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77 Cards in this Set
- Front
- Back
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What is the integer zero?
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An even number, which is neither negative nor positive
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What are the rules for addition of integers?
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even + even = even
odd + odd = even odd + even = odd |
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What are the rules for multiplication of integers?
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even * even = even
odd * odd = odd odd * even = even |
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What are the squares of integers: 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12?
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1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144
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If 0 < n < 1, then is n^2 < n or is n^2 > n ?
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n^2 < n
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What is the reciprocal of a number?
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1 divided by that number
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How do you express a mixed number as an improper number? ex: 2 1/3
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Multiply the whole number in front of the fraction by the denominator, then add that number to the numerator. In the improper fraction, that final value is placed as numerator, the denominator being the mixed number denominator. ex: 2 * 3 + 1 = 7;
2 1/3 = 7/3 |
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How do you express a improper fraction as a mixed number? ex: 17/4
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Divide the numerator by the denominator. The quotient becomes the whole number and the remainder is the numerator of the new fraction, the denominator remaining unchanged. ex: 17/4=4 with a remainder of 1; 17/4 = 4 1/4
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What is the reciprocal of zero?
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Zero does not have a reciprocal.
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What are factors of a number?
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They are positive integers that can be divided evenly into the number (no remainder).
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What are multiples of a number?
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They are numbers that can be divided by that given number without a remainder.
ex: 8, 16, 32, 40, 48 are some multiples of 8. |
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What is a common multiple?
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Given two or more numbers, a common multiple is the multiple of all of the given numbers. ex 48 and 96 are common multiples of 8 and 12.
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What restriction is there to the remainder when you divide any positive integer by 3 ?
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The remainder must be less than or equal to 2.
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What are prime factors?
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They are factors of a number that cannot be factored further.
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Give the first eight prime numbers.
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2, 3, 5, 7, 11, 13, 17, 19
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What is a proportion?
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It is an equation in which two ratios are set equal to each other.
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What is a geometric sequence?
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It is an ordered list of numbers (def. of sequence) in which there is a constant ratio between the consecutive terms (geometric). ex: 7, 21, 63, 189, ...
because 21/7 = 3 ; 63/21 = 3 ; 189/63 = 3 |
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What is the Nth term of the last geometric sequence: 7, 21, 63, 189, ...?
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7*3^(N-1) for any positive integer n;
or more abstractly N=n*r^(n-1) |
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For a sequence , in general, what is the Nth term of that sequence if we have for example the following: 3, 7, 11, 15, ... ?
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3+ 4 (N-1) for any positive integer n;
or more abstractly N=n+r*(n-1) |
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What is the union of two sets?
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All the elements that are in either or both of the sets.
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What is the intersection of two sets?
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The set consisting of the common elements of both sets.
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What is the Fundamental Counting Principle?
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It is the principle that allows you to figure out how many possibilities there are for selecting members of different groups. That is: If one event can happen in n ways and a second, independent event can happen in m ways, the total ways in which the two events can happen in n * m.
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Factor a^2 - b^2
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a^2 - b^2 = (a+b)*(a-b)
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When multiplying expressions with the same base, you ... the exponents
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add
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When dividing expressions with the same base, you ... exponents
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subtract
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When a number raised to an exponent is raised to a second exponent, you....the exponents
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multiply
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The absolute value of a number is....
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its distance from zero on the number line; the 'size' of that number
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"A number y decreased by 60" means
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y-60
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"5 less than a number k" means
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k-5
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"x less than 5" means
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5-x
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"20 divided by n" means
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20/5
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"20 divided into a number y" means
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y/20
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When multiplying or divided both sides of an inequality by a negative number, what happens to the inequality sign?
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It flips the direction of the sign
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Translate mathematically: " Tom has 5 fewer marbles than twice the number Jane has."
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T = 2J-5
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Translate math.: "The difference between Tom's height and Jane's height is 22 centimeters"
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abs value of T-J = 22
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Translate: " 20% of Tom's socks are red"
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R = 0.2 * T
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Translate: "Jane ate 3/4 of the candy"
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J = 3/4 * C
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Translate: "Jane won 3 games for every 2 that Tom won"
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J/T = 3/2
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What is the domain of a function?
