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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.
Don't refresh. All questions and answers are randomly picked and ordered every time you load a test.

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. How do you calculate a weighted average?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
The set of all ordered pairs (x -y) such that y = f(x).
An angle formed by extending the side of the polygon.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

2. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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.
A = 6(l^2)
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

3. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
V = l^3
A^m*b^m = (ab)^m
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

4. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
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.
V = l^3

5. Law of exponents 1
(n - 2)(180°)
For any number a: a * 1 = a and a / 1 = a.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
B^m*b^n = b^m+n

6. Properties of one 4
A fraction whose denominator is 100 i.e. 17% = 17/100
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
1 is the smallest positive odd integer.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

7. What are the properties of a parallelogram?
Even numbers are divisible by 2 and odd numbers are not.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Then the quotient y/x is a constant.

8. In a circle of radius r - what is the formula for the circumference?
360°
(x + y)(x - y) = x^2 - y^2
C = p2r
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

9. What is true about the measures of the two acute angles in a right triangle?
Their sum is 90°.
A = 6(l^2)
A = [(s^2*v3)/4]
D = 2r

10. What is the formula for the area of a parallelogram?
A = bh
Avg = sum of n numbers/n
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.

11. Properties of square roots
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
0 is the only number that is neither positive nor negative.
Is a right triangle with a ratio of sides x:xv3:2x.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

12. What is a ratio?

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13. How you convert a fraction or a decimal to a percent?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For any right triangle - a^2 + b^2 = c^2.
Divide - then multiply by 100.
C = p2r

14. Properties of zero 2
No matter how many angles there are - the sum around the point is 360°.
If a is negative and b is positive - then a < 0 < b.
(b^m)^n = b^mn
Is a right triangle with a ratio of sides x:xv3:2x.

15. What does it mean if y is inversely proportional to x?
A^m/b^m = (a/b)^m
Then the product xy is a constant.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
A = (1/2)bh.

16. What is true about the measures of the three angles in a triangle?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A^m/b^m = (a/b)^m
Their sum is 180°.
For any number b: b = -b if and only if b = 0.

17. What are similar triangles?
V = lwh
They are both the same. A divisor or factor of an integer leaves no remainder.
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.

18. What is a divisor and a factor of an integer?
Set x = 0 - and solve.
They are both the same. A divisor or factor of an integer leaves no remainder.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = (1/2)bh.

19. 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.
(Circumference/diameter) of a circle - or approximately 3.14.
Is a right triangle with a ratio of sides x:xv3:2x.
360°

20. What is an exterior angle of a polygon?
A = [(s^2*v3)/4]
They are both the same. A divisor or factor of an integer leaves no remainder.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
An angle formed by extending the side of the polygon.

21. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
V = l^3

22. What is the probability of an event that cannot occur? That must occur?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A = (1/2)bh.
Cannot is 0 - must is 1 - all others are in between.
Arc = (x°/360)(2pr) where x is the central angle.

23. Properties of zero 3
0 is a multiple of every integer.
(b^m)^n = b^mn
V = l^3
An angle formed by extending the side of the polygon.

24. In a circle of radius r - what is the formula for the area?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A = pr^2
B^m/b^n = b^m-n
A fraction whose denominator is 100 i.e. 17% = 17/100

25. What is the formula for the volume of a rectangular solid?
0 is a multiple of every integer.
V = l^3
Shifted right 2 units.
V = lwh

26. What is the formula for the volume of a cylinder?
V = pr^2h
1 is a divisor (or factor) of every integer.
The set of all ordered pairs (x -y) such that y = f(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.

27. What is the formula for the surface area of a cube?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
A = 6(l^2)
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.
1 is the smallest positive odd integer.

28. What is the formula for the area of a triangle?
A = (1/2)bh.
Even numbers are divisible by 2 and odd numbers are not.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

29. What is the measure of a straight angle?
Write the percent as a decimal - and multiply.
180°. If two or more angles form a straight angle - their sum is 180°.
A = bh
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

30. Law of exponents 4
(x + y)(x - y) = x^2 - y^2
In the expression x^b - x is the base and b is the exponent.
180°. If two or more angles form a straight angle - their sum is 180°.
A^m*b^m = (ab)^m

31. What is true about the slopes of parallel lines?
0 is a multiple of every integer.
Equal slopes.
1 is the smallest positive odd integer.
At least one of the factors is 0.

32. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
Shifted up 2 units.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

33. Properties of one 3
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Set x = 0 - and solve.
The two pairs of opposite angles formed are equal to each other.
1 is a divisor (or factor) of every integer.

34. If the product of two or more numbers is 0 - what do you know about the numbers?
In the expression x^b - x is the base and b is the exponent.
At least one of the factors is 0.
For any number a: a * 1 = a and a / 1 = a.
For any right triangle - a^2 + b^2 = c^2.

35. What is the formula for the surface area of a rectangular solid?
Then the quotient y/x is a constant.
The product of their slopes is -1 (negative reciprocal).
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = 2(lw + lh + hw)

36. Important binomial 2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
They are both the same. A divisor or factor of an integer leaves no remainder.
Write the percent as a decimal - and multiply.
V = lwh

37. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
They are both the same. A divisor or factor of an integer leaves no remainder.
360°
M = (y2 - y1)/(x2 - x1)

38. What is a function?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Shifted right 2 units.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

39. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
[(x1 + x2)/2] -[(y1 + y2)/2]
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.

40. What is a percent?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(b^m)^n = b^mn
A fraction whose denominator is 100 i.e. 17% = 17/100
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

41. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
The ratio of corresponding sides of similar triangles.
Their sum is 180°.
Shifted down 2 units.
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.

42. What are the properties of a rectangle?
Set y = 0 - and solve.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
V = pr^2h
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

43. What is the area of a square?
In the expression x^b - x is the base and b is the exponent.
Is a right triangle with a ratio of sides x:xv3:2x.
A = s^2 or A =d^2/2 where d is the diagonal
0 is the only number that is neither positive nor negative.

44. In a circle of radius r - what is the formula for the diameter?
(b^m)^n = b^mn
1 is a divisor (or factor) of every integer.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
D = 2r

45. What is a composite number?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
An integer greater than one that is not prime.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
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.

46. What is the Pythagorean theorem?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For any right triangle - a^2 + b^2 = c^2.

47. What is a multiple of an integer?
Set y = 0 - and solve.
V = pr^2h
A fraction whose denominator is 100 i.e. 17% = 17/100
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.

48. What is an exterior angle of a triangle?
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
In the expression x^b - x is the base and b is the exponent.
A = lw

49. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
An integer greater than one that is not prime.
Shifted right 2 units.

50. Law of exponents 5
B^m/b^n = b^m-n
A = lw
A^m/b^m = (a/b)^m
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.