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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. Properties of zero 5
For any number b: b = -b if and only if b = 0.
V = lwh
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
For any right triangle - a^2 + b^2 = c^2.

2. What is the area of a square?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Their sum is 90°.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = s^2 or A =d^2/2 where d is the diagonal

3. What is the distributive law?
Is a right triangle with a ratio of sides x:xv3:2x.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Then the product xy is a constant.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

4. Properties of one 4
B^m*b^n = b^m+n
No matter how many angles there are - the sum around the point is 360°.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
1 is the smallest positive odd integer.

5. What do we mean by the slope of the line?
The set of all ordered pairs (x -y) such that y = f(x).
How steep the line is. Horizontal line = 0 - vertical has no slope.
Equal slopes.
They are both the same. A divisor or factor of an integer leaves no remainder.

6. What is a Venn diagram?
Set y = 0 - and solve.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Even numbers are divisible by 2 and odd numbers are not.

7. How do we write the equation of a line?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Area = (x°/360)(pr^2) where x is the central angle.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

8. Law of exponents 1
B^m*b^n = b^m+n
V = l^3
If a is negative and b is positive - then a < 0 < b.
For any right triangle - a^2 + b^2 = c^2.

9. If the product of two or more numbers is 0 - what do you know about the numbers?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
At least one of the factors is 0.
A = lw
Avg = sum of n numbers/n

10. What is true about the areas of similar triangles?
M = (y2 - y1)/(x2 - x1)
0 is the only number that is neither positive nor negative.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

11. In a circle of radius r - what is the formula for the diameter?
At least one of the factors is 0.
D = 2r
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.

12. What is an exterior angle of a triangle?
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
V = pr^2h
Their sum is 90°.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

13. What is a composite number?
An integer greater than one that is not prime.
Corresponding sides of similar triangles are in proportion.
Shifted down 2 units.
V = l^3

14. What is the formula for the area of a rectangle?
(b^m)^n = b^mn
Their sum is 180°.
M = (y2 - y1)/(x2 - x1)
A = lw

15. How do you find the length of an arc of a circle?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
An angle formed by extending the side of the polygon.
Arc = (x°/360)(2pr) where x is the central angle.
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. Properties of square roots
For any number a: a * 1 = a and a / 1 = a.
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
360°
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

17. What is the sum of the measures of all angles around a point?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A = s^2 or A =d^2/2 where d is the diagonal
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
No matter how many angles there are - the sum around the point is 360°.

18. Important binomial 3
Set x = 0 - and solve.
B^m*b^n = b^m+n
0 is a multiple of every integer.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

19. What is a proportion?
An equation that states that two ratios are equivalent. 4/6 = 10/15
All positive and negative whole numbers - and zero.
(n - 2)(180°)
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

20. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
A fraction whose denominator is 100 i.e. 17% = 17/100
360°
0 is a multiple of every integer.

21. What is true about the slopes of perpendicular lines?
A = lw
The product of their slopes is -1 (negative reciprocal).
Then the product xy is a constant.
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°.

22. What is the formula for the area of a parallelogram?
P(e) = (# of favorable outcomes)/(# of possible outcomes)
A = bh
B^m*b^n = b^m+n
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.

23. What is true about the measures of the three angles in a triangle?
Shifted right 2 units.
Their sum is 180°.
V = l^3
A = pr^2

24. For what values of a function is the function undefined?
For any integer n: 1^n = 1.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Corresponding sides of similar triangles are in proportion.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.

25. What is a prime number?
Set y = 0 - and solve.
360°
An integer greater than one that is not prime.
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.

26. What is the relationship between the graph of f(x) the graph of y = f(x + 2)?
(b^m)^n = b^mn
A = [(s^2*v3)/4]
Shifted left 2 units.
V = pr^2h

27. What are the median and the mode of a set of data?
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
All positive and negative whole numbers - and zero.

28. What are the properties of a parallelogram?
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.
If a is negative and b is positive - then a < 0 < b.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.

29. What is a negative exponent?
360°
D = 2r
For any number n: x^-n means 1/x^n.
C = p2r

30. What is the relationship between a radius of a circle and a line that is tangent to the circle?
360°
For any number n: x^-n means 1/x^n.
Equal slopes.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

31. What is the formula for the area of a triangle?
An integer greater than one that is not prime.
A = (1/2)bh.
Shifted down 2 units.
Divide - then multiply by 100.

32. What are the important properties of a 45-45 - 90 triangle?
A = (1/2)bh.
A = pr^2
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Avg = sum of n numbers/n

33. What is the measure of a straight angle?
A = (1/2)bh.
Then the product xy is a constant.
A fraction whose denominator is 100 i.e. 17% = 17/100
180°. If two or more angles form a straight angle - their sum is 180°.

34. Important binomial 1
Shifted up 2 units.
(b^m)^n = b^mn
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
(x + y)(x - y) = x^2 - y^2

35. How do you find the area of a sector of a circle?
How steep the line is. Horizontal line = 0 - vertical has no slope.
Area = (x°/360)(pr^2) where x is the central angle.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A fraction whose denominator is 100 i.e. 17% = 17/100

36. What are the properties of a square?
Shifted up 2 units.
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.
Cannot is 0 - must is 1 - all others are in between.
Set x = 0 - and solve.

37. What are the important properties of 30-60-90 triangle?
Is a right triangle with a ratio of sides x:xv3:2x.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
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.

38. How do you calculate a weighted average?
360°
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

39. What is the formula for the surface area of a cube?
No matter how many angles there are - the sum around the point is 360°.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
The ratio of corresponding sides of similar triangles.
A = 6(l^2)

40. Properties of one 2
For any integer n: 1^n = 1.
(Circumference/diameter) of a circle - or approximately 3.14.
Shifted up 2 units.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

41. What is a divisor and a factor of an integer?
No matter how many angles there are - the sum around the point is 360°.
Then the quotient y/x is a constant.
They are both the same. A divisor or factor of an integer leaves no remainder.
Write the percent over 100 and reduce.

42. What does it mean if y is directly proportional to x?
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.
Then the product xy is a constant.
A = 6(l^2)

43. Law of exponents 3
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Set x = 0 - and solve.
(b^m)^n = b^mn
D = 2r

44. Law of exponents 4
A^m*b^m = (ab)^m
Shifted left 2 units.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
The two pairs of opposite angles formed are equal to each other.

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
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Shifted up 2 units.

46. How you convert a fraction or a decimal to a percent?
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.
Divide - then multiply by 100.
Area = (x°/360)(pr^2) where x is the central angle.
A^m*b^m = (ab)^m

47. How do you find the x-intercept of a graph?
Set y = 0 - and solve.
Corresponding sides of similar triangles are in proportion.
Even numbers are divisible by 2 and odd numbers are not.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

48. What is the formula for the volume of a rectangular solid?
360°
An angle formed by extending the side of the polygon.
Shifted down 2 units.
V = lwh

49. How do you convert a percent to a fraction or a decimal?
Write the percent over 100 and reduce.
The product of their slopes is -1 (negative reciprocal).
Even numbers are divisible by 2 and odd numbers are not.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

50. What is the graph of a function?
Shifted up 2 units.
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.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
The set of all ordered pairs (x -y) such that y = f(x).