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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 does it mean if y is inversely proportional to x?
1 is the smallest positive odd integer.
M = (y2 - y1)/(x2 - x1)
(Circumference/diameter) of a circle - or approximately 3.14.
Then the product xy is a constant.

2. How do you calculate percent increases and decreases?
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.
No matter how many angles there are - the sum around the point is 360.
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.

3. Law of exponents 2
B^m/b^n = b^m-n
A = bh
The product of their slopes is -1 (negative reciprocal).
Arc = (x/360)(2pr) where x is the central angle.

4. What is the volume of a cube?
Set y = 0 - and solve.
Arc = (x/360)(2pr) where x is the central angle.
V = l^3
Shifted up 2 units.

5. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
For any number a: a * 1 = a and a / 1 = a.
For any number n: x^-n means 1/x^n.
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.

6. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
Then the quotient y/x is a constant.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For any integer n: 1^n = 1.

7. Properties of one 2
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any integer n: 1^n = 1.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

8. What is a composite number?
If a is negative and b is positive - then a < 0 < b.
1 is a divisor (or factor) of every integer.
An integer greater than one that is not prime.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

9. Properties of zero 3
Shifted down 2 units.
(n - 2)(180)
0 is a multiple of every integer.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

10. What is the formula for the volume of a rectangular solid?
[(x1 + x2)/2] -[(y1 + y2)/2]
Shifted down 2 units.
V = lwh
0 is the only number that is neither positive nor negative.

11. How do you find the area of a sector of a circle?
They are both the same. A divisor or factor of an integer leaves no remainder.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Their sum is 180.
Area = (x/360)(pr^2) where x is the central angle.

12. What is the formula for the area of a parallelogram?
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 = bh
A = lw
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

13. What are similar triangles?
An angle formed by extending the side of the polygon.
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
An integer greater than one that is not prime.

14. What is the formula for the volume of a cylinder?
Then the quotient y/x is a constant.
Shifted down 2 units.
V = pr^2h
V = lwh

15. What is the probability of an event that cannot occur? That must occur?
No matter how many angles there are - the sum around the point is 360.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Cannot is 0 - must is 1 - all others are in between.
(Circumference/diameter) of a circle - or approximately 3.14.

16. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
V = l^3
Write the percent over 100 and reduce.
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.

17. What is the formula for the area of a rectangle?
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.
A = lw
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.
Set x = 0 - and solve.

18. What is true about the measures of the two acute angles in a right triangle?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
V = pr^2h
Their sum is 90.
An integer greater than one that is not prime.

19. What is a divisor and a factor of an integer?
360
For any right triangle - a^2 + b^2 = c^2.
They are both the same. A divisor or factor of an integer leaves no remainder.
No matter how many angles there are - the sum around the point is 360.

20. What are the properties of a square?
Even numbers are divisible by 2 and odd numbers are not.
Write the percent over 100 and reduce.
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.
A^m/b^m = (a/b)^m

21. What is the formula for the surface area of a cube?
All positive and negative whole numbers - and zero.
0 is the only number that is neither positive nor negative.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = 6(l^2)

22. In a circle of radius r - what is the formula for the area?
Cannot is 0 - must is 1 - all others are in between.
Shifted right 2 units.
Then the quotient y/x is a constant.
A = pr^2

23. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
The product of their slopes is -1 (negative reciprocal).
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

24. What is p?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = 6(l^2)
(x + y)(x - y) = x^2 - y^2
(Circumference/diameter) of a circle - or approximately 3.14.

25. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(180)
V = pr^2h
Divide - then multiply by 100.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

26. Important binomial 3
An integer greater than one that is not prime.
The product of their slopes is -1 (negative reciprocal).
A = lw
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

27. What are the sum - difference - products - and quotient of two numbers?
For any number n: x^-n means 1/x^n.
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.
An angle formed by extending the side of the polygon.

28. What is a function?
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A fraction whose denominator is 100 i.e. 17% = 17/100
For any number b: b = -b if and only if b = 0.

29. What is a negative exponent?
Shifted down 2 units.
For any number n: x^-n means 1/x^n.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A = 2(lw + lh + hw)

30. What are the important properties of 30-60-90 triangle?
No matter how many angles there are - the sum around the point is 360.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Is a right triangle with a ratio of sides x:xv3:2x.

31. Important binomial 2
Avg = sum of n numbers/n
The ratio of corresponding sides of similar triangles.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = 2(lw + lh + hw)

32. For what values of a function is the function undefined?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Then the product xy is a constant.

33. What is an integer?
An equation that states that two ratios are equivalent. 4/6 = 10/15
[(x1 + x2)/2] -[(y1 + y2)/2]
Even numbers are divisible by 2 and odd numbers are not.
All positive and negative whole numbers - and zero.

34. What is the square root of a number?
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.
For any number n: x^-n means 1/x^n.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

35. What is the graph of a function?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The set of all ordered pairs (x -y) such that y = f(x).
Write the percent as a decimal - and multiply.
Divide - then multiply by 100.

36. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.
Shifted left 2 units.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

37. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
V = lwh
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

38. What is the Pythagorean theorem?
C = p2r
For any right triangle - a^2 + b^2 = c^2.
An equation that states that two ratios are equivalent. 4/6 = 10/15
The product of their slopes is -1 (negative reciprocal).

39. What is the sum of the measures of all angles around a point?
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.
No matter how many angles there are - the sum around the point is 360.
Equal slopes.
A = lw

40. What is an exterior angle of a triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(b^m)^n = b^mn
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = (1/2)bh.

41. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
360
0 is the only number that is neither positive nor negative.
An integer greater than one that is not prime.

42. What formula is used for an average?
Avg = sum of n numbers/n
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.
A = bh

43. Law of exponents 3
(b^m)^n = b^mn
V = pr^2h
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Their sum is 180.

44. What is a Venn diagram?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = lw
(x + y)(x - y) = x^2 - y^2

45. If the product of two or more numbers is 0 - what do you know about the numbers?
At least one of the factors is 0.
B^m*b^n = b^m+n
A = 2(lw + lh + hw)
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

46. What is a ratio?
B^m*b^n = b^m+n
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Arc = (x/360)(2pr) where x is the central angle.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

47. What are the quotient and the remainder?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
0 is a multiple of every integer.
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.

48. What important property do similar triangles have?
Shifted down 2 units.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Corresponding sides of similar triangles are in proportion.

49. What is true about the areas of similar triangles?
A = bh
M = (y2 - y1)/(x2 - x1)
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
360

50. What is the measure of a straight angle?
In the expression x^b - x is the base and b is the exponent.
180. If two or more angles form a straight angle - their sum is 180.
Set y = 0 - and solve.
Shifted down 2 units.

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