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The set of all the values for which the function is defined. The x-axis if the function is y=f(x)
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What is the range of a function?
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The set of all values that are the output, or result, of applying the function. The y-axis if the function is y=f(x)
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In which direction is the graph y=f(x) + c shifted?
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Up c units in the y-direction if c > 0
Down c unit in the y-direction if c < 0 |
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In which direction is the graph y=f(x+c) shifted?
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To the left c units (x-direction) if c > 0
To the right c unit (x-direction) if c < 0 |
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How do you graph y = f(-x)?
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Reflect each point of the graph y=f(x) in the y-axis
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How do you graph y = -f(x)?
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Reflect the graph of f(x) in the x-axis
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The midpoint of a segment is?
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It is the point that divided the segment into two segments of equal length
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Two opposite angles formed by two intersecting lines are called ....?
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vertical angles
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Two angles whose measures have a sum of 180° are called...?
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supplementary angles
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Two angles whose measures have a sum of 90° are called ...?
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complementary angles
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Characteristics of an equilateral triangle?
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The three sides are equal in length, the angles are equal as well, and each measure 60°
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Characteristics of an isosceles triangle?
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Two sides are equal in length, and the two angles opposite the equal sides are also equal.
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What are the three classic right triangles?
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30°-60°-90°, of which the length of the sides are in the ratio of 1 : sqrt3 : 2
45°-45°-90°, with lengths in the ratio of 1 : 1 : sqrt2 triangles with lengths in the ratio of 3 : 4 : 5 |
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What are congruent triangles?
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Triangles that have the same size and shape.
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What does the triangle inequality state?
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It states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side.
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In a parallelogram, the opposite angles are of...and the opposite sides are of...
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equal measure, and equal length
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What is the area of a parallelogram?
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Area = length * height
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What is a regular polygon?
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A polygon whose sides all have the same length and whose angles all have the same measure
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State the formula for the sum of interior angles in a polygon based on the number of sides it has?
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n (n° sides) = 180 * (n-2)
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Area and circumference of a circle?
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circumference: c = 2*pi*r
area: a = pi*r^2 |
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What is the formula for the volume of a rectangular solid?
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V = l*w*h [length*width*height]
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What is the formula for the volume of a right circular cylinder?
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V = pi*r^2*h [are of the base *height]
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What is a right circular cone?
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A cone in which the line coming down from the vertex to the center of its base is perpendicular to that base.
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Formula for the volume of a cone?
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V = 1/3 * pi* r^2 * h
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What is a regular pyramid?
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A pyramid with a base that is a regular polygon, and where the triangular faces are all congruent isosceles triangles.
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Formula for the volume of a pyramid?
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V = 1/3 * b* h [1/3 * base* height]
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Surface area of a cube?
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6*x^2
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Two lines are perpendicular when the .... of their slopes equals...
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product of their slopes equals -1
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State the Midpoint formula?
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The midpoint of a line segment is given by M = [ (x1+x2)/2 ; (y1+y2)/2 ]
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What is the formula for the distance between two points ?
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d = sqrt [ (x2-x1)^2 + (y2-y1)^2 ]
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If a rectangle is rotated 180° around P, the result is the same rectangle. The rectangle is said to be symmetric around the point P. What is the point P called?
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The point of symmetry
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How is the arithmetic mean calculated?
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sum of a list of values / the number of values in the list
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What is the median?
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The middle value of a list when the numbers are in order. With an even number of values, it is the arithmetic mean of the two middle values.
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What is the mode?
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The value of values that appear the greatest number of times
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What is a weighted average?
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The average of two or more groups that do not all have the same number of members. To find the weighted average, multiply the average by the number of students that correspond to that average, all divided by the number of students.
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Two events are independant if....
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the outcome of either event has no effect on the other
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How do you find the probability of two or more independent event occurring together?
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Multiply the probabilities of the individual events
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Volume of a sphere?
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4/3*pi*r^3
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Surface area of a sphere?
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4*pi*r^2
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