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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. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Avg = sum of n numbers/n
A = 6(l^2)
A = pr^2
360°

2. What is an even and an odd number?
V = l^3
A fraction whose denominator is 100 i.e. 17% = 17/100
Even numbers are divisible by 2 and odd numbers are not.
For any integer n: 1^n = 1.

3. In a circle of radius r - what is the formula for the circumference?
A = 2(lw + lh + hw)
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.
An equation that states that two ratios are equivalent. 4/6 = 10/15
C = p2r

4. What is the measure of a straight angle?
Area = (x°/360)(pr^2) where x is the central angle.
180°. If two or more angles form a straight angle - their sum is 180°.
Equal slopes.
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.

5. What are similar triangles?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
C = p2r
A = (1/2)bh.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

6. What is a prime number?
180°. If two or more angles form a straight angle - their sum is 180°.
A = [(s^2*v3)/4]
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.
They are both the same. A divisor or factor of an integer leaves no remainder.

7. What is a percent?
All positive and negative whole numbers - and zero.
The product of their slopes is -1 (negative reciprocal).
(b^m)^n = b^mn
A fraction whose denominator is 100 i.e. 17% = 17/100

8. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
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.
Arc = (x°/360)(2pr) where x is the central angle.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

9. What is the triangle inequality?
In the expression x^b - x is the base and b is the exponent.
B^m*b^n = b^m+n
All positive and negative whole numbers - and zero.
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.

10. What are the sum - difference - products - and quotient of two numbers?
A = lw
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Shifted up 2 units.
The product of their slopes is -1 (negative reciprocal).

11. What is true about the measures of the four angles formed by two intersecting lines?
V = lwh
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
All positive and negative whole numbers - and zero.
The two pairs of opposite angles formed are equal to each other.

12. What is true about the slopes of perpendicular lines?
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).
Is a right triangle with a ratio of sides x:xv3:2x.
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.

13. What is p?
A = [(s^2*v3)/4]
All positive and negative whole numbers - and zero.
(Circumference/diameter) of a circle - or approximately 3.14.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

14. What important property do similar triangles have?
The set of all ordered pairs (x -y) such that y = f(x).
The product of their slopes is -1 (negative reciprocal).
V = l^3
Corresponding sides of similar triangles are in proportion.

15. What are the important properties of a 45-45 - 90 triangle?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

16. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The two pairs of opposite angles formed are equal to each other.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
V = l^3

17. What is a multiple of an integer?
An angle formed by extending the side of the polygon.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Even numbers are divisible by 2 and odd numbers are not.
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.

18. What is a divisor and a factor of an integer?
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Shifted right 2 units.
They are both the same. A divisor or factor of an integer leaves no remainder.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

19. How do you find the length of an arc of a circle?
For any integer n: 1^n = 1.
(Circumference/diameter) of a circle - or approximately 3.14.
Cannot is 0 - must is 1 - all others are in between.
Arc = (x°/360)(2pr) where x is the central angle.

20. Law of exponents 2
An equation that states that two ratios are equivalent. 4/6 = 10/15
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
B^m/b^n = b^m-n
360°

21. In a circle of radius r - what is the formula for the area?
A = pr^2
Arc = (x°/360)(2pr) where x is the central angle.
Then the quotient y/x is a constant.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

22. Law of exponents 5
A^m/b^m = (a/b)^m
Then the product xy is a constant.
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.
(n - 2)(180°)

23. How do you find the y-intercept of a graph?
Even numbers are divisible by 2 and odd numbers are not.
Set x = 0 - and solve.
For any right triangle - a^2 + b^2 = c^2.
Then the product xy is a constant.

24. Important binomial 2
The ratio of corresponding sides of similar triangles.
A^m/b^m = (a/b)^m
Shifted up 2 units.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

25. In a circle of radius r - what is the formula for the diameter?
D = 2r
Cannot is 0 - must is 1 - all others are in between.
B^m*b^n = b^m+n
Divide - then multiply by 100.

26. 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.
1 is the smallest positive odd integer.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Even numbers are divisible by 2 and odd numbers are not.

27. What is the distributive law?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
B^m*b^n = b^m+n
For any number b: b = -b if and only if b = 0.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

28. What does it mean if y is directly proportional to x?
B^m*b^n = b^m+n
Then the quotient y/x is a constant.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

29. If you were given the graph of y = f(x) - what does f(a) represent?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
The product of their slopes is -1 (negative reciprocal).
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.
They are both the same. A divisor or factor of an integer leaves no remainder.

30. What is the probability of an event that cannot occur? That must occur?
Set y = 0 - and solve.
Cannot is 0 - must is 1 - all others are in between.
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.
How steep the line is. Horizontal line = 0 - vertical has no slope.

31. What is the formula for the area of a triangle?
(Circumference/diameter) of a circle - or approximately 3.14.
360°
A = (1/2)bh.
A = [(s^2*v3)/4]

32. What is the formula for the area of a rectangle?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
A = lw
M = (y2 - y1)/(x2 - x1)

33. What is the midpoint formula?
A^m*b^m = (ab)^m
[(x1 + x2)/2] -[(y1 + y2)/2]
Their sum is 180°.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

34. What is a fractional exponent?
Their sum is 90°.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For any integer n: 1^n = 1.
Then the product xy is a constant.

35. How do you find the x-intercept of a graph?
Write the percent as a decimal - and multiply.
0 is the only number that is neither positive nor negative.
Set y = 0 - and solve.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

36. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
V = pr^2h
The two pairs of opposite angles formed are equal to each other.
The ratio of corresponding sides of similar triangles.

37. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Divide - then multiply by 100.
Shifted right 2 units.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
A = lw

38. Properties of zero 1
0 is the only number that is neither positive nor negative.
How steep the line is. Horizontal line = 0 - vertical has no slope.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
D = 2r

39. What is an exterior angle of a polygon?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
An angle formed by extending the side of the polygon.
For any number a: a * 1 = a and a / 1 = a.
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.

40. What does it mean if y is inversely proportional to x?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
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.
A^m*b^m = (ab)^m
Then the product xy is a constant.

41. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
An integer greater than one that is not prime.
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°.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

42. How do you find the probability that an event will occur?
V = pr^2h
Equal slopes.
For any integer n: 1^n = 1.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

43. What is the formula for the surface area of a rectangular solid?
A = 2(lw + lh + hw)
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Write the percent over 100 and reduce.
If a is negative and b is positive - then a < 0 < b.

44. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
(Circumference/diameter) of a circle - or approximately 3.14.
For any number n: x^-n means 1/x^n.

45. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
If a is negative and b is positive - then a < 0 < b.
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 any right triangle - a^2 + b^2 = c^2.

46. What is a function?
C = p2r
A^m*b^m = (ab)^m
The ratio of corresponding sides of similar triangles.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

47. What is a negative exponent?
For any number n: x^-n means 1/x^n.
A = 6(l^2)
A = [(s^2*v3)/4]
(Circumference/diameter) of a circle - or approximately 3.14.

48. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = (1/2)bh.
Area = (x°/360)(pr^2) where x is the central angle.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

49. What is the sum of the measures of all angles around a point?
Then the product xy is a constant.
1 is a divisor (or factor) of every integer.
No matter how many angles there are - the sum around the point is 360°.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

50. How do you find the area of a sector of a circle?
Set x = 0 - and solve.
Area = (x°/360)(pr^2) where x is the central angle.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
D = 2r