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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 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.
Write the percent over 100 and reduce.
(n - 2)(180°)
Write the percent as a decimal - and multiply.

2. What is the formula for the surface area of a cube?
V = lwh
A = (1/2)bh.
A = 6(l^2)
P(e) = (# of favorable outcomes)/(# of possible outcomes)

3. What is an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
(Circumference/diameter) of a circle - or approximately 3.14.
A = (1/2)bh.
A = s^2 or A =d^2/2 where d is the diagonal

4. What is the sum of the measures of the four angles in a quadrilateral?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = [(s^2*v3)/4]
360°
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.

5. How do we write the equation of a line?
[(x1 + x2)/2] -[(y1 + y2)/2]
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
B^m*b^n = b^m+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.

6. What are the properties of a parallelogram?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
If a is negative and b is positive - then a < 0 < b.
Their sum is 90°.
An angle formed by extending the side of the polygon.

7. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
If a is negative and b is positive - then a < 0 < b.
A = 2(lw + lh + hw)
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

8. What is the formula for the area of a rectangle?
For any number a: a * 1 = a and a / 1 = a.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
0 is the only number that is neither positive nor negative.
A = lw

9. Properties of zero 5
The set of all ordered pairs (x -y) such that y = f(x).
Is a right triangle with a ratio of sides x:xv3:2x.
For any number b: b = -b if and only if b = 0.
Arc = (x°/360)(2pr) where x is the central angle.

10. How do you convert a percent to a fraction or a decimal?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Even numbers are divisible by 2 and odd numbers are not.
Write the percent over 100 and reduce.
[(x1 + x2)/2] -[(y1 + y2)/2]

11. Properties of zero 1
0 is the only number that is neither positive nor negative.
[(x1 + x2)/2] -[(y1 + y2)/2]
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = lw

12. What is a function?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
360°
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

13. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
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.
1 is a divisor (or factor) of every integer.
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.

14. What is the probability of an event that cannot occur? That must occur?
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°.
Cannot is 0 - must is 1 - all others are in between.
A^m*b^m = (ab)^m
Is a right triangle with a ratio of sides x:xv3:2x.

15. What is true about the areas of similar triangles?
A^m*b^m = (ab)^m
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
360°
Write the percent over 100 and reduce.

16. What is a ratio?

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17. If you were given the graph of y = f(x) - what does f(a) represent?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = s^2 or A =d^2/2 where d is the diagonal

18. Important binomial 3
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.
360°
(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

19. How do you calculate a weighted average?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Corresponding sides of similar triangles are in proportion.
No matter how many angles there are - the sum around the point is 360°.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

20. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
The two pairs of opposite angles formed are equal to each other.
1 is the smallest positive odd integer.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

21. How you convert a fraction or a decimal to a percent?
Their sum is 180°.
Divide - then multiply by 100.
For any number b: b = -b if and only if b = 0.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

22. What is the square root of a number?
If a is negative and b is positive - then a < 0 < b.
B^m/b^n = b^m-n
A fraction whose denominator is 100 i.e. 17% = 17/100
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

23. What is true about the measures of the two acute angles in a right triangle?
D = 2r
Their sum is 90°.
Shifted down 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°.

24. What is the midpoint formula?
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
[(x1 + x2)/2] -[(y1 + y2)/2]

25. What do we mean by the slope of the line?
A = s^2 or A =d^2/2 where d is the diagonal
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.
0 is the only number that is neither positive nor negative.
How steep the line is. Horizontal line = 0 - vertical has no slope.

26. What is an exponent?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
In the expression x^b - x is the base and b is the exponent.
Then the quotient y/x is a constant.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

27. What is an exterior angle of a triangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Their sum is 180°.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A = 2(lw + lh + hw)

28. How do you find the slope of a line?
In the expression x^b - x is the base and b is the exponent.
M = (y2 - y1)/(x2 - x1)
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For any number b: b = -b if and only if b = 0.

29. What is an integer?
For any integer n: 1^n = 1.
All positive and negative whole numbers - and zero.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Avg = sum of n numbers/n

30. 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.
Their sum is 180°.
V = pr^2h
The product of their slopes is -1 (negative reciprocal).

31. Properties of zero 2
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = bh
If a is negative and b is positive - then a < 0 < b.

32. What is a negative exponent?
(x + y)(x - y) = x^2 - y^2
A = s^2 or A =d^2/2 where d is the diagonal
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For any number n: x^-n means 1/x^n.

33. What formula is used for an average?
For any number b: b = -b if and only if b = 0.
In the expression x^b - x is the base and b is the exponent.
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.
Avg = sum of n numbers/n

34. How do you find the length of an arc of a circle?
A = bh
For any integer n: 1^n = 1.
(b^m)^n = b^mn
Arc = (x°/360)(2pr) where x is the central angle.

35. What is the formula for the volume of a rectangular solid?
An angle formed by extending the side of the polygon.
V = lwh
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Set y = 0 - and solve.

36. What is a divisor and a factor of an integer?
They are both the same. A divisor or factor of an integer leaves no remainder.
Divide - then multiply by 100.
For any right triangle - a^2 + b^2 = c^2.
A = [(s^2*v3)/4]

37. How do you find the area of a sector of a circle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
1 is a divisor (or factor) of every integer.
Area = (x°/360)(pr^2) 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.

38. What is a Venn diagram?
Equal slopes.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
V = pr^2h
B^m/b^n = b^m-n

39. What is a multiple of an integer?
Equal slopes.
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.
A = 2(lw + lh + hw)
1 is a divisor (or factor) of every integer.

40. What is special formula for the area of an equilateral triangle?
For any integer n: 1^n = 1.
A = [(s^2*v3)/4]
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Even numbers are divisible by 2 and odd numbers are not.

41. What does it mean if y is directly proportional to x?
They are both the same. A divisor or factor of an integer leaves no remainder.
Then the quotient y/x is a constant.
A = (1/2)bh.
The two pairs of opposite angles formed are equal to each other.

42. How do you find the y-intercept of a graph?
They are both the same. A divisor or factor of an integer leaves no remainder.
Set x = 0 - and solve.
A = [(s^2*v3)/4]
(n - 2)(180°)

43. In a circle of radius r - what is the formula for the area?
1 is the smallest positive odd integer.
A = (1/2)bh.
A = pr^2
A^m/b^m = (a/b)^m

44. What is the sum of the measures of all angles around a point?
(Circumference/diameter) of a circle - or approximately 3.14.
Shifted left 2 units.
No matter how many angles there are - the sum around the point is 360°.
Write the percent over 100 and reduce.

45. What is a composite number?
360°
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.
A = 6(l^2)

46. How do you calculate percent increases and decreases?
C = p2r
An equation that states that two ratios are equivalent. 4/6 = 10/15
A^m/b^m = (a/b)^m
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

47. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = [(s^2*v3)/4]
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Write the percent over 100 and reduce.

48. What is true about the measures of the three angles in a triangle?
A^m/b^m = (a/b)^m
Their sum is 180°.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
1 is the smallest positive odd integer.

49. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
M = (y2 - y1)/(x2 - x1)
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

50. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
0 is the only number that is neither positive nor negative.