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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 triangle inequality?
An equation that states that two ratios are equivalent. 4/6 = 10/15
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 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.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3

2. If you were given the graph of y = f(x) - what does f(a) represent?
A fraction whose denominator is 100 i.e. 17% = 17/100
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
Shifted down 2 units.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

3. What is the square root of a number?
The two pairs of opposite angles formed are equal to each other.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A = lw

4. What are the sum - difference - products - and quotient of two numbers?
0 is a multiple of every integer.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

5. Properties of zero 4
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
Their sum is 90°.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

6. Important binomial 3
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
1 is the smallest positive odd integer.
The ratio of corresponding sides of similar triangles.
Shifted left 2 units.

7. Law of exponents 5
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
Their sum is 90°.
A^m/b^m = (a/b)^m
D = 2r

8. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
A = pr^2
Shifted up 2 units.
Write the percent as a decimal - and multiply.

9. What is the sum of the measures of the n angles of a polygon with n sides?
A = 2(lw + lh + hw)
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.
(n - 2)(180°)

10. What is a function?
An integer greater than one that is not prime.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
0 is a multiple of every integer.

11. What are the important properties of 30-60-90 triangle?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
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.
(Circumference/diameter) of a circle - or approximately 3.14.
Is a right triangle with a ratio of sides x:xv3:2x.

12. 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.
Increase is [(actual increase)/(original amount)]100 and decrease is [(actual decrease)/(original amount)]100.
Shifted down 2 units.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.

13. What are the quotient and the remainder?

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14. In a circle of radius r - what is the formula for the diameter?
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
Write the percent as a decimal - and multiply.
D = 2r
In the expression x^b - x is the base and b is the exponent.

15. What is the formula for the area of a parallelogram?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
A = (1/2)bh.
A = bh
They are both the same. A divisor or factor of an integer leaves no remainder.

16. What is a multiple of an integer?
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 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 number b: b = -b if and only if b = 0.
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.

17. In a circle of radius r - what is the formula for the circumference?
C = p2r
Corresponding sides of similar triangles are in proportion.
1 is a divisor (or factor) of every integer.
Area = (x°/360)(pr^2) where x is the central angle.

18. If the product of two or more numbers is 0 - what do you know about the numbers?
All positive and negative whole numbers - and zero.
At least one of the factors is 0.
Their sum is 180°.
A = [(s^2*v3)/4]

19. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
A = (1/2)bh.
V = pr^2h
The two pairs of opposite angles formed are equal to each other.

20. What are the properties of a rectangle?
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Corresponding sides of similar triangles are in proportion.
The ratio of corresponding sides of similar triangles.
Write the percent as a decimal - and multiply.

21. What is p?
(Circumference/diameter) of a circle - or approximately 3.14.
A = (1/2)bh.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2
1 is the smallest positive odd integer.

22. Properties of one 4
1 is the smallest positive odd integer.
A^m/b^m = (a/b)^m
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
Is a right triangle with a ratio of sides x:xv3:2x.

23. What is the volume of a cube?
V = l^3
All positive and negative whole numbers - and zero.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
For any integer n: 1^n = 1.

24. 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.
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 = s^2 or A =d^2/2 where d is the diagonal
B^m*b^n = b^m+n

25. What is the formula for the volume of a cylinder?
(Circumference/diameter) of a circle - or approximately 3.14.
The ratio of corresponding sides of similar triangles.
0 is the only number that is neither positive nor negative.
V = pr^2h

26. What is the midpoint formula?
[(x1 + x2)/2] -[(y1 + y2)/2]
Their sum is 180°.
B^m/b^n = b^m-n
Avg = sum of n numbers/n

27. What is true about the slopes of parallel lines?
The set of all ordered pairs (x -y) such that y = f(x).
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.
Equal slopes.
[(x1 + x2)/2] -[(y1 + y2)/2]

28. What is a percent?
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.
The product of their slopes is -1 (negative reciprocal).
A fraction whose denominator is 100 i.e. 17% = 17/100
Then the product xy is a constant.

