A = s^2 or A =d^2/2 where d is the diagonal
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.
Their sum is 180°.

7. What is the formula for the area of a parallelogram?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Set y = 0 - and solve.
A = bh

8. What is a fractional exponent?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For any number n: x^-n means 1/x^n.
The set of all ordered pairs (x -y) such that y = f(x).

9. What is a percent?
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.
A fraction whose denominator is 100 i.e. 17% = 17/100
An equation that states that two ratios are equivalent. 4/6 = 10/15

10. What is a negative exponent?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
For any right triangle - a^2 + b^2 = c^2.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any number n: x^-n means 1/x^n.

11. What is the formula for the surface area of a cube?
A = 6(l^2)
(Circumference/diameter) of a circle - or approximately 3.14.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(n - 2)(180°)

12. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
A = 2(lw + lh + hw)
V = lwh
An equation that states that two ratios are equivalent. 4/6 = 10/15

13. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
For any integer n: 1^n = 1.
A = (1/2)bh.
For any right triangle - a^2 + b^2 = c^2.

14. If the product of two or more numbers is 0 - what do you know about the numbers?
(b^m)^n = b^mn
At least one of the factors is 0.
A = 6(l^2)
0 is a multiple of every integer.

15. For what values of a function is the function undefined?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A^m*b^m = (ab)^m
The set of all ordered pairs (x -y) such that y = f(x).

16. Properties of one 3
1 is a divisor (or factor) of every integer.
Shifted down 2 units.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

17. 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.
Set x = 0 - and solve.
How steep the line is. Horizontal line = 0 - vertical has no slope.
In the expression x^b - x is the base and b is the exponent.

18. What is the formula for the area of a triangle?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For any number n: x^-n means 1/x^n.
360°
A = (1/2)bh.

19. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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°.
Then the quotient y/x is a constant.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
B^m/b^n = b^m-n

20. What is the Pythagorean theorem?
Their sum is 180°.
For any right triangle - a^2 + b^2 = c^2.
180°. If two or more angles form a straight angle - their sum is 180°.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

21. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

22. What is the formula for the area of a rectangle?
A = lw
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Corresponding sides of similar triangles are in proportion.
Equal slopes.

23. What is the distance formula?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
All positive and negative whole numbers - and zero.
180°. If two or more angles form a straight angle - their sum is 180°.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

24. What is the formula for the volume of a cylinder?
No matter how many angles there are - the sum around the point is 360°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
V = pr^2h

25. How do you calculate a weighted average?
A = (1/2)bh.
At least one of the factors is 0.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

26. What is the probability of an event that cannot occur? That must occur?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = 2(lw + lh + hw)
Cannot is 0 - must is 1 - all others are in between.
For any integer n: 1^n = 1.

27. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
Equal slopes.
For any integer n: 1^n = 1.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

28. How do you find the area of a sector of a circle?
A = [(s^2*v3)/4]
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Area = (x°/360)(pr^2) where x is the central angle.
A fraction whose denominator is 100 i.e. 17% = 17/100

29. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
If a is negative and b is positive - then a < 0 < b.
A = (1/2)bh.
Shifted left 2 units.
Shifted right 2 units.

30. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
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.
Is a right triangle with a ratio of sides x:xv3:2x.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

31. What are the sum - difference - products - and quotient of two numbers?
V = lwh
For any integer n: 1^n = 1.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A^m*b^m = (ab)^m

32. What is the triangle inequality?
(b^m)^n = b^mn
If a is negative and b is positive - then a < 0 < b.
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.
Is a right triangle with a ratio of sides x:xv3:2x.

33. Properties of zero 5
For any number b: b = -b if and only if b = 0.
Write the percent over 100 and reduce.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
An equation that states that two ratios are equivalent. 4/6 = 10/15

34. How do you convert a percent to a fraction or a decimal?
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 angle formed by extending the side of the polygon.
B^m/b^n = b^m-n
Write the percent over 100 and reduce.

35. What does it mean if y is inversely proportional to x?
(b^m)^n = b^mn
Then the product xy is a constant.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A fraction whose denominator is 100 i.e. 17% = 17/100

36. How do we write the equation of a line?
D = 2r
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
0 is the only number that is neither positive nor negative.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

37. If you were given the graph of y = f(x) - what does f(a) represent?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Write the percent over 100 and reduce.
V = lwh
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

38. Properties of zero 1
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
0 is the only number that is neither positive nor negative.
V = l^3
Their sum is 90°.

39. In a circle of radius r - what is the formula for the area?
Then the product xy is a constant.
A = pr^2
Area = (x°/360)(pr^2) where x is the central angle.
Write the percent over 100 and reduce.

40. Properties of one 2
Shifted up 2 units.
For any integer n: 1^n = 1.
For any right triangle - a^2 + b^2 = c^2.
For any number a: a * 1 = a and a / 1 = a.

41. 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.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Even numbers are divisible by 2 and odd numbers are not.

42. What is a proportion?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Set x = 0 - and solve.
Their sum is 90°.

43. What is true about the slopes of parallel lines?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Then the quotient y/x is a constant.
Equal slopes.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

44. What is the ratio of similitude?
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.
B^m/b^n = b^m-n
The ratio of corresponding sides of similar triangles.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

45. What is true about the areas of similar triangles?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^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.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(Circumference/diameter) of a circle - or approximately 3.14.

46. What are the important properties of 30-60-90 triangle?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
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.
Set y = 0 - and solve.

47. Law of exponents 3
(n - 2)(180°)
A = bh
An equation that states that two ratios are equivalent. 4/6 = 10/15
(b^m)^n = b^mn

48. What is a ratio?

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49. Law of exponents 1
B^m*b^n = b^m+n
Shifted right 2 units.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.

50. Law of exponents 5
A^m/b^m = (a/b)^m
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Area = (x°/360)(pr^2) where x is the central angle.
Write the percent as a decimal - and multiply.

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