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57 Cards in this Set
- Front
- Back
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Non integers
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Numbers that have a factional part 3 ½, 3.75, pi
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Multiplying negative numbers -3x-4x-2
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If an odd number of negatives attach a negative sign So -3x-2=6 -3x-4x-6= negative number
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Multiple operations 3^2(3-4)x(2-3)6^4
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PEMDAS, paranthesis, exponents, x and divide, add and subtract.
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Counting integers? The number of integers between 13 and 31.
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Subtract 31-13=18 and add 1. So its 19
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Absolute value?
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The distance from 0 on the number line. -8=8 8=8
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Factors and multiples
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12 is a factor of 24, 24 is a multiple of 12
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Prime
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Positive integer greater than 1 only positive factors are one and the number its self.
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Common multiples?
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Number that both numbers can go into, if they both are not prime then there may be a Least common multiple
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Finding least common multiple
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12 and 15, 15+15=30 (not LCM of 12) 15x3=45 (not LCM of 12) 15x4 =60 (winner)
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Greatest common factor
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Break down both integers into their greatest prime factors and multiply all prime factors they have in common. 36 2x2x3x3 and 48 2x2x2x2x2x3 So the have 2,2’s in common and one 3, so the GCF is 12
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How do you know if an integer is divisible by 3?
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The sum of all digits is divisible by 3, same goes for 9. If the sum of all digits is divisible by 9
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How do you reduce a fraction 28/36
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Factor out and cancel out what the neumerator and denominator have in common. 28/36 4x7/4x9 7/9 So 56/32?
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Adding and subtracting fractions? 2/15 + 3/10
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Find the LCM of the denominators and add accordingly
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Multiplying fractions 2/4 x 6/7
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Just multiply across
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How do divide fractions? 2/4 (divided by) 4/7
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Invert the second fraction and multiply so 2/4 x7/4
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How would you find the original whole number before a % increase or decrease, after 5% increase the population was 59,346,,, What was the population before the increase?
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1.05x=59346 if it was 20% then 120/59346
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How do you determine the combined effect of multiple % increases?
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One year went up 10% the following year went up 20% …. Start with 100 first year 10, the next year 110 and 20%= 132. (Also can do % in increaments so 100 went up 20% and 20% of 10 is 2 so total was 12%. And then total for the year was 32%
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What should you keep in mind when dealing with units… such as inches feet, and cm meters?
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Be sure to keep them straight, Raining at 1 foot every 7 hours how man inches will fall in 59 minutes?
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Calculating average rates, What is the average speed for a guy who drove 120 miles at 40 mph and another 120 miles at 60 mph. How long did it actually take him.
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Don’t just average the two speeds, 120+120=240 The times are 3 hours for the first and 2 hours for the second so 5 hours total, so 240/5 = 48 mph
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How would you find the missing number if an average of 4 numbers is 7. And Three of the numbers are 3, 5, 8 What is the missing number?
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Take 4x7=28 and then add 3, 5, and 8 which gives you 26 so the missing number 12
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Median?
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12345 median is 3, 1,2,10,12,14,15 the median is 11,
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Mode
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12233444567 the mode is 4, 1234455678 the mode is 4 AND 5, the most reoccurring number
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Standard Deviation
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0, 10, 20 standard deviation of 8.17 9,10,11 standard deviation of 0.82 both have an average of 10 but the first is greater so it has a greater standard deviation
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Probability of two events occurring? 3 red marbels and 4 blue marbals in a bag, propability of with drawing two blue marbles in a row and the marbel is not replaced?
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4/7 x 3/6= 4/14= 2/7 is the reduced possibility.
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X^3 x X^4 =?
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X ^7
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Y^13 (divided by) Y^8 =?
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Y^5
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(X^3)^4 = ?
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X^12
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2^-3 = X^-2=
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1/2^3 = 1/8 1/x^2
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(square root of) 12 or ∑12 simplify the ∑
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∑12 ∑4x3 ∑4 x∑3 = 2∑3
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Rules for adding and subtracting ∑ (square roots)
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When the square root is the same you can add 2∑3 +3∑3= 5∑3 if the ∑’s are different there is not much you can do for the equation
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∑=(square root) ∑3 x ∑5 =
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∑15 you can multiply what is under the ∑ sign
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∑6/∑3 =
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∑6/3 = ∑2 You just divide what is under the square roots
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2a+3a=
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5a
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(3x2+5x-7) – (x2+12)=
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Not real sure, study polynomials http://www.purplemath.com/modules/polyadd.htm
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2a x 3a=
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6a2
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(x+3) . (x+4)
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x2+7x+12 (use foil method)
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Factor out a common divisor 3x3+12x2-6x
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3x(x2+4x-2)
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Factoring the difference of squares a2-b2 = . . Or x2-9=
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(a-b)(a+b) (the test makers favorite factorables) (x-3)(x+3)
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5x-12=-2x+9
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X=3
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Solving a system of equations 4x+3y=8 x+y=3 solve for x and y
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Take the second equation x-3 (-3x-3y=-9) now add the two equations to remove y from the equation. So you get x=-1 plug that number in to then get y and you will find y=4
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-5x=7<-3
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Remember to reverse the sign if you multiply or divide both sides by a negative number. So the answer is x>2
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(2,3) on a plotted line graph
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Points with a positive x are to the right of the y chart, points with a positive y are above the x line.
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Find the difference between two points. On a right triangle
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so P(-2,2) and Q(1,-2) so the answer is 5 (#70 in work book)
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How to find slope? (-2,2) (1,-2)
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Change in y / Change in x =Rise / Run the equation is y2-y1/x2-x1 Answer is 2
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Find the slope of a line from an equation,
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Y=mx+b http://www.purplemath.com/modules/strtlneq.htm
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The exterior angle of triangle is equal to what?
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The sum of the remote interior angles
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What is the area of a triangle?
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Base times height divided by 2 or (times ½)
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Deciding the length of a triangle one side is 7 one side is 3 the other side is what a.2 b.3 c.5 d.11
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One side of triangle must be greater than the difference and less than the sum of the lengths of the other two sides
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Isosceles triangles? Equilateral triangles
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Two equal sides, all three sides are equal
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If a right triangles leg is 3.4. or one side 3 and one side 4 what is hypotenuse?
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5 cause a leg is 3.4.5
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What legs are there on a hypotenuse triangle,,
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5:12:13 also 30-60-90 so if the angles are 30-60-90 then the equation is x:x(square root 3):2x ….. if 45-45-90 then the equation is x:x:x(square root 2)
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Circumference of a circle
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2πr
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Length of an arch
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(n/360)(2πr)
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Area of a circle
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πr2
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Area of a sector of a circle, or essentially the area of peace of the circle
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(n/60) (πr2)
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Surface area of a rectangular box
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2LW+2HL+2hw
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Volume of a cylinder
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πr2h
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