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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. What is the formula for the volume of a cylinder?
V = pr^2h
(b^m)^n = b^mn
All positive and negative whole numbers - and zero.
For any number n: x^-n means 1/x^n.

2. What is the distance formula?
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.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.

3. Properties of one 4
P(e) = (# of favorable outcomes)/(# of possible outcomes)
For any integer n: 1^n = 1.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
1 is the smallest positive odd integer.

4. What is a prime number?
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°.
For any integer n: 1^n = 1.
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.
Equal slopes.

5. What is a multiple of an integer?
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.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
V = l^3
A = s^2 or A =d^2/2 where d is the diagonal

6. 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.
Is a right triangle with a ratio of sides x:xv3:2x.
(b^m)^n = b^mn
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

7. What is a negative exponent?
Cannot is 0 - must is 1 - all others are in between.
V = l^3
For any number n: x^-n means 1/x^n.
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

8. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
360°
A = [(s^2*v3)/4]
Divide - then multiply by 100.

9. What is the graph of a function?
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
(n - 2)(180°)
For any number n: x^-n means 1/x^n.
The set of all ordered pairs (x -y) such that y = f(x).

10. What is the volume of a cube?
0 is the only number that is neither positive nor negative.
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.
V = l^3

11. Law of exponents 5
No matter how many angles there are - the sum around the point is 360°.
An angle formed by extending the side of the polygon.
A^m/b^m = (a/b)^m
Avg = sum of n numbers/n

12. What are the important properties of 30-60-90 triangle?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Is a right triangle with a ratio of sides x:xv3:2x.
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.
Then the product xy is a constant.

13. What is the sum of the measures of the four angles in a quadrilateral?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Area = (x°/360)(pr^2) where x is the central angle.
A fraction whose denominator is 100 i.e. 17% = 17/100
360°

14. What is the probability of an event that cannot occur? That must occur?
(x + y)(x - y) = x^2 - y^2
For any number n: x^-n means 1/x^n.
All positive and negative whole numbers - and zero.
Cannot is 0 - must is 1 - all others are in between.

15. What is the square root of a number?
(x + y)(x - y) = x^2 - y^2
360°
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.

16. Properties of zero 1
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
1 is a divisor (or factor) of every integer.
0 is the only number that is neither positive nor negative.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

17. Law of exponents 4
For any number a: a * 1 = a and a / 1 = a.
For any number b: b = -b if and only if b = 0.
A^m*b^m = (ab)^m
Shifted right 2 units.

18. What do we mean by the slope of the line?
Shifted left 2 units.
How steep the line is. Horizontal line = 0 - vertical has no slope.
A^m*b^m = (ab)^m
For any integer n: 1^n = 1.

19. What is the sum of the measures of all angles around a point?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Set x = 0 - and solve.
No matter how many angles there are - the sum around the point is 360°.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

20. What important property do similar triangles have?
Corresponding sides of similar triangles are in proportion.
D = 2r
An angle formed by extending the side of the polygon.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.

21. What are the properties of a square?
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.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + 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.

22. What is a divisor and a factor of an integer?
V = pr^2h
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
They are both the same. A divisor or factor of an integer leaves no remainder.
An equation that states that two ratios are equivalent. 4/6 = 10/15

23. What is the triangle inequality?
The product of their slopes is -1 (negative reciprocal).
A = (1/2)bh.
An integer greater than one that is not prime.
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.

24. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
C = p2r
Shifted right 2 units.
A = 2(lw + lh + hw)
Divide - then multiply by 100.

25. What formula is used for an average?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Avg = sum of n numbers/n
For any number a: a * 1 = a and a / 1 = a.
(x + y)(x - y) = x^2 - y^2

26. What are similar triangles?
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
A = s^2 or A =d^2/2 where d is the diagonal
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.

27. Law of exponents 3
0 is a multiple of every integer.
For any integer n: 1^n = 1.
For any right triangle - a^2 + b^2 = c^2.
(b^m)^n = b^mn

28. How do you find the area of a sector of a circle?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
Area = (x°/360)(pr^2) where x is the central angle.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
An angle formed by extending the side of the polygon.

29. What is the formula for the surface area of a cube?
An angle formed by extending the side of the polygon.
Divide - then multiply by 100.
A = 6(l^2)
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.

30. What is true about the measures of the three angles in a triangle?
In the expression x^b - x is the base and b is the exponent.
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
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.
Their sum is 180°.

31. What is the sum of the measures of the n angles of a polygon with n sides?
(n - 2)(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 fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
B^m*b^n = b^m+n

32. What is the area of a square?
A = 6(l^2)
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
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.

33. What is the ratio of similitude?
A = bh
The ratio of corresponding sides of similar triangles.
A^m*b^m = (ab)^m
How steep the line is. Horizontal line = 0 - vertical has no slope.

34. In a circle of radius r - what is the formula for the circumference?
C = p2r
Equal slopes.
Shifted down 2 units.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.

35. What is a ratio?

36. In a circle of radius r - what is the formula for the diameter?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
V = l^3
D = 2r
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°.

37. For what values of a function is the function undefined?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
For the GRE - when a denominator will equal 0 or when a negative will appear under a square root.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Area = (x°/360)(pr^2) where x is the central angle.

38. What are the median and the mode of a set of data?
180°. If two or more angles form a straight angle - their sum is 180°.
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.
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.

39. How do you find the x-intercept of a graph?
An integer greater than one that is not prime.
Set y = 0 - and solve.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Is a right triangle with a ratio of sides x:xv3:2x.

40. Properties of zero 4
V = l^3
Divide - then multiply by 100.
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 every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

41. What is true about the slopes of parallel lines?
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
The ratio of corresponding sides of similar triangles.
Then the product xy is a constant.
Equal slopes.

42. What is an even and an odd number?
360°
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
Even numbers are divisible by 2 and odd numbers are not.

43. What does it mean if y is directly proportional to x?
Area = (x°/360)(pr^2) where x is the central angle.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
[(x1 + x2)/2] -[(y1 + y2)/2]
Then the quotient y/x is a constant.

44. Properties of zero 3
0 is a multiple of every integer.
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.
Set x = 0 - and solve.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

45. What is p?
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
(Circumference/diameter) of a circle - or approximately 3.14.
For any integer n: 1^n = 1.
Then the product xy is a constant.

46. If a polygon has n sides - the sum of the measures of its n exterior angles - taking one angle at each vertex?
D = 2r
(n - 2)(180°)
360°
If a is negative and b is positive - then a < 0 < b.

47. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Shifted down 2 units.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
An equation that states that two ratios are equivalent. 4/6 = 10/15
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. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Their sum is 180°.
A fraction whose denominator is 100 i.e. 17% = 17/100
Shifted down 2 units.
M = (y2 - y1)/(x2 - x1)

49. Properties of square roots
D = 2r
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
180°. If two or more angles form a straight angle - their sum is 180°.

50. 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°.
M = (y2 - y1)/(x2 - x1)
Equal slopes.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.