29. What is the area of a square?
(Circumference/diameter) of a circle - or approximately 3.14.
360°
A = s^2 or A =d^2/2 where d is the diagonal
0 is the only number that is neither positive nor negative.

30. What is the ratio of similitude?
360°
The ratio of corresponding sides of similar triangles.
For any number b: b = -b if and only if b = 0.
(b^m)^n = b^mn

31. How do we write the equation of a line?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
0 is the only number that is neither positive nor negative.
A = pr^2
Is a right triangle with a ratio of sides x:xv3:2x.

32. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Shifted left 2 units.
A^m*b^m = (ab)^m
States that for any numbers a - b - and c: a (b + c) = ab + ac and a(b - c) = ab - ac.
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.

33. What is the graph of a function?
For any number a: a * 1 = a and a / 1 = a.
The set of all ordered pairs (x -y) such that y = f(x).
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.
For any number b: b = -b if and only if b = 0.

34. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
Shifted up 2 units.
For any integer n: 1^n = 1.
Then the product xy is a constant.
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.

35. How do you find the probability that an event will occur?
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.
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.
In the expression x^b - x is the base and b is the exponent.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

36. What is a prime number?
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.
Equal slopes.
At least one of the factors is 0.
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.

37. How you convert a fraction or a decimal to a percent?
180°. If two or more angles form a straight angle - their sum is 180°.
Divide - then multiply by 100.
A = lw
P(e) = (# of favorable outcomes)/(# of possible outcomes)

38. What is an even and an odd number?
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
B^m/b^n = b^m-n
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Even numbers are divisible by 2 and odd numbers are not.

39. In a circle of radius r - what is the formula for the area?
A = pr^2
A = 2(lw + lh + hw)
In the expression x^b - x is the base and b is the exponent.
P(e) = (# of favorable outcomes)/(# of possible outcomes)

40. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
A = 2(lw + lh + hw)
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.
Then the quotient y/x is a constant.
Shifted down 2 units.

41. What is the formula for the area of a rectangle?
A = 2(lw + lh + hw)
A = lw
The product of their slopes is -1 (negative reciprocal).
For any right triangle - a^2 + b^2 = c^2.

42. Important binomial 1
B^m*b^n = b^m+n
P(e) = (# of favorable outcomes)/(# of possible outcomes)
1 is the smallest positive odd integer.
(x + y)(x - y) = x^2 - y^2

43. What is an integer?
At least one of the factors is 0.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
V = l^3
All positive and negative whole numbers - and zero.

44. How do you calculate a weighted average?
M = (y2 - y1)/(x2 - x1)
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
A^m/b^m = (a/b)^m
V = lwh

45. How do you find the slope of a line?
A = 6(l^2)
V = lwh
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.
M = (y2 - y1)/(x2 - x1)

46. Properties of zero 5
V = pr^2h
For any number b: b = -b if and only if b = 0.
[(x1 + x2)/2] -[(y1 + y2)/2]
Area = (x°/360)(pr^2) where x is the central angle.

47. What formula is used for an average?
How steep the line is. Horizontal line = 0 - vertical has no slope.
For any number a: a * 1 = a and a / 1 = a.
A = (1/2)bh.
Avg = sum of n numbers/n

48. What is the measure of a straight angle?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
180°. If two or more angles form a straight angle - their sum is 180°.
For any integer n: 1^n = 1.
B^m/b^n = b^m-n

49. Law of exponents 1
For any number a: a * 1 = a and a / 1 = a.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.
B^m*b^n = b^m+n
Avg = sum of n numbers/n

50. Properties of one 2
The set of all ordered pairs (x -y) such that y = f(x).
For any integer n: 1^n = 1.
A^m/b^m = (a/b)^m
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.