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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 triangle inequality?
Even numbers are divisible by 2 and odd numbers are not.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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 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.

2. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
(Circumference/diameter) of a circle - or approximately 3.14.
Even numbers are divisible by 2 and odd numbers are not.
A^m/b^m = (a/b)^m

3. What is a function?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The two pairs of opposite angles formed are equal to each other.
The set of all ordered pairs (x -y) such that y = f(x).

4. What is an even and an odd number?
Shifted left 2 units.
Even numbers are divisible by 2 and odd numbers are not.
At least one of the factors is 0.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

5. What is the formula for the area of a parallelogram?
Area = (x/360)(pr^2) where x is the central angle.
A = bh
All positive and negative whole numbers - and zero.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

6. Important binomial 3
[(x1 + x2)/2] -[(y1 + y2)/2]
A = pr^2
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A = bh

7. What is the square root of a number?
Shifted down 2 units.
(b^m)^n = b^mn
(n - 2)(180)
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

8. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
V = lwh
Their sum is 90.
For any integer n: 1^n = 1.

9. How do we write the equation of a line?
[(x1 + x2)/2] -[(y1 + y2)/2]
A = [(s^2*v3)/4]
Divide - then multiply by 100.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

10. What is a proportion?
360
Their sum is 90.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any number a: a * 1 = a and a / 1 = a.

11. What is p?
Shifted left 2 units.
(Circumference/diameter) of a circle - or approximately 3.14.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Set y = 0 - and solve.

12. How do you convert a percent to a fraction or a decimal?
For any right triangle - a^2 + b^2 = c^2.
At least one of the factors is 0.
Write the percent over 100 and reduce.
A = (1/2)bh.

13. What is an exponent?
0 is the only number that is neither positive nor negative.
In the expression x^b - x is the base and b is the exponent.
For any number n: x^-n means 1/x^n.
Shifted right 2 units.

14. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
Shifted right 2 units.
If a is negative and b is positive - then a < 0 < b.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180 - and the diagonals bisect.

15. What is a fractional exponent?
Write the percent as a decimal - and multiply.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
B^m/b^n = b^m-n

16. What is the sum of the measures of the n angles of a polygon with n sides?
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.
Write the percent as a decimal - and multiply.
(n - 2)(180)

17. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
(x + y)(x - y) = x^2 - y^2
How steep the line is. Horizontal line = 0 - vertical has no slope.
Shifted up 2 units.

18. What are the properties of a parallelogram?
Shifted left 2 units.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180 - and the diagonals bisect.
The ratio of corresponding sides of similar triangles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

19. What does it mean if y is inversely proportional to x?
A^m/b^m = (a/b)^m
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 product xy is a constant.
Their sum is 180.

20. What are the sum - difference - products - and quotient of two numbers?
A = 6(l^2)
Divide - then multiply by 100.
Area = (x/360)(pr^2) where x is the central angle.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

21. What is a composite number?
No matter how many angles there are - the sum around the point is 360.
An integer greater than one that is not prime.
Corresponding sides of similar triangles are in proportion.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

22. What important property do similar triangles have?
A = 6(l^2)
[(x1 + x2)/2] -[(y1 + y2)/2]
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Corresponding sides of similar triangles are in proportion.

23. What is the ratio of similitude?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
An equation that states that two ratios are equivalent. 4/6 = 10/15
[(x1 + x2)/2] -[(y1 + y2)/2]
The ratio of corresponding sides of similar triangles.

24. Properties of zero 1
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 a: a * 1 = a and a / 1 = a.
(x + y)(x - y) = x^2 - y^2
0 is the only number that is neither positive nor negative.

25. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
A = 2(lw + lh + hw)
For any integer n: 1^n = 1.
Shifted down 2 units.
At least one of the factors is 0.

26. What are the properties of a square?
C = p2r
V = pr^2h
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 = (1/2)bh.

27. Properties of zero 4
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Shifted left 2 units.
An equation that states that two ratios are equivalent. 4/6 = 10/15
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

28. Important binomial 1
Write the percent as a decimal - and multiply.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(x + y)(x - y) = x^2 - y^2
1 is the smallest positive odd integer.

29. What is the volume of a cube?
V = l^3
Avg = sum of n numbers/n
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Is a right triangle with a ratio of sides x:xv3:2x.

30. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
An angle formed by extending the side of the polygon.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
For any right triangle - a^2 + b^2 = c^2.

31. What is the measure of a straight angle?
A = (1/2)bh.
C = p2r
180. If two or more angles form a straight angle - their sum is 180.
Avg = sum of n numbers/n

32. If the product of two or more numbers is 0 - what do you know about the numbers?
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.
At least one of the factors is 0.
180. If two or more angles form a straight angle - their sum is 180.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

33. What is a Venn diagram?
1 is the smallest positive odd integer.
Corresponding sides of similar triangles are in proportion.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
An integer greater than one that is not prime.

34. 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.
The two pairs of opposite angles formed are equal to each other.
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.
Divide - then multiply by 100.

35. How do you calculate a weighted average?
A = 6(l^2)
Divide - then multiply by 100.
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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

36. What is the sum of the measures of all angles around a point?
0 is a multiple of every integer.
No matter how many angles there are - the sum around the point is 360.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Equal slopes.

37. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360
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.
Then the product xy is a constant.

38. Law of exponents 4
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
B^m/b^n = b^m-n
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A^m*b^m = (ab)^m

39. What are the important properties of 30-60-90 triangle?
A^m*b^m = (ab)^m
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Is a right triangle with a ratio of sides x:xv3:2x.
Equal slopes.

40. What is the formula for the area of a rectangle?
(x + y)(x - y) = x^2 - y^2
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = [(s^2*v3)/4]
A = lw

41. What is true about the slopes of parallel lines?
Shifted right 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.
V = lwh
Equal slopes.

42. What are the quotient and the remainder?
A = (1/2)bh.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
B^m/b^n = b^m-n
A = pr^2

43. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
(b^m)^n = b^mn
In the expression x^b - x is the base and b is the exponent.
For any integer n: 1^n = 1.
Shifted right 2 units.

44. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
An integer greater than one that is not prime.
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.
B^m/b^n = b^m-n
Shifted left 2 units.

45. What is true about the slopes of perpendicular lines?
All positive and negative whole numbers - and zero.
The product of their slopes is -1 (negative reciprocal).
Cannot is 0 - must is 1 - all others are in between.
At least one of the factors is 0.

46. What are the median and the mode of a set of data?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
An integer greater than one that is not prime.
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 = [(s^2*v3)/4]

47. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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.
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.
360

48. What is true about the areas of similar triangles?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

49. What is an integer?
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.
All positive and negative whole numbers - and zero.
They are both the same. A divisor or factor of an integer leaves no remainder.
For any number n: x^-n means 1/x^n.

50. Law of exponents 2
B^m/b^n = b^m-n
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Equal slopes.
A^m/b^m = (a/b)^m

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