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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.
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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 graph of a function?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
The set of all ordered pairs (x -y) such that y = f(x).
A = lw
V = pr^2h

2. What is a prime number?
B^m/b^n = b^m-n
360
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

3. How do you calculate a weighted average?
Write the percent over 100 and reduce.
180. If two or more angles form a straight angle - their sum is 180.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
The product of their slopes is -1 (negative reciprocal).

4. Law of exponents 3
(b^m)^n = b^mn
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
For any number n: x^-n means 1/x^n.
Then the quotient y/x is a constant.

5. What is true about the measures of the three angles in a triangle?
Their sum is 180.
The set of all ordered pairs (x -y) such that y = f(x).
A = [(s^2*v3)/4]
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

6. What is the distributive law?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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 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 = 6(l^2)

7. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Set x = 0 - and solve.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

8. What is special formula for the area of an equilateral triangle?
The set of all ordered pairs (x -y) such that y = f(x).
A = [(s^2*v3)/4]
[(x1 + x2)/2] -[(y1 + y2)/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.

9. What are similar triangles?
A = [(s^2*v3)/4]
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

10. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
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.
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.

11. What is a multiple of an integer?
For any number b: b = -b if and only if b = 0.
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.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
The product of their slopes is -1 (negative reciprocal).

12. What are the properties of a rectangle?
1 is the smallest positive odd integer.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.
B^m*b^n = b^m+n

13. Important binomial 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.
V = l^3
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

14. How do you find the length of an arc of a circle?
No matter how many angles there are - the sum around the point is 360.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180 - and the diagonals bisect.
Arc = (x/360)(2pr) where x is the central angle.
1 is the smallest positive odd integer.

15. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
The ratio of corresponding sides of similar triangles.
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
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.

16. What is the Pythagorean theorem?
C = p2r
For any right triangle - a^2 + b^2 = c^2.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

17. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Shifted right 2 units.
Shifted up 2 units.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

18. What is a negative exponent?
For any number n: x^-n means 1/x^n.
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 positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
A = pr^2

19. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
They are both the same. A divisor or factor of an integer leaves no remainder.
An integer greater than one that is not prime.

20. How do you find the y-intercept of a graph?
For any right triangle - a^2 + b^2 = c^2.
C = p2r
Set x = 0 - and solve.
An integer greater than one that is not prime.

21. What is the square root of a number?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
1 is the smallest positive odd integer.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

22. What is an even and an odd number?
Write the percent over 100 and reduce.
A = 2(lw + lh + hw)
Even numbers are divisible by 2 and odd numbers are not.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

23. What is a divisor and a factor of an integer?
C = p2r
How steep the line is. Horizontal line = 0 - vertical has no slope.
They are both the same. A divisor or factor of an integer leaves no remainder.
Even numbers are divisible by 2 and odd numbers are not.

24. What formula is used for an average?
(x + y)(x - y) = x^2 - y^2
V = l^3
An angle formed by extending the side of the polygon.
Avg = sum of n numbers/n

25. Properties of one 4
360
Then the quotient y/x is a constant.
1 is the smallest positive odd integer.
0 is the only number that is neither positive nor negative.

26. What is true about the measures of the two acute angles in a right triangle?
A fraction whose denominator is 100 i.e. 17% = 17/100
Their sum is 90.
Avg = sum of n numbers/n
(Circumference/diameter) of a circle - or approximately 3.14.

27. What is an exterior angle of a polygon?
180. If two or more angles form a straight angle - their sum is 180.
A = 6(l^2)
D = 2r
An angle formed by extending the side of the polygon.

28. How do you find the probability that an event will occur?
All positive and negative whole numbers - and zero.
M = (y2 - y1)/(x2 - x1)
P(e) = (# of favorable outcomes)/(# of possible outcomes)
No matter how many angles there are - the sum around the point is 360.

29. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
Equal slopes.
A^m/b^m = (a/b)^m
A = 6(l^2)

30. Important binomial 1
360
Set y = 0 - and solve.
V = lwh
(x + y)(x - y) = x^2 - y^2

31. What is true about the slopes of parallel lines?
0 is a multiple of every integer.
Set y = 0 - and solve.
Equal slopes.
An integer greater than one that is not prime.

32. What do we mean by the slope of the line?
0 is the only number that is neither positive nor negative.
How steep the line is. Horizontal line = 0 - vertical has no slope.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
In the expression x^b - x is the base and b is the exponent.

33. What is the probability of an event that cannot occur? That must occur?
A = 6(l^2)
Cannot is 0 - must is 1 - all others are in between.
For any integer n: 1^n = 1.
Shifted down 2 units.

34. What is the triangle inequality?
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.
For any right triangle - a^2 + b^2 = c^2.
An integer greater than one that is not prime.

35. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
360
Shifted right 2 units.
(x + y)(x - y) = x^2 - y^2
1 is a divisor (or factor) of every integer.

36. What are the sum - difference - products - and quotient of two numbers?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
An angle formed by extending the side of the polygon.
The two pairs of opposite angles formed are equal to each other.

37. What is the relationship between a radius of a circle and a line that is tangent to the circle?
Set x = 0 - and solve.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = lw

38. How do you convert a percent to a fraction or a decimal?
C = p2r
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.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Write the percent over 100 and reduce.

39. What is true about the measures of the four angles formed by two intersecting lines?
The two pairs of opposite angles formed are equal to each other.
C = p2r
A = pr^2
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

40. What does it mean if y is directly proportional to x?
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Then the quotient y/x is a constant.

41. What is a composite number?
A fraction whose denominator is 100 i.e. 17% = 17/100
An integer greater than one that is not prime.
Their sum is 180.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

42. What is an integer?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
All positive and negative whole numbers - and zero.
360
A = bh

43. What is the formula for the area of a triangle?
A = (1/2)bh.
All positive and negative whole numbers - and zero.
Then the product xy is a constant.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

44. If you were given the graph of y = f(x) - what does f(a) represent?
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.
180. If two or more angles form a straight angle - their sum is 180.
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.

45. What is a percent?
For any number n: x^-n means 1/x^n.
A fraction whose denominator is 100 i.e. 17% = 17/100
Their sum is 90.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.

46. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Same as a parallelogram - as well as each angle is 90 - and the diagonals are congruent.
(b^m)^n = b^mn
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Shifted down 2 units.

47. What is true about the areas of similar triangles?
Corresponding sides of similar triangles are in proportion.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Write the percent over 100 and reduce.
Shifted down 2 units.

48. What is the sum of the measures of the four angles in a quadrilateral?
D = 2r
360
Opposite sides and angles are congruent - the sum of any two consecutive angles is180 - and the diagonals bisect.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

49. Law of exponents 1
B^m*b^n = b^m+n
Then the quotient y/x is a constant.
Their sum is 180.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

50. What are the important properties of 30-60-90 triangle?
For any integer n: 1^n = 1.
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 fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Is a right triangle with a ratio of sides x:xv3:2x.

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