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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 important properties of 30-60-90 triangle?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Is a right triangle with a ratio of sides x:xv3:2x.
A = 2(lw + lh + hw)

2. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The two pairs of opposite angles formed are equal to each other.
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. What is a negative exponent?
An angle formed by extending the side of the polygon.
For any number n: x^-n means 1/x^n.
(n - 2)(180°)
A = 2(lw + lh + hw)

4. How do you find the probability that an event will 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°.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
360°
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

5. Important binomial 2
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The two pairs of opposite angles formed are equal to each other.
180°. If two or more angles form a straight angle - their sum is 180°.

6. What is the sum of the measures of the four angles in a quadrilateral?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(n - 2)(180°)
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.

7. What is the formula for the volume of a rectangular solid?
Then the product xy is a constant.
For any integer n: 1^n = 1.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
V = lwh

8. How do you calculate percent increases and decreases?
1 is a divisor (or factor) of every integer.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A^m*b^m = (ab)^m
Equal slopes.

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.
M = (y2 - y1)/(x2 - x1)
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Set y = 0 - and solve.

10. 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.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = (1/2)bh.
A fraction whose denominator is 100 i.e. 17% = 17/100

11. What is the area of a square?
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 product of their slopes is -1 (negative reciprocal).
A = s^2 or A =d^2/2 where d is the diagonal
C = p2r

12. How do you find a percent of a number?
Set x = 0 - and solve.
Set y = 0 - and solve.
Write the percent as a decimal - and multiply.
(n - 2)(180°)

13. What is a percent?
1 is the smallest positive odd integer.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Area = (x°/360)(pr^2) where x is the central angle.
A fraction whose denominator is 100 i.e. 17% = 17/100

14. What is the sum of the measures of the n angles of a polygon with n sides?
They are both the same. A divisor or factor of an integer leaves no remainder.
(n - 2)(180°)
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
360°

15. What are the sum - difference - products - and quotient of two numbers?
The product of their slopes is -1 (negative reciprocal).
They are both the same. A divisor or factor of an integer leaves no remainder.
1 is the smallest positive odd integer.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

16. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
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.
V = lwh
Even numbers are divisible by 2 and odd numbers are not.

17. What is a ratio?

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18. Properties of zero 1
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.
0 is the only number that is neither positive nor negative.
V = lwh

19. What do we mean by the slope of the line?
For any number n: x^-n means 1/x^n.
A fraction whose denominator is 100 i.e. 17% = 17/100
How steep the line is. Horizontal line = 0 - vertical has no slope.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

20. What is the distributive law?
(x + y)(x - y) = x^2 - y^2
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
For any number n: x^-n means 1/x^n.

21. What are the properties of a rectangle?
An angle formed by extending the side of the polygon.
1 is the smallest positive odd integer.
They are both the same. A divisor or factor of an integer leaves no remainder.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

22. What are the important properties of a 45-45 - 90 triangle?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Shifted right 2 units.
The ratio of corresponding sides of similar triangles.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

23. How you convert a fraction or a decimal to a percent?
Divide - then multiply by 100.
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.
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. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
C = p2r
Shifted up 2 units.
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.

25. If the product of two or more numbers is 0 - what do you know about the numbers?
The product of their slopes is -1 (negative reciprocal).
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
At least one of the factors is 0.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

26. Law of exponents 1
B^m*b^n = b^m+n
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
For any number n: x^-n means 1/x^n.
For any number a: a * 1 = a and a / 1 = a.

27. What is a composite number?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
An integer greater than one that is not prime.
M = (y2 - y1)/(x2 - x1)
1 is a divisor (or factor) of every integer.

28. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
(b^m)^n = b^mn
Shifted right 2 units.
360°
1 is a divisor (or factor) of every integer.

29. What is the formula for the surface area of a rectangular solid?
A = [(s^2*v3)/4]
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
No matter how many angles there are - the sum around the point is 360°.
A = 2(lw + lh + hw)

30. What is an even and an odd number?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Even numbers are divisible by 2 and odd numbers are not.
If a is negative and b is positive - then a < 0 < b.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

31. What does it mean if y is directly proportional to x?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Equal slopes.
Then the quotient y/x is a constant.
D = 2r

32. What is the volume of a cube?
A = s^2 or A =d^2/2 where d is the diagonal
V = l^3
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Then the product xy is a constant.

33. How do you convert a percent to a fraction or a decimal?
1 is the smallest positive odd integer.
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 over 100 and reduce.
For any number b: b = -b if and only if b = 0.

34. What is true about the slopes of parallel lines?
Equal slopes.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

35. Properties of zero 2
If a is negative and b is positive - then a < 0 < b.
B^m*b^n = b^m+n
C = p2r
M = (y2 - y1)/(x2 - x1)

36. What is true about the slopes of perpendicular lines?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
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°.
At least one of the factors is 0.
The product of their slopes is -1 (negative reciprocal).

37. What are similar triangles?
The two pairs of opposite angles formed are equal to each other.
Then the quotient y/x is a constant.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
No matter how many angles there are - the sum around the point is 360°.

38. What is an exterior angle of a triangle?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
An integer greater than one that is not prime.
Divide - then multiply by 100.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

39. Properties of zero 3
0 is a multiple of every integer.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Avg = sum of n numbers/n
A^m*b^m = (ab)^m

40. What are the median and the mode of a set of data?
A^m*b^m = (ab)^m
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
The two pairs of opposite angles formed are equal to each other.

41. What is the square root of a number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Shifted left 2 units.
A = lw
An angle formed by extending the side of the polygon.

42. Properties of one 3
At least one of the factors is 0.
Arc = (x°/360)(2pr) where x is the central angle.
1 is a divisor (or factor) of every integer.
B^m/b^n = b^m-n

43. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
For any number b: b = -b if and only if b = 0.
Arc = (x°/360)(2pr) where x is the central angle.
Shifted up 2 units.
Shifted right 2 units.

44. Important binomial 1
A = lw
A = [(s^2*v3)/4]
(x + y)(x - y) = x^2 - y^2
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

45. Properties of one 4
Cannot is 0 - must is 1 - all others are in between.
(x + y)(x - y) = x^2 - y^2
1 is the smallest positive odd integer.
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.

46. 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.
For any number a: a * 1 = a and a / 1 = a.
The set of all ordered pairs (x -y) such that y = f(x).
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

47. What is the formula for the surface area of a cube?
A = 6(l^2)
Equal slopes.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = lw

48. What is the measure of a straight angle?
A^m*b^m = (ab)^m
Set x = 0 - and solve.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
180°. If two or more angles form a straight angle - their sum is 180°.

49. Law of exponents 2
B^m/b^n = b^m-n
The product of their slopes is -1 (negative reciprocal).
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

50. Properties of zero 5
For any number b: b = -b if and only if b = 0.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Corresponding sides of similar triangles are in proportion.
A = bh