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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. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
A = lw
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.
No matter how many angles there are - the sum around the point is 360°.
360°

2. What is the relationship between a radius of a circle and a line that is tangent to the circle?
The two pairs of opposite angles formed are equal to each other.
1 is a divisor (or factor) of every integer.
Shifted right 2 units.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

3. What is true about the areas of similar triangles?
For any right triangle - a^2 + b^2 = c^2.
B^m/b^n = b^m-n
A^m/b^m = (a/b)^m
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

4. Important binomial 2
A^m*b^m = (ab)^m
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
B^m*b^n = b^m+n
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

5. Law of exponents 3
For any number a: a * 1 = a and a / 1 = a.
The set of all ordered pairs (x -y) such that y = f(x).
Set x = 0 - and solve.
(b^m)^n = b^mn

6. How do you find the probability that an event will occur?
For any integer n: 1^n = 1.
V = pr^2h
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)

7. What is true about the slopes of perpendicular lines?
B^m*b^n = b^m+n
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
The product of their slopes is -1 (negative reciprocal).
[(x1 + x2)/2] -[(y1 + y2)/2]

8. What is an exterior angle of a polygon?
A^m/b^m = (a/b)^m
An angle formed by extending the side of the polygon.
0 is a multiple of every integer.
In the expression x^b - x is the base and b is the exponent.

9. How do you find a percent of a number?
C = p2r
Write the percent as a decimal - and multiply.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

10. What is the relationship between the graph of f(x) the graph of y = f(x) + 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.
Shifted up 2 units.
V = pr^2h
Equal slopes.

11. In a circle of radius r - what is the formula for the diameter?
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°.
No matter how many angles there are - the sum around the point is 360°.
D = 2r
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

12. In a circle of radius r - what is the formula for the circumference?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
(Circumference/diameter) of a circle - or approximately 3.14.
C = p2r
A = pr^2

13. What is the square root of a number?
V = l^3
A^m/b^m = (a/b)^m
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Corresponding sides of similar triangles are in proportion.

14. How do you find the area of a sector of a circle?
Area = (x°/360)(pr^2) where x is the central angle.
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 = 2(lw + lh + hw)
0 is the only number that is neither positive nor negative.

15. What is the measure of a straight angle?
All positive and negative whole numbers - and zero.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Shifted left 2 units.
180°. If two or more angles form a straight angle - their sum is 180°.

16. How do you find the y-intercept of a graph?
Set x = 0 - and solve.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
The ratio of corresponding sides of similar triangles.
For any integer n: 1^n = 1.

17. Properties of one 2
For any integer n: 1^n = 1.
For any right triangle - a^2 + b^2 = c^2.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
360°

18. If the product of two or more numbers is 0 - what do you know about the numbers?
At least one of the factors is 0.
Arc = (x°/360)(2pr) where x is the central angle.
The two pairs of opposite angles formed are equal to each other.
Even numbers are divisible by 2 and odd numbers are not.

19. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
0 is a multiple of every integer.
For any number b: b = -b if and only if b = 0.
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 as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

20. In a circle of radius r - what is the formula for the area?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
A = pr^2
180°. If two or more angles form a straight angle - their sum is 180°.

21. What does it mean if y is directly proportional to x?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
180°. If two or more angles form a straight angle - their sum is 180°.
Then the quotient y/x is a constant.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

22. What are the median and the mode of a set of data?
The ratio of corresponding sides of similar triangles.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.
V = l^3

23. What are the quotient and the remainder?

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24. What is a divisor and a factor of an integer?
(Circumference/diameter) of a circle - or approximately 3.14.
They are both the same. A divisor or factor of an integer leaves no remainder.
At least one of the factors is 0.
180°. If two or more angles form a straight angle - their sum is 180°.

25. What is a function?
In the expression x^b - x is the base and b is the exponent.
The ratio of corresponding sides of similar triangles.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(n - 2)(180°)

26. What is an integer?
The set of all ordered pairs (x -y) such that y = f(x).
All positive and negative whole numbers - and zero.
Their sum is 180°.
For any integer n: 1^n = 1.

27. Properties of zero 4
If a is negative and b is positive - then a < 0 < b.
0 is a multiple of every integer.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
Corresponding sides of similar triangles are in proportion.

28. How do you convert a percent to a fraction or a decimal?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A = 6(l^2)
B^m/b^n = b^m-n
Write the percent over 100 and reduce.

29. What are similar triangles?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
(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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

30. What is an even and an odd number?
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 = pr^2
Divide - then multiply by 100.
Even numbers are divisible by 2 and odd numbers are not.

31. What is a Venn diagram?
A = pr^2
180°. If two or more angles form a straight angle - their sum is 180°.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
A = s^2 or A =d^2/2 where d is the diagonal

32. What are the properties of a rectangle?
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.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
C = p2r
For any number a: a * 1 = a and a / 1 = a.

33. What is a ratio?

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34. What is true about the measures of the three angles in a triangle?
Set y = 0 - and solve.
A = lw
Shifted down 2 units.
Their sum is 180°.

35. What is an exponent?
(Circumference/diameter) of a circle - or approximately 3.14.
In the expression x^b - x is the base and b is the exponent.
An integer greater than one that is not prime.
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.

36. Properties of square roots
Arc = (x°/360)(2pr) where x is the central angle.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Then the quotient y/x is a constant.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

37. What is the graph of a function?
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.
For any number a: a * 1 = a and a / 1 = a.
V = lwh

38. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
An angle formed by extending the side of the polygon.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
All positive and negative whole numbers - and zero.

39. What is a multiple of an integer?
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 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 down 2 units.
A^m*b^m = (ab)^m

40. What is the formula for the volume of a cylinder?
Shifted up 2 units.
The product of their slopes is -1 (negative reciprocal).
V = pr^2h
A = lw

41. How you convert a fraction or a decimal to a percent?
1 is a divisor (or factor) of every integer.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
All positive and negative whole numbers - and zero.
Divide - then multiply by 100.

42. What is the Pythagorean theorem?
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.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
For any right triangle - a^2 + b^2 = c^2.
180°. If two or more angles form a straight angle - their sum is 180°.

43. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
Shifted left 2 units.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
(b^m)^n = b^mn

44. Properties of zero 3
A^m*b^m = (ab)^m
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
0 is a multiple of every 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.

45. Properties of one 3
1 is a divisor (or factor) of every integer.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
0 is a multiple of every integer.

46. Law of exponents 2
B^m/b^n = b^m-n
For any number a: a * 1 = a and a / 1 = a.
Equal slopes.
A = s^2 or A =d^2/2 where d is the diagonal

47. For what values of a function is the function undefined?
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.
Divide - then multiply by 100.
(b^m)^n = b^mn
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

48. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
The two pairs of opposite angles formed are equal to each other.
Shifted up 2 units.
For any right triangle - a^2 + b^2 = c^2.

49. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
Shifted right 2 units.
A^m/b^m = (a/b)^m
1 is a divisor (or factor) of every integer.

50. What is the sum of the measures of the n angles of a polygon with n sides?
V = pr^2h
360°
(n - 2)(180°)
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.