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GRE Math: Facts

Subjects : gre, math

Instructions:

Answer 50 questions in 15 minutes.
If you are not ready to take this test, you can study here.
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. Properties of zero 3
0 is a multiple of every integer.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
360°

2. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
A fraction whose denominator is 100 i.e. 17% = 17/100
B^m/b^n = b^m-n
For any number n: x^-n means 1/x^n.

3. What is true about the measures of the three angles in a triangle?
A = pr^2
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Their sum is 180°.
Arc = (x°/360)(2pr) where x is the central angle.

4. In a circle of radius r - what is the formula for the circumference?
Area = (x°/360)(pr^2) where x is the central angle.
At least one of the factors is 0.
C = p2r
Write the percent over 100 and reduce.

5. What is an even and an odd number?
360°
Even numbers are divisible by 2 and odd numbers are not.
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°.
An angle formed by extending the side of the polygon.

6. In a circle of radius r - what is the formula for the diameter?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Shifted down 2 units.
Their sum is 90°.
D = 2r

7. What is the distance formula?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = lw
An integer greater than one that is not prime.
Shifted up 2 units.

8. Law of exponents 2
Shifted up 2 units.
360°
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

9. Properties of zero 2
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
If a is negative and b is positive - then a < 0 < b.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Then the quotient y/x is a constant.

10. What is a ratio?

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11. What is an integer?
180°. If two or more angles form a straight angle - their sum is 180°.
An angle formed by extending the side of the polygon.
All positive and negative whole numbers - and zero.
Set x = 0 - and solve.

12. What is an exterior angle of a polygon?
An angle formed by extending the side of the polygon.
Avg = sum of n numbers/n
They are both the same. A divisor or factor of an integer leaves no remainder.
Shifted left 2 units.

13. What are the properties of a square?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
The two pairs of opposite angles formed are equal to each other.
All positive and negative whole numbers - and zero.
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.

14. What is the formula for the volume of a cylinder?
V = pr^2h
Arc = (x°/360)(2pr) where x is the central angle.
360°
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

15. What is the sum of the measures of all angles around a point?
A = bh
An equation that states that two ratios are equivalent. 4/6 = 10/15
No matter how many angles there are - the sum around the point is 360°.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

16. What are similar triangles?
A fraction whose denominator is 100 i.e. 17% = 17/100
A = pr^2
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

17. What is the formula for the surface area of a rectangular solid?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
A = 2(lw + lh + hw)
Shifted down 2 units.
For any number b: b = -b if and only if b = 0.

18. What is a Venn diagram?
For any right triangle - a^2 + b^2 = c^2.
1 is a divisor (or factor) of every integer.
Write the percent as a decimal - and multiply.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

19. What is true about the slopes of parallel lines?
The ratio of corresponding sides of similar triangles.
For any number b: b = -b if and only if b = 0.
A = (1/2)bh.
Equal slopes.

20. If you were given the graph of y = f(x) - what does f(a) represent?
The ratio of corresponding sides of similar triangles.
An integer greater than one that is not prime.
For any number a: a * 1 = a and a / 1 = a.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

21. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Shifted right 2 units.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = s^2 or A =d^2/2 where d is the diagonal

22. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
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.
V = pr^2h
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.

23. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
If a is negative and b is positive - then a < 0 < b.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
M = (y2 - y1)/(x2 - x1)

24. Law of exponents 1
Area = (x°/360)(pr^2) where x is the central angle.
(n - 2)(180°)
B^m*b^n = b^m+n
Set x = 0 - and solve.

25. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
B^m/b^n = b^m-n
A = bh
360°
Area = (x°/360)(pr^2) where x is the central angle.

26. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.
Then the quotient y/x is a constant.
All positive and negative whole numbers - and zero.

27. What is the ratio of similitude?
The ratio of corresponding sides of similar triangles.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
A^m*b^m = (ab)^m
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

28. What is the measure of a straight angle?
180°. If two or more angles form a straight angle - their sum is 180°.
A = [(s^2*v3)/4]
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

29. What does it mean if y is directly proportional to x?
An integer greater than one that is not prime.
Then the quotient y/x is a constant.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

30. What is an exponent?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
In the expression x^b - x is the base and b is the exponent.
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.

31. 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.
360°
In the expression x^b - x is the base and b is the exponent.
The set of all ordered pairs (x -y) such that y = f(x).

32. What is the triangle inequality?
M = (y2 - y1)/(x2 - x1)
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.
Write the percent over 100 and reduce.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

33. What is the formula for the surface area of a cube?
D = 2r
Is a right triangle with a ratio of sides x:xv3:2x.
For any right triangle - a^2 + b^2 = c^2.
A = 6(l^2)

34. What is the sum of the measures of the four angles in a quadrilateral?
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 every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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.
360°

35. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
360°
Divide - then multiply by 100.
Shifted down 2 units.
In the expression x^b - x is the base and b is the exponent.

36. What is the Pythagorean theorem?
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any number a: a * 1 = a and a / 1 = a.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For any right triangle - a^2 + b^2 = c^2.

37. 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.
C = p2r
The two pairs of opposite angles formed are equal to each other.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

38. How do you find a percent of a number?
0 is the only number that is neither positive nor negative.
A = (1/2)bh.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Write the percent as a decimal - and multiply.

39. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
(n - 2)(180°)
Avg = sum of n numbers/n
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

40. 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.
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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Write the percent over 100 and reduce.

41. Important binomial 1
Corresponding sides of similar triangles are in proportion.
For any right triangle - a^2 + b^2 = c^2.
(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.

42. What is a composite number?
Set x = 0 - and solve.
In the expression x^b - x is the base and b is the exponent.
An equation that states that two ratios are equivalent. 4/6 = 10/15
An integer greater than one that is not prime.

43. What is true about the areas of similar triangles?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

44. What is the sum of the measures of the n angles of a polygon with n sides?
Their sum is 180°.
Their sum is 90°.
(n - 2)(180°)
C = p2r

45. 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.
0 is a multiple of every integer.
The product of their slopes is -1 (negative reciprocal).
Shifted right 2 units.

46. What is a prime number?
(x + y)(x - y) = x^2 - y^2
A = lw
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 the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

47. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
(n - 2)(180°)
(b^m)^n = b^mn
For any number b: b = -b if and only if b = 0.

48. 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 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.
1 is a divisor (or factor) of every integer.
A = [(s^2*v3)/4]

49. How do we write the equation of a line?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.
Write the percent as a decimal - and multiply.

50. How do you find the area of a sector of a circle?
Even numbers are divisible by 2 and odd numbers are not.
Then the product xy is a constant.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Area = (x°/360)(pr^2) where x is the central angle.