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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 find the probability that an event will occur?
V = l^3
Then the product xy is a constant.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A = (1/2)bh.

2. Important binomial 3
Corresponding sides of similar triangles are in proportion.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
P(e) = (# of favorable outcomes)/(# of possible outcomes)

3. What is the measure of a straight angle?
Then the quotient y/x is a constant.
Arc = (x°/360)(2pr) where x is the central angle.
180°. If two or more angles form a straight angle - their sum is 180°.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

4. How do you convert a percent to a fraction or a decimal?
180°. If two or more angles form a straight angle - their sum is 180°.
V = l^3
M = (y2 - y1)/(x2 - x1)
Write the percent over 100 and reduce.

5. What are the properties of a rectangle?
1 is a divisor (or factor) of every integer.
Their sum is 90°.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

6. What is a proportion?
Write the percent as a decimal - and multiply.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
For any number b: b = -b if and only if b = 0.
An equation that states that two ratios are equivalent. 4/6 = 10/15

7. What is a divisor and a factor of an integer?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
The set of all ordered pairs (x -y) such that y = f(x).
They are both the same. A divisor or factor of an integer leaves no remainder.

8. How you convert a fraction or a decimal to a percent?
An equation that states that two ratios are equivalent. 4/6 = 10/15
In the expression x^b - x is the base and b is the exponent.
C = p2r
Divide - then multiply by 100.

9. What are the important properties of 30-60-90 triangle?
A = s^2 or A =d^2/2 where d is the diagonal
B^m*b^n = b^m+n
Is a right triangle with a ratio of sides x:xv3:2x.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

10. In a circle of radius r - what is the formula for the diameter?
A = 6(l^2)
Avg = sum of n numbers/n
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
D = 2r

11. What is the sum of the measures of all angles around a point?
A = 2(lw + lh + hw)
No matter how many angles there are - the sum around the point is 360°.
A = (1/2)bh.
A = 6(l^2)

12. If you were given the graph of y = f(x) - what does f(a) represent?
A^m/b^m = (a/b)^m
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

13. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.
360°

14. Law of exponents 1
360°
A = 2(lw + lh + hw)
B^m*b^n = b^m+n
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

15. What is the probability of an event that cannot occur? That must occur?
An equation that states that two ratios are equivalent. 4/6 = 10/15
360°
Cannot is 0 - must is 1 - all others are in between.
M = (y2 - y1)/(x2 - x1)

16. Important binomial 1
(x + y)(x - y) = x^2 - y^2
A = bh
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(n - 2)(180°)

17. Properties of zero 5
For any number b: b = -b if and only if b = 0.
M = (y2 - y1)/(x2 - x1)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
V = pr^2h

18. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Shifted left 2 units.
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^m*b^m = (ab)^m
All positive and negative whole numbers - and zero.

19. How do you calculate percent increases and decreases?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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.
0 is a multiple of every integer.
Area = (x°/360)(pr^2) where x is the central angle.

20. If the product of two or more numbers is 0 - what do you know about the numbers?
Write the percent as a decimal - and multiply.
Avg = sum of n numbers/n
D = 2r
At least one of the factors is 0.

21. What is the volume of a cube?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
V = l^3
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

22. What are the properties of a square?
A = s^2 or A =d^2/2 where d is the diagonal
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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°

23. What are the sum - difference - products - and quotient of two numbers?
A = pr^2
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

24. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
Their sum is 180°.
(n - 2)(180°)
For any number n: x^-n means 1/x^n.

25. What is an integer?
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
All positive and negative whole numbers - and zero.
1 is a divisor (or factor) of every integer.
Write the percent over 100 and reduce.

26. Properties of one 2
1 is a divisor (or factor) of every integer.
For any integer n: 1^n = 1.
Then the quotient y/x is a constant.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

27. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
(x + y)(x - y) = x^2 - y^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 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.

28. In a circle of radius r - what is the formula for the area?
For any integer n: 1^n = 1.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
B^m/b^n = b^m-n
A = pr^2

29. Properties of one 4
1 is the smallest positive odd integer.
For any right triangle - a^2 + b^2 = c^2.
0 is a multiple of every integer.
(Circumference/diameter) of a circle - or approximately 3.14.

30. How do you find a percent of a number?
Write the percent as a decimal - and multiply.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
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 = 2(lw + lh + hw)

31. How do you find the area of a sector of a circle?
Shifted left 2 units.
A = pr^2
Area = (x°/360)(pr^2) where x is the central angle.
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.

32. What is an exterior angle of a polygon?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
0 is the only number that is neither positive nor negative.
An angle formed by extending the side of the polygon.
For any number b: b = -b if and only if b = 0.

33. How do we write the equation of a line?
An equation that states that two ratios are equivalent. 4/6 = 10/15
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted up 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

34. How do you find the slope of a line?
M = (y2 - y1)/(x2 - x1)
Shifted left 2 units.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

35. What important property do similar triangles have?
A fraction whose denominator is 100 i.e. 17% = 17/100
Corresponding sides of similar triangles are in proportion.
The two pairs of opposite angles formed are equal to each other.
360°

36. What is the formula for the surface area of a cube?
180°. If two or more angles form a straight angle - their sum is 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 = 6(l^2)
A = bh

37. What is the sum of the measures of the four angles in a quadrilateral?
Shifted right 2 units.
All positive and negative whole numbers - and zero.
Write the percent as a decimal - and multiply.
360°

38. What are the quotient and the remainder?

39. What is the formula for the area of a rectangle?
Set y = 0 - and solve.
A = lw
1 is a divisor (or factor) of every integer.
M = (y2 - y1)/(x2 - x1)

40. What is a prime number?
C = p2r
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 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.
A^m/b^m = (a/b)^m

41. What is true about the measures of the four angles formed by two intersecting lines?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
The two pairs of opposite angles formed are equal to each other.
C = p2r
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.

42. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^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 longest side is opposite the largest angle - the shortest side is opposite the smallest angle - and same length sides are opposite same measure angles.
The set of all ordered pairs (x -y) such that y = f(x).

43. How do you find the x-intercept of a graph?
A = 6(l^2)
Set y = 0 - and solve.
Is a right triangle with a ratio of sides x:xv3:2x.
Avg = sum of n numbers/n

44. What is a percent?
A fraction whose denominator is 100 i.e. 17% = 17/100
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.
Write the percent as a decimal - and multiply.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

45. What is the area of a square?
Is a right triangle with a ratio of sides x:xv3:2x.
A = s^2 or A =d^2/2 where d is the diagonal
Arc = (x°/360)(2pr) where x is the central angle.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

46. What is true about the areas of similar triangles?
Area = (x°/360)(pr^2) where x is the central angle.
A = lw
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Divide - then multiply by 100.

47. What is the graph of a function?
No matter how many angles there are - the sum around the point is 360°.
Even numbers are divisible by 2 and odd numbers are not.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
The set of all ordered pairs (x -y) such that y = f(x).

48. What is the distributive law?
A = bh
Shifted down 2 units.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

49. What is the distance formula?
A = [(s^2*v3)/4]
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
(b^m)^n = b^mn
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

50. What is the sum of the measures of the n angles of a polygon with n sides?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
At least one of the factors is 0.
No matter how many angles there are - the sum around the point is 360°.
(n - 2)(180°)