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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. How do you calculate a weighted average?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A = 6(l^2)
Set x = 0 - and solve.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

2. What is the formula for the area of a triangle?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A = (1/2)bh.
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.
All positive and negative whole numbers - and zero.

3. What is a proportion?
M = (y2 - y1)/(x2 - x1)
0 is a multiple of every integer.
For any integer n: 1^n = 1.
An equation that states that two ratios are equivalent. 4/6 = 10/15

4. 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.
No matter how many angles there are - the sum around the point is 360°.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
An integer greater than one that is not prime.

5. Properties of one 4
(b^m)^n = b^mn
1 is the smallest positive odd integer.
Shifted down 2 units.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

6. What is the graph of a function?
V = pr^2h
A = pr^2
At least one of the factors is 0.
The set of all ordered pairs (x -y) such that y = f(x).

7. What is a composite number?
An integer greater than one that is not prime.
An angle formed by extending the side of the polygon.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
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.

8. In a circle of radius r - what is the formula for the area?
Shifted right 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Then the quotient y/x is a constant.
A = pr^2

9. How you convert a fraction or a decimal to a percent?
Corresponding sides of similar triangles are in proportion.
Divide - then multiply by 100.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The ratio of corresponding sides of similar triangles.

10. What is an exponent?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
180°. If two or more angles form a straight angle - their sum is 180°.
A = lw
In the expression x^b - x is the base and b is the exponent.

11. What is the Pythagorean theorem?
For any right triangle - a^2 + b^2 = c^2.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
No matter how many angles there are - the sum around the point is 360°.
Shifted up 2 units.

12. What are the properties of a square?
C = p2r
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

13. What are the median and the mode of a set of data?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The product of their slopes is -1 (negative reciprocal).
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 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.

14. Important binomial 2
An equation that states that two ratios are equivalent. 4/6 = 10/15
For any right triangle - a^2 + b^2 = c^2.
Write the percent as a decimal - and multiply.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

15. What is a multiple of an integer?
All positive and negative whole numbers - and zero.
(n - 2)(180°)
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 = bh

16. Properties of one 1
For any number a: a * 1 = a and a / 1 = a.
0 is the only number that is neither positive nor negative.
Divide - then multiply by 100.
A = 6(l^2)

17. What is the sum of the measures of the n angles of a polygon with n sides?
Avg = sum of n numbers/n
D = 2r
(n - 2)(180°)
A = bh

18. How do you find the y-intercept of a graph?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Set x = 0 - and solve.
If a is negative and b is positive - then a < 0 < b.
Shifted down 2 units.

19. What is the volume of a cube?
Shifted down 2 units.
V = l^3
An angle formed by extending the side of the polygon.
0 is a multiple of every integer.

20. What is true about the slopes of parallel lines?
1 is the smallest positive odd integer.
V = lwh
Equal slopes.
Area = (x°/360)(pr^2) where x is the central angle.

21. Important binomial 3
An integer greater than one that is not prime.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Divide - then multiply by 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.

22. What does it mean if y is inversely proportional to x?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
360°
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Then the product xy is a constant.

23. If you were given the graph of y = f(x) - what does f(a) represent?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

24. What is the formula for the area of a parallelogram?
A = bh
All positive and negative whole numbers - and zero.
Then the product xy is a constant.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

25. Properties of one 3
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.
1 is a divisor (or factor) of every integer.
For any number a: a * 1 = a and a / 1 = a.

26. Law of exponents 4
Then the product xy is a constant.
Their sum is 90°.
Divide - then multiply by 100.
A^m*b^m = (ab)^m

27. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
B^m/b^n = b^m-n
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

28. What is the triangle inequality?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Their sum is 90°.
Write the percent as a decimal - and multiply.
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.

29. What is a Venn diagram?
A = bh
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
0 is the only number that is neither positive nor negative.
At least one of the factors is 0.

30. What is true about the slopes of perpendicular lines?
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
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°.
The product of their slopes is -1 (negative reciprocal).
Write the percent as a decimal - and multiply.

31. Properties of zero 4
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.
Shifted right 2 units.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

32. Law of exponents 2
Then the product xy is a constant.
B^m/b^n = b^m-n
A^m/b^m = (a/b)^m
For any number n: x^-n means 1/x^n.

33. In a circle of radius r - what is the formula for the circumference?
C = p2r
At least one of the factors is 0.
A = bh
An angle formed by extending the side of the polygon.

34. Law of exponents 5
(x + y)(x - y) = x^2 - y^2
A^m/b^m = (a/b)^m
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
The product of their slopes is -1 (negative reciprocal).

35. What is an exterior angle of a triangle?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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°.
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.

36. What formula is used for an average?
0 is a multiple of every integer.
Avg = sum of n numbers/n
Is a right triangle with a ratio of sides x:xv3:2x.
0 is the only number that is neither positive nor negative.

37. Properties of one 2
Shifted down 2 units.
A = pr^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
For any integer n: 1^n = 1.

38. Properties of square roots
V = lwh
V = l^3
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

39. What is a function?
The set of all ordered pairs (x -y) such that y = f(x).
(x + y)(x - y) = x^2 - y^2
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

40. What are the important properties of 30-60-90 triangle?
The ratio of corresponding sides of similar triangles.
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.
Is a right triangle with a ratio of sides x:xv3:2x.
They are both the same. A divisor or factor of an integer leaves no remainder.

41. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
For any number b: b = -b if and only if b = 0.
Set x = 0 - and solve.
The product of their slopes is -1 (negative reciprocal).

42. What are similar triangles?
The set of all ordered pairs (x -y) such that y = f(x).
(n - 2)(180°)
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

43. What is a divisor and a factor of an integer?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A^m*b^m = (ab)^m
Then the product xy is a constant.
They are both the same. A divisor or factor of an integer leaves no remainder.

44. How do you find a percent of a number?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Write the percent as a decimal - and multiply.
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.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

45. Properties of zero 2
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 set of all ordered pairs (x -y) such that y = f(x).
If a is negative and b is positive - then a < 0 < b.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

46. What is the measure of a straight angle?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Is a right triangle with a ratio of sides x:xv3:2x.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
180°. If two or more angles form a straight angle - their sum is 180°.

47. For what values of a function is the function undefined?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
The two pairs of opposite angles formed are equal to each other.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

48. What is a ratio?

49. What is the formula for the volume of a cylinder?
The product of their slopes is -1 (negative reciprocal).
V = pr^2h
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
M = (y2 - y1)/(x2 - x1)

50. 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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Corresponding sides of similar triangles are in proportion.
Then the product xy is a constant.