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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 are the quotient and the remainder?

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2. How do you find the length of an arc of a circle?
Arc = (x°/360)(2pr) where x is the central angle.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
P(e) = (# of favorable outcomes)/(# of possible outcomes)
Then the quotient y/x is a constant.

3. What is the graph of a function?
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.
The ratio of corresponding sides of similar triangles.
F(a) is the y-coordinate of the point on the graph of y = f(x) whose x-coordinate is a.

4. What are the sum - difference - products - and quotient of two numbers?
360°
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
Corresponding sides of similar triangles are in proportion.
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°.

5. What is p?
Is a right triangle with a ratio of sides x:xv3:2x.
The ratio of corresponding sides of similar triangles.
(n - 2)(180°)
(Circumference/diameter) of a circle - or approximately 3.14.

6. How do you convert a percent to a fraction or a decimal?
B^m/b^n = b^m-n
Write the percent over 100 and reduce.
A = bh
Then the product xy is a constant.

7. What is an exterior angle of a polygon?
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.
Avg = sum of n numbers/n
An angle formed by extending the side of the polygon.
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.

8. Properties of zero 5
For any number b: b = -b if and only if b = 0.
Shifted up 2 units.
A = s^2 or A =d^2/2 where d is the diagonal
For any number a: a * 1 = a and a / 1 = a.

9. Properties of one 2
For any integer n: 1^n = 1.
Even numbers are divisible by 2 and odd numbers are not.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
A = (1/2)bh.

10. What is the relationship between the graph of f(x) the graph of y = f(x) - 2?
Shifted down 2 units.
Area = (x°/360)(pr^2) where x is the central angle.
Multiply each number by its weight (number of girls - boys - etc.) - add together - then divide by total.
Shifted left 2 units.

11. What is true about the measures of the four angles formed by two intersecting lines?
The ratio of corresponding sides of similar triangles.
The two pairs of opposite angles formed are equal to each other.
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.

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.
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.
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.

13. What is a multiple of an integer?
Divide - then multiply by 100.
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.
No matter how many angles there are - the sum around the point is 360°.
Set x = 0 - and solve.

14. What are the median and the mode of a set of data?
Corresponding sides of similar triangles are in proportion.
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.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Shifted down 2 units.

15. If the product of two or more numbers is 0 - what do you know about the numbers?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.
A fraction whose denominator is 100 i.e. 17% = 17/100
At least one of the factors is 0.

16. What is a function?
V = lwh
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
Divide - then multiply by 100.
[(x1 + x2)/2] -[(y1 + y2)/2]

17. What is the relationship between the lengths of the sides of a triangle and the measures of the angles of the triangle?
Then the quotient y/x is a constant.
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.
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.

18. Properties of zero 2
For any right triangle - a^2 + b^2 = c^2.
Even numbers are divisible by 2 and odd numbers are not.
Shifted right 2 units.
If a is negative and b is positive - then a < 0 < b.

19. What is the Pythagorean theorem?
At least one of the factors is 0.
Their sum is 180°.
For any right triangle - a^2 + b^2 = c^2.
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

20. What is the relationship between the graph of f(x) the graph of y = f(x) + 2?
At point they intersect - they are perpendicular. Creating quadrilaterals will show unknown angles.
Shifted up 2 units.
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

21. How do you find the y-intercept of a graph?
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.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Set x = 0 - and solve.

22. What is a composite number?
A = 2(lw + lh + hw)
It is isosceles - right triangle - with a ratio of sides x:x:xv2.
(Circumference/diameter) of a circle - or approximately 3.14.
An integer greater than one that is not prime.

23. Properties of one 1
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
The two pairs of opposite angles formed are equal to each other.
For any number a: a * 1 = a and a / 1 = a.
Then the product xy is a constant.

24. What is a Venn diagram?
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.
Write the percent over 100 and reduce.
Their sum is 90°.
All positive and negative whole numbers - and zero.

25. What is a percent?
A = 6(l^2)
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
(b^m)^n = b^mn
A fraction whose denominator is 100 i.e. 17% = 17/100

26. What are similar triangles?
V = pr^2h
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.
C = p2r

27. What is true about the slopes of parallel lines?
In the expression x^b - x is the base and b is the exponent.
Equal slopes.
A = 2(lw + lh + hw)
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.

28. How you convert a fraction or a decimal to a percent?
They are both the same. A divisor or factor of an integer leaves no remainder.
How steep the line is. Horizontal line = 0 - vertical has no slope.
Pythagorean theorem - or d = v[(x2 - x1)^2 + (y2 - y1)^2]
Divide - then multiply by 100.

