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Adding with same denominator (a/b)+c/b)=((a+c)/b) Subtracting with same denominator (a/b)-(c/b)=((a-c)/b) Adding with different denominator (a/b)+(c/d)=((ad)+(cb))/bd Subtracting with different denominator (a/b)-(c/d)=((ad)-(cb))/bd Multiplying Factors (a/b)(c/d)=(ac)/(b*d) Dividing Factors (a/b)/(c/d)=(ad)/(bc) Factoring numbers a(c/d)= a+(c/d)= (ad+c)/d Intergers {...,−3,−2,−1,0,1,2,3,...}
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Adding with same denominator (a/b)+c/b)=((a+c)/b) Subtracting with same denominator (a/b)-(c/b)=((a-c)/b) Adding with different denominator (a/b)+(c/d)=((ad)+(cb))/bd Subtracting with different denominator (a/b)-(c/d)=((ad)-(cb))/bd Multiplying Factors (a/b)(c/d)=(ac)/(b*d) Dividing Factors (a/b)/(c/d)=(ad)/(bc) Factoring numbers a(c/d)= a+(c/d)= (ad+c)/d Intergers {...,−3,−2,−1,0,1,2,3,...}
Real Numbers All numbers that are on number line. Integers plus fractions, decimals, and irrationals PEMDAS Parentheses, Exponents, Multiplication, Division, Addition, Subtraction Percentages part = (percent / 100) x whole percent of change ((New value - old value)/old value) X 100 Distance from A to B √(x2 − x1)^2 + (y2 − y1)^ Parallel and Perpendicular lines Parallel lines have equal slopes. Perpendicular lines (i.e., those that make a 90 ∘90° angle where they intersect) have negative reciprocal slopes: 𝑚 