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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. For what values of a function is the function undefined?
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.
How steep the line is. Horizontal line = 0 - vertical has no slope.
The product of their slopes is -1 (negative reciprocal).

2. How do you convert a percent to a fraction or a decimal?
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
B^m/b^n = b^m-n
Write the percent over 100 and reduce.

3. What is a negative exponent?
For any number n: x^-n means 1/x^n.
1 is a divisor (or factor) of every 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.
An integer greater than one that is not prime.

4. How do you find the probability that an event will occur?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Arc = (x°/360)(2pr) where x is the central angle.
A fraction whose denominator is 100 i.e. 17% = 17/100

5. How do you find the slope of a line?
Arc = (x°/360)(2pr) where x is the central angle.
(x + y)(x - y) = x^2 - y^2
M = (y2 - y1)/(x2 - x1)
They are both the same. A divisor or factor of an integer leaves no remainder.

6. Important binomial 3
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Equal slopes.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

7. How do you calculate a weighted average?
Then the quotient y/x is a constant.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Cannot is 0 - must is 1 - all others are in between.
A = (1/2)bh.

8. What are the properties of a parallelogram?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
An equation that states that two ratios are equivalent. 4/6 = 10/15
0 is a multiple of every integer.

9. What are the properties of a rectangle?
0 is the only number that is neither positive nor negative.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = pr^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.

10. What is the square root of a number?
B^m*b^n = b^m+n
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = s^2 or A =d^2/2 where d is the diagonal
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

11. Important binomial 2
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Avg = sum of n numbers/n
A = (1/2)bh.

12. How do you find the y-intercept of a graph?
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Set x = 0 - and solve.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
A = s^2 or A =d^2/2 where d is the diagonal

13. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
No matter how many angles there are - the sum around the point is 360°.
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.
C = p2r
A = lw

14. 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.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
(n - 2)(180°)
0 is the only number that is neither positive nor negative.

15. Properties of square roots
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
[(x1 + x2)/2] -[(y1 + y2)/2]
For any right triangle - a^2 + b^2 = c^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.

16. How do you find the length of an arc of a circle?
A = bh
Arc = (x°/360)(2pr) where x is the central angle.
V = lwh
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]

17. What does it mean if y is inversely proportional to x?
For any number a: a * 1 = a and a / 1 = a.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
An equation that states that two ratios are equivalent. 4/6 = 10/15
Then the product xy is a constant.

18. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Shifted right 2 units.
V = l^3
A = [(s^2*v3)/4]

19. How do we write the equation of a line?
A^m/b^m = (a/b)^m
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
If a is negative and b is positive - then a < 0 < b.
0 is the only number that is neither positive nor negative.

20. What are the properties of a square?
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
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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

21. Important binomial 1
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
(x + y)(x - y) = x^2 - y^2
A = (1/2)bh.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

22. In a circle of radius r - what is the formula for the circumference?
Shifted down 2 units.
For any number n: x^-n means 1/x^n.
C = p2r
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

23. What are the important properties of a 45-45 - 90 triangle?
Even numbers are divisible by 2 and odd numbers are not.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
For any number b: b = -b if and only if b = 0.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.

24. How do you find the x-intercept of a graph?
C = p2r
Set y = 0 - and solve.
For any integer n: 1^n = 1.
For any right triangle - a^2 + b^2 = c^2.

25. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
Write the percent over 100 and reduce.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
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°.
Shifted left 2 units.

26. Law of exponents 3
For any number a: a * 1 = a and a / 1 = a.
A^m/b^m = (a/b)^m
Is a right triangle with a ratio of sides x:xv3:2x.
(b^m)^n = b^mn

27. Law of exponents 2
B^m/b^n = b^m-n
At least one of the factors is 0.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

28. When a pair of parallel lines is intersected by a third line - what is true about the eight angles that are formed?
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 quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Equal slopes.

29. Law of exponents 5
A^m/b^m = (a/b)^m
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
1 is a divisor (or factor) of every integer.

30. Law of exponents 1
Area = (x°/360)(pr^2) where x is the central angle.
The two pairs of opposite angles formed are equal to each other.
B^m*b^n = b^m+n
Shifted right 2 units.

31. What is the area of a square?
An integer greater than one that is not prime.
A = bh
1 is the smallest positive odd integer.
A = s^2 or A =d^2/2 where d is the diagonal

32. What do we mean by the slope of the line?
Write the percent over 100 and reduce.
Then the product xy is a constant.
At least one of the factors is 0.
How steep the line is. Horizontal line = 0 - vertical has no slope.

33. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
The set of all ordered pairs (x -y) such that y = f(x).
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

34. What is an integer?
All positive and negative whole numbers - and zero.
Write the percent over 100 and reduce.
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.

35. If the product of two or more numbers is 0 - what do you know about the numbers?
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
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.
At least one of the factors is 0.
The set of all ordered pairs (x -y) such that y = f(x).

36. What is special formula for the area of an equilateral triangle?
A = [(s^2*v3)/4]
A = pr^2
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
The two pairs of opposite angles formed are equal to each other.

37. What are the sum - difference - products - and quotient of two numbers?
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
No matter how many angles there are - the sum around the point is 360°.
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).

38. In a circle of radius r - what is the formula for the area?
(Circumference/diameter) of a circle - or approximately 3.14.
A = [(s^2*v3)/4]
A = s^2 or A =d^2/2 where d is the diagonal
A = pr^2

39. Law of exponents 4
A^m*b^m = (ab)^m
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
A = bh
Avg = sum of n numbers/n

40. Properties of one 3
For any integer n: 1^n = 1.
A^m*b^m = (ab)^m
1 is a divisor (or factor) of every integer.
A = (1/2)bh.

41. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted up 2 units.
Shifted left 2 units.

42. What is an exterior angle of a triangle?
They are both the same. A divisor or factor of an integer leaves no remainder.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2

43. What is true about the slopes of parallel lines?
For any number n: x^-n means 1/x^n.
Equal slopes.
M = (y2 - y1)/(x2 - x1)
A = s^2 or A =d^2/2 where d is the diagonal

44. How you convert a fraction or a decimal to a percent?
Then the quotient y/x is a constant.
0 is a multiple of every integer.
180°. If two or more angles form a straight angle - their sum is 180°.
Divide - then multiply by 100.

45. Properties of zero 4
Shifted right 2 units.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any number n: x^-n means 1/x^n.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

46. What is the distance formula?
An equation that states that two ratios are equivalent. 4/6 = 10/15
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

47. What is a fractional exponent?
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.

48. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
At least one of the factors is 0.
360°
Area = (x°/360)(pr^2) where x is the central angle.
An angle formed by extending the side of the polygon.

49. What is a proportion?
V = lwh
A = 6(l^2)
A^m/b^m = (a/b)^m
An equation that states that two ratios are equivalent. 4/6 = 10/15

50. Properties of zero 5
360°
They are both the same. A divisor or factor of an integer leaves no remainder.
Equal slopes.
For any number b: b = -b if and only if b = 0.