29. What is special formula for the area of an equilateral triangle?
0 is the only number that is neither positive nor negative.
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Shifted up 2 units.
A = [(s^2*v3)/4]

30. What is an exponent?
In the expression x^b - x is the base and b is the exponent.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
Shifted right 2 units.
Their sum is 90°.

31. Properties of zero 4
If x is positive and n is a positive integer: x^1/n means nvx i.e 9^1/2 = v9.
Corresponding sides of similar triangles are in proportion.
Even numbers are divisible by 2 and odd numbers are not.
For every number a: a + 0 = a; a - 0 = a; a * 0 = 0; a / 0 is undefined.

32. Important binomial 1
An integer greater than one that is not prime.
(x + y)(x - y) = x^2 - y^2
For any positive numbers a and b: vab = va*vb and v(a/b) = va/vb.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.

33. What is a prime number?
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.
Even numbers are divisible by 2 and odd numbers are not.
For any number b: b = -b if and only if b = 0.
Sum is addition - difference in subtraction - product is multiplication - and quotient is division.

34. What is the sum of the measures of the four angles in a quadrilateral?
Is a right triangle with a ratio of sides x:xv3:2x.
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
A = s^2 or A =d^2/2 where d is the diagonal
360°

35. In a circle of radius r - what is the formula for the area?
Vertical line is x = a - horizontal is y = b - any other is y = mx + b.
Set y = 0 - and solve.
A^m/b^m = (a/b)^m
A = pr^2

36. What is the distributive law?
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.
If x is positive - the square root of x (vx) is the integer - n - multiplied by itself to result in x.
A fraction expressed using the word 'To' or a colon. 3 to 5 - 3:5 - and 3/5.

37. What is an integer?
B^m*b^n = b^m+n
Then the product xy is a constant.
1 is a divisor (or factor) of every integer.
All positive and negative whole numbers - and zero.

38. What do we mean by the slope of the line?
Ex. f(anything) = 2(anything) + 3 i.e. f(x) = 2x + 3
How steep the line is. Horizontal line = 0 - vertical has no slope.
Formed by extending a side of the triangle. Equal to the sum of the two opposite interior angles.
Their sum is 180°.

39. Important binomial 2
C = p2r
V = pr^2h
(x + y)^2 = (x + y)(x + y) = x^2 + 2xy + y^2
An integer greater than one that is not prime.

40. What is the sum of the measures of the n angles of a polygon with n sides?
If two triangles are similar with a ratio of similitude of k - the ratio of their areas is k^2.
M = (y2 - y1)/(x2 - x1)
(n - 2)(180°)
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.

41. What is true about the measures of the three angles in a triangle?
Opposite sides and angles are congruent - the sum of any two consecutive angles is180° - and the diagonals bisect.
Shifted up 2 units.
Their sum is 180°.
(n - 2)(180°)

42. How do you find the probability that an event will occur?
A = s^2 or A =d^2/2 where d is the diagonal
P(e) = (# of favorable outcomes)/(# of possible outcomes)
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
Shifted right 2 units.

43. What is the formula for the area of a rectangle?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
A = lw
B^m/b^n = b^m-n
1 is the smallest positive odd integer.

44. Properties of zero 1
0 is the only number that is neither positive nor negative.
For any number a: a * 1 = a and a / 1 = a.
Their sum is 180°.
(x - y)^2 = (x - y)(x - y) = x^2 - 2xy + y^2

45. What is the area of a square?
A = s^2 or A =d^2/2 where d is the diagonal
A = [(s^2*v3)/4]
Even numbers are divisible by 2 and odd numbers are not.
Two or more circles overlapping each other - often enclosed by a square - used to help solve counting problems.

46. What is the midpoint formula?
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.
[(x1 + x2)/2] -[(y1 + y2)/2]
Shifted left 2 units.
No matter how many angles there are - the sum around the point is 360°.

47. What is the relationship between the graph of f(x) the graph of y = f(x - 2)?
Shifted right 2 units.
Then the product xy is a constant.
Set x = 0 - and solve.
Avg = sum of n numbers/n

48. Law of exponents 2
Then the quotient y/x is a constant.
Set x = 0 - and solve.
B^m/b^n = b^m-n
In the expression x^b - x is the base and b is the exponent.

49. What are the properties of a rectangle?
C = p2r
Same shape triangles with equal measures of each angle. Any two equilateral - 45-45-90 - and 30-60-90 triangles are similar.
Same as a parallelogram - as well as each angle is 90° - and the diagonals are congruent.
The product of their slopes is -1 (negative reciprocal).

50. What are the important properties of 30-60-90 triangle?
The quotient is the answer in division and the remainder is any left over amount when the numbers aren'T divisible evenly.
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.
No matter how many angles there are - the sum around the point is 360°.
Is a right triangle with a ratio of sides x:xv3:2x.