Review

y = mx + b or m = rise ÷ run

Any + or – whole number or zero is an integer. Watch for what the question asks you…sometimes it will ask which is not an integer.

Question: How many distinct digits are there in ? Answer: There are 4 distinct digits…3, 4, 7 and 2

Be able to recognize a pattern. 12, 16, 20, 24, 28… 4 is being added to each number, so the next number will be 32.

Parentheses Exponents Multiply Divide Add Subtract

Question: How many positive integers factor into the number 18? Answer: 6 1 ∙ 18; 2 ∙ 9; 3 ∙ 6 Don’t forget about the number itself x 1, that’s a common mistake and they will put an answer on the test match that mistake!

Question: What is the least common multiple of 3 and 7? Hint: List the increasing multiples of the largest number until you have one that the smallest number will factor into. 7, 14, 21 …….. 3 goes into 21 Answer: 21

Question: What is the greatest common factor of 36 and 48? Hint: Factor out each number and find the prime numbers that match. Then multiply all of the prime numbers.

Question: How many integers are there from 13 through 31, inclusive? Hint: Subtract the smallest from the largest and add 1. Answer: – = 19

Question: What is the remainder when 487 is divided by 5? Hint: Look for the nearest multiple of 5 see how many away you are from that number. Answer: is a multiple of 5, 487 is 2 more than 485.

Question: Which of the following is a multiple of 3, but not a multiple of 9? 109, 117, 260, 361, 459, 957, 1001 Hint: It is divisible by 3 if its sum is divisible by 3, same goes for = 10 (neither) = 9 (both) = 8 (neither) = 10 (neither) = 18 (both) = 21 (3, not 9) Answer: 957

Question: Which of the following is a multiple of 2, but not a multiple of 4 ? 124, 352, 483, 562, 708, 984 Hint: If the last digit is even, it is a multiple of 2. If the last 2 digits are a multiple of 4, then the entire number is a multiple of 4. Answer: 562 Of the even numbers, only 62 is NOT a multiple of 4.

Question: What number is 25% more than 40? Answer: 50 Add the % to 100%... 25% + 100% = 125% Convert to a decimal… 125% = 1.25 Multiply the decimal by the number… 1.25 x 40 = 50

Question: What is the mean of 5, 10, 5 and 4 ? Answer: 6 Add the numbers together: = 24 Divide by the number of numbers you added together: 24 ÷ 4 = 6

Question: What is the median of 2, 10, 6, 12, 8 ? Answer: 8 Put the numbers in numerical order...2, 6, 8, 10, 12 8 is in the middle

If you have two numbers in the middle… 2, 6, 8, 10, 12, 14 Take the average of the two in the middle… The average of 8 and 10 is 9 Answer: 9

Question: What is the mode in following list of numbers? 6, 8, 12, 8, 4, 6, 8 Answer: 8 8 occurs more often than any other number in the list.

Speed = Distance ÷ Time Be sure you are using the same units throughout the problem!!! For instance, if your speed is in feet/sec, your time should be in seconds and your distance should be in feet! Also…with any division problem, you can always use the triangle…

 3 3 = 3 x 3 x 3 = 27  Multiplying Exponents: x 3 ∙ x 4 = x (3+4) = x 7  Dividing Exponents: x 13 ÷ x 8 = x (13-8) = x 5

A negative number raised to an even power gives a positive result: (-1) 56 = 1 A negative number raised to an odd power gives a negative result: (-1) 57 = -1

Multiply the Exponents (x 3 ) 4 = x (3∙4) = x 12

2a + 3a = 5a

2a ∙ 3a = (2∙3)(a∙a) = 6a 2

(2x 2 + 3x + 24) + (4x 2 + 1x + 5) (2x 2 + 3x + 24) +(4x 2 + 1x + 5) 6x 2 + 4x + 29

First, Outside, Inside, Last (x + 3)(x + 4) x 2 + 4x + 3x + 12 x 2 + 7x + 12

3x – 10y = -5x + 6y 3x + 5x – 10 y = 6y 3x + 5x = 6y + 10y 8x = 16y X = 2y

Part 3

A bisector divides an angle in half.

 1 and 2 are adjacent.  1 and 2 add up to 180° because they are also supplementary, like A and B.

 1 and 3 are vertical angles  They are opposite angles  They are equal in degree value

4 = 3 = 7 = 6 (all obtuse angles, greater than 90°) 1 = 8 = 2 = 5 (all acute angles, less than 90°)

 All angles are 90°  Opposite sides are equal  Perimeter = sum of all 4 sides  Area = length ∙ width (side 2 for a square)

 2 pairs of parallel sides  Opposite sides are equal  Opposite angles are equal  Consecutive angles add up to 180°

 Perimeter = sum of all 4 sides  Area = base ∙ height

 All exterior angles add up to 360°

 The longest side on a triangle is opposite the largest angle.

a 2 + b 2 = c 2 leg leg 2 2 = hypotenuse 2

3 : 4 : 5 a = 153 ∙ 5 = 15 b = ? c = 255 ∙ 5 = 25 4 ∙ 5 = 20 b = 20

5 : 12 : 13 a = ? b = 3612 ∙ 3 = 36 c = 3913 ∙ 3 = 39 5 ∙ 3 = 15 a = 15

A = π r 2

Area = Length ∙ Width ∙ Height A = 7 ∙ 2 ∙ 4 A = 56