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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 a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
1 is a divisor (or factor) of every integer.
Cannot is 0 - must is 1 - all others are in between.
No matter how many angles there are - the sum around the point is 360°.

2. How do you find a percent of a number?
In the expression x^b - x is the base and b is the exponent.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Write the percent as a decimal - and multiply.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

3. Properties of zero 5
For any integer n: 1^n = 1.
For any number b: b = -b if and only if b = 0.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
For any right triangle - a^2 + b^2 = c^2.

4. What is an exponent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
For any number b: b = -b if and only if b = 0.
Set x = 0 - and solve.
In the expression x^b - x is the base and b is the exponent.

5. What are the properties of a parallelogram?
(x + y)(x - y) = x^2 - y^2
C = p2r
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Avg = sum of n numbers/n

6. What is an exterior angle of a triangle?
A = [(s^2*v3)/4]
(b^m)^n = b^mn
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.

7. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
V = pr^2h
For any number a: a * 1 = a and a / 1 = a.
M = (y2 - y1)/(x2 - x1)

8. 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.
Divide - then multiply by 100.
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.
The ratio of corresponding sides of similar triangles.

9. In a circle of radius r - what is the formula for the circumference?
At least one of the factors is 0.
Shifted up 2 units.
C = p2r
V = l^3

10. What is true about the slopes of parallel lines?
Write the percent as a decimal - and multiply.
Equal slopes.
Set y = 0 - and solve.
An angle formed by extending the side of the polygon.

11. How do we write the equation of a line?
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^m*b^m = (ab)^m
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = 2(lw + lh + hw)

12. What is the probability of an event that cannot occur? That must occur?
A fraction whose denominator is 100 i.e. 17% = 17/100
Cannot is 0 - must is 1 - all others are in between.
Equal slopes.
A^m/b^m = (a/b)^m

13. How do you find the y-intercept of a graph?
A = lw
Divide - then multiply by 100.
Set x = 0 - and solve.
(Circumference/diameter) of a circle - or approximately 3.14.

14. What is a fractional exponent?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
(Circumference/diameter) of a circle - or approximately 3.14.
A = s^2 or A =d^2/2 where d is the diagonal
Write the percent as a decimal - and multiply.

15. What are the sum - difference - products - and quotient of two numbers?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A^m*b^m = (ab)^m
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

16. What is a ratio?

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17. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
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 = [(s^2*v3)/4]
A fraction whose denominator is 100 i.e. 17% = 17/100

18. What important property do similar triangles have?
V = l^3
A^m*b^m = (ab)^m
Corresponding sides of similar triangles are in proportion.
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.

19. How do you convert a percent to a fraction or a decimal?
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 = (ab)^m
Write the percent over 100 and reduce.
B^m*b^n = b^m+n

20. Properties of one 4
[(x1 + x2)/2] -[(y1 + y2)/2]
1 is the smallest positive odd integer.
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

21. How do you find the length of an arc of a circle?
Their sum is 180°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A fraction whose denominator is 100 i.e. 17% = 17/100
Arc = (x°/360)(2pr) where x is the central angle.

22. How do you calculate a weighted average?
A = s^2 or A =d^2/2 where d is the diagonal
The product of their slopes is -1 (negative reciprocal).
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.

23. What is an even and an odd number?
A = 2(lw + lh + hw)
Even numbers are divisible by 2 and odd numbers are not.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
At least one of the factors is 0.

24. Important binomial 2
An equation that states that two ratios are equivalent. 4/6 = 10/15
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
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.

25. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

26. In a circle of radius r - what is the formula for the diameter?
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°.
D = 2r
Shifted left 2 units.
(Circumference/diameter) of a circle - or approximately 3.14.

27. What is the sum of the measures of the four angles in a quadrilateral?
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.
The set of all ordered pairs (x -y) such that y = f(x).
360°
P(e) = (# of favorable outcomes)/(# of possible outcomes)

28. What is true about the slopes of perpendicular lines?
360°
At least one of the factors is 0.
For any number a: a * 1 = a and a / 1 = a.
The product of their slopes is -1 (negative reciprocal).

29. What is a composite number?
B^m*b^n = b^m+n
A = s^2 or A =d^2/2 where d is the diagonal
An integer greater than one that is not prime.
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.

30. What is the area of a square?
No matter how many angles there are - the sum around the point is 360°.
[(x1 + x2)/2] -[(y1 + y2)/2]
(b^m)^n = b^mn
A = s^2 or A =d^2/2 where d is the diagonal

31. Properties of one 1
(Circumference/diameter) of a circle - or approximately 3.14.
Cannot is 0 - must is 1 - all others are in between.
For any number a: a * 1 = a and a / 1 = a.
C = p2r

32. What is the sum of the measures of the n angles of a polygon with n sides?
A = [(s^2*v3)/4]
Shifted left 2 units.
(n - 2)(180°)
A = (1/2)bh.

33. What is the formula for the volume of a cylinder?
Their sum is 180°.
V = pr^2h
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

34. What is the formula for the area of a rectangle?
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.
Cannot is 0 - must is 1 - all others are in between.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

35. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
For any number b: b = -b if and only if b = 0.
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 fraction whose denominator is 100 i.e. 17% = 17/100

36. Law of exponents 1
A = lw
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
B^m*b^n = b^m+n
All positive and negative whole numbers - and zero.

37. What does it mean if y is directly proportional to x?
0 is a multiple of every integer.
360°
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.
Then the quotient y/x is a constant.

38. How do you find the slope of a line?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = lw
M = (y2 - y1)/(x2 - x1)
Equal slopes.

39. What is a proportion?
Even numbers are divisible by 2 and odd numbers are not.
An equation that states that two ratios are equivalent. 4/6 = 10/15
V = l^3
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

40. What is a negative exponent?
Shifted up 2 units.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any number n: x^-n means 1/x^n.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

41. What is the triangle inequality?
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°.
(b^m)^n = b^mn
Set x = 0 - and solve.
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.

42. What is an integer?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Set x = 0 - and solve.
A = lw
All positive and negative whole numbers - and zero.

43. What is a multiple of an integer?
For any number a: a * 1 = a and a / 1 = a.
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.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
(b^m)^n = b^mn

44. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
0 is a multiple of every integer.
For any number b: b = -b if and only if b = 0.
The set of all ordered pairs (x -y) such that y = f(x).
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.

45. What is p?
A^m*b^m = (ab)^m
(Circumference/diameter) of a circle - or approximately 3.14.
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.
Divide - then multiply by 100.

46. Law of exponents 4
Even numbers are divisible by 2 and odd numbers are not.
A^m*b^m = (ab)^m
A = (1/2)bh.
180°. If two or more angles form a straight angle - their sum is 180°.

47. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
A = [(s^2*v3)/4]
Write the percent over 100 and reduce.
(Circumference/diameter) of a circle - or approximately 3.14.

48. Properties of zero 1
0 is the only number that is neither positive nor negative.
Avg = sum of n numbers/n
Write the percent over 100 and reduce.
Shifted right 2 units.

49. What is true about the measures of the three angles in a triangle?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Their sum is 180°.
Is a right triangle with a ratio of sides x:xv3:2x.
For any integer n: 1^n = 1.

50. What formula is used for an average?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The product of their slopes is -1 (negative reciprocal).
Avg = sum of n numbers/n
A = 2(lw + lh + hw)