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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. What is the sum of the measures of the n angles of a polygon with n sides?
Then the quotient y/x is a constant.
If a is negative and b is positive - then a < 0 < b.
For any number b: b = -b if and only if b = 0.
(n - 2)(180°)

2. What is an integer?
1 is the smallest positive odd integer.
Write the percent over 100 and reduce.
A fraction whose denominator is 100 i.e. 17% = 17/100
All positive and negative whole numbers - and zero.

3. What is the probability of an event that cannot occur? That must occur?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Cannot is 0 - must is 1 - all others are in between.
A = (1/2)bh.
An angle formed by extending the side of the polygon.

4. How do you calculate percent increases and decreases?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
B^m*b^n = b^m+n

5. What is p?
Set y = 0 - and solve.
Write the percent over 100 and reduce.
(Circumference/diameter) of a circle - or approximately 3.14.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

6. What is the graph of a function?
The set of all ordered pairs (x -y) such that y = f(x).
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°.
They are both the same. A divisor or factor of an integer leaves no remainder.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

7. What is the formula for the area of a parallelogram?
A = bh
The ratio of corresponding sides of similar triangles.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

8. What is true about the slopes of perpendicular lines?
Is a right triangle with a ratio of sides x:xv3:2x.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
The product of their slopes is -1 (negative reciprocal).
A = 6(l^2)

9. What is an even and an odd number?
Even numbers are divisible by 2 and odd numbers are not.
A = s^2 or A =d^2/2 where d is the diagonal
Then the quotient y/x is a constant.
1 is the smallest positive odd integer.

10. How do you find the probability that an event will occur?
M = (y2 - y1)/(x2 - x1)
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For any integer n: 1^n = 1.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

11. Important binomial 1
For any integer n: 1^n = 1.
(x + y)(x - y) = x^2 - y^2
V = pr^2h
360°

12. What do we mean by the slope of the line?
For any integer n: 1^n = 1.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For any number a: a * 1 = a and a / 1 = a.
How steep the line is. Horizontal line = 0 - vertical has no slope.

13. What is the ratio of similitude?
A = lw
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.
Area = (x°/360)(pr^2) where x is the central angle.

14. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
They are both the same. A divisor or factor of an integer leaves no remainder.
A^m/b^m = (a/b)^m
(n - 2)(180°)

15. Properties of zero 2
An integer greater than one that is not prime.
[(x1 + x2)/2] -[(y1 + y2)/2]
If a is negative and b is positive - then a < 0 < b.
The set of all ordered pairs (x -y) such that y = f(x).

16. What formula is used for an average?
Write the percent as a decimal - and multiply.
Avg = sum of n numbers/n
A = [(s^2*v3)/4]
The product of their slopes is -1 (negative reciprocal).

17. Law of exponents 3
M = (y2 - y1)/(x2 - x1)
A = s^2 or A =d^2/2 where d is the diagonal
(b^m)^n = b^mn
180°. If two or more angles form a straight angle - their sum is 180°.

18. If you were given the graph of y = f(x) - what does f(a) represent?
Set x = 0 - and solve.
Arc = (x°/360)(2pr) where x is the central angle.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A^m/b^m = (a/b)^m

19. How do you find the y-intercept of a graph?
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.
For any number a: a * 1 = a and a / 1 = a.
Set x = 0 - and solve.

20. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

21. What is the Pythagorean theorem?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
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 fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
For any right triangle - a^2 + b^2 = c^2.

22. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Then the quotient y/x is a constant.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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°.
A = lw

23. What is an exterior angle of a triangle?
0 is a multiple of every integer.
B^m/b^n = b^m-n
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

24. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
360°
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.
Shifted up 2 units.

25. What are the important properties of a 45-45 - 90 triangle?
(x + y)(x - y) = x^2 - y^2
(b^m)^n = b^mn
Divide - then multiply by 100.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

26. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
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°.
Shifted down 2 units.

27. What is an exterior angle of a polygon?
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.
An angle formed by extending the side of the polygon.
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°.

28. What are the median and the mode of a set of data?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Divide - then multiply by 100.
For any number n: x^-n means 1/x^n.
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.

29. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
For any number a: a * 1 = a and a / 1 = a.
V = lwh
(x + y)(x - y) = x^2 - y^2

30. What is a percent?
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.
1 is the smallest positive odd integer.
All positive and negative whole numbers - and zero.

31. How do you find a percent of a number?
(n - 2)(180°)
Write the percent as a decimal - and multiply.
Avg = sum of n numbers/n
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

32. Properties of one 4
A = [(s^2*v3)/4]
Shifted down 2 units.
1 is the smallest positive odd integer.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

33. What are similar triangles?
Area = (x°/360)(pr^2) where x is the central angle.
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°.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

34. What are the sum - difference - products - and quotient of two numbers?
180°. If two or more angles form a straight angle - their sum is 180°.
In the expression x^b - x is the base and b is the exponent.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

35. What is true about the slopes of parallel lines?
A = bh
Shifted left 2 units.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Equal slopes.

36. Properties of zero 1
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
C = p2r
0 is the only number that is neither positive nor negative.

37. What are the quotient and the remainder?

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38. What is the sum of the measures of all angles around a point?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
No matter how many angles there are - the sum around the point is 360°.
Their sum is 180°.
A = s^2 or A =d^2/2 where d is the diagonal

39. What are the properties of a rectangle?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(n - 2)(180°)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
D = 2r

40. What does it mean if y is inversely proportional to x?
Then the product xy is a constant.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
(Circumference/diameter) of a circle - or approximately 3.14.
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.

41. What is a function?
Their sum is 180°.
A fraction whose denominator is 100 i.e. 17% = 17/100
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

42. What is the triangle inequality?
360°
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.
For any number a: a * 1 = a and a / 1 = a.

43. Properties of one 3
Set x = 0 - and solve.
1 is a divisor (or factor) of every integer.
Their sum is 90°.
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.

44. Law of exponents 1
Write the percent as a decimal - and multiply.
How steep the line is. Horizontal line = 0 - vertical has no slope.
360°
B^m*b^n = b^m+n

45. What is a ratio?

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46. What is special formula for the area of an equilateral triangle?
Area = (x°/360)(pr^2) where x is the central angle.
1 is the smallest positive odd integer.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = [(s^2*v3)/4]

47. Properties of zero 5
A fraction whose denominator is 100 i.e. 17% = 17/100
For any number b: b = -b if and only if b = 0.
Set x = 0 - and solve.
Is a right triangle with a ratio of sides x:xv3:2x.

48. What are the properties of a square?
Cannot is 0 - must is 1 - all others are in between.
180°. If two or more angles form a straight angle - their sum is 180°.
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.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

49. What are the properties of a parallelogram?
1 is the smallest positive odd integer.
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.
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.

50. How do we write the equation of a line?
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.
For any number b: b = -b if and only if b = 0.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.