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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 the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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.

2. What is the probability of an event that cannot occur? That must occur?
Write the percent as a decimal - and multiply.
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.
Cannot is 0 - must is 1 - all others are in between.
Shifted up 2 units.

3. Properties of one 3
1 is a divisor (or factor) of every integer.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Is a right triangle with a ratio of sides x:xv3:2x.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

4. What is a proportion?
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°.
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 equation that states that two ratios are equivalent. 4/6 = 10/15
The two pairs of opposite angles formed are equal to each other.

5. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Shifted down 2 units.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

6. Properties of zero 3
A = [(s^2*v3)/4]
Set x = 0 - and solve.
0 is a multiple of every integer.
A fraction whose denominator is 100 i.e. 17% = 17/100

7. 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.
For any number a: a * 1 = a and a / 1 = a.
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°.
A = [(s^2*v3)/4]

8. What is the formula for the area of a parallelogram?
A = bh
For any number n: x^-n means 1/x^n.
The ratio of corresponding sides of similar triangles.
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.

9. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any right triangle - a^2 + b^2 = c^2.

10. What is a multiple of an integer?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For any integer n: 1^n = 1.
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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

11. Important binomial 1
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
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.
(x + y)(x - y) = x^2 - y^2

12. What is an even and an odd number?
Cannot is 0 - must is 1 - all others are in between.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Even numbers are divisible by 2 and odd numbers are not.
360°

13. What is a composite number?
(x + y)(x - y) = x^2 - y^2
Write the percent as a decimal - and multiply.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
An integer greater than one that is not prime.

14. How do you convert a percent to a fraction or a decimal?
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any right triangle - a^2 + b^2 = c^2.
Write the percent over 100 and reduce.
They are both the same. A divisor or factor of an integer leaves no remainder.

15. What is true about the measures of the four angles formed by two intersecting lines?
The two pairs of opposite angles formed are equal to each other.
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.
For any number b: b = -b if and only if b = 0.
180°. If two or more angles form a straight angle - their sum is 180°.

16. What is the triangle inequality?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
180°. If two or more angles form a straight angle - their sum is 180°.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
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.

17. 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.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

18. What is a fractional exponent?
1 is a divisor (or factor) of every integer.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
[(x1 + x2)/2] -[(y1 + y2)/2]
A = (1/2)bh.

19. What is true about the areas of similar triangles?
If a is negative and b is positive - then a < 0 < b.
For any integer n: 1^n = 1.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

20. What is the formula for the volume of a rectangular solid?
Shifted right 2 units.
V = lwh
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
B^m*b^n = b^m+n

21. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any number a: a * 1 = a and a / 1 = a.
A fraction whose denominator is 100 i.e. 17% = 17/100

22. What is the volume of a cube?
V = l^3
C = p2r
1 is a divisor (or factor) of every integer.
V = pr^2h

23. What is true about the slopes of parallel lines?
An integer greater than one that is not prime.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(b^m)^n = b^mn
Equal slopes.

24. What are the properties of a square?
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.
Write the percent as a decimal - and multiply.
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

25. What is an integer?
All positive and negative whole numbers - and zero.
Equal slopes.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

26. What is the formula for the surface area of a cube?
An equation that states that two ratios are equivalent. 4/6 = 10/15
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Write the percent as a decimal - and multiply.
A = 6(l^2)

27. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
At least one of the factors is 0.
A fraction whose denominator is 100 i.e. 17% = 17/100
How steep the line is. Horizontal line = 0 - vertical has no slope.

28. What is a Venn diagram?
360°
All positive and negative whole numbers - and zero.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

29. In a circle of radius r - what is the formula for the area?
In the expression x^b - x is the base and b is the exponent.
A = pr^2
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Shifted left 2 units.

30. What is the formula for the area of a triangle?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
If a is negative and b is positive - then a < 0 < b.
For any right triangle - a^2 + b^2 = c^2.
A = (1/2)bh.

31. What is an exponent?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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 positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
In the expression x^b - x is the base and b is the exponent.

32. Important binomial 2
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A = pr^2
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

33. Law of exponents 2
Equal slopes.
A = lw
Shifted left 2 units.
B^m/b^n = b^m-n

34. Law of exponents 5
A^m/b^m = (a/b)^m
Avg = sum of n numbers/n
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A = 6(l^2)

35. 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
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Their sum is 180°.
Equal slopes.

36. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(Circumference/diameter) of a circle - or approximately 3.14.

37. Properties of one 1
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.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Then the quotient y/x is a constant.

38. What is the formula for the surface area of a rectangular solid?
A fraction whose denominator is 100 i.e. 17% = 17/100
A^m*b^m = (ab)^m
Then the quotient y/x is a constant.
A = 2(lw + lh + hw)

39. In a circle of radius r - what is the formula for the diameter?
D = 2r
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.
They are both the same. A divisor or factor of an integer leaves no remainder.
An equation that states that two ratios are equivalent. 4/6 = 10/15

40. What is the distance formula?
A = 6(l^2)
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
1 is a divisor (or factor) of every integer.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

41. How do you find the area of a sector of a circle?
The two pairs of opposite angles formed are equal to each other.
Then the quotient y/x is a constant.
Area = (x°/360)(pr^2) where x is the central angle.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

42. How do you calculate a weighted average?
(n - 2)(180°)
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
All positive and negative whole numbers - and zero.
A = [(s^2*v3)/4]

43. What is true about the slopes of perpendicular lines?
The product of their slopes is -1 (negative reciprocal).
Corresponding sides of similar triangles are in proportion.
Avg = sum of n numbers/n
C = p2r

44. What is the graph of a function?
Divide - then multiply by 100.
The set of all ordered pairs (x -y) such that y = f(x).
Then the quotient y/x is a constant.
An integer greater than one that is not prime.

45. What is the distributive law?
If a is negative and b is positive - then a < 0 < b.
Their sum is 90°.
Arc = (x°/360)(2pr) where x is the central angle.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

46. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
A = lw
A = (1/2)bh.
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.
Shifted left 2 units.

47. What is a percent?
A = [(s^2*v3)/4]
A fraction whose denominator is 100 i.e. 17% = 17/100
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
M = (y2 - y1)/(x2 - x1)

48. How do you find a percent of a number?
M = (y2 - y1)/(x2 - x1)
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
In the expression x^b - x is the base and b is the exponent.
Write the percent as a decimal - and multiply.

49. What are the important properties of 30-60-90 triangle?
Write the percent as a decimal - and multiply.
For any number n: x^-n means 1/x^n.
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.

50. What are the quotient and the remainder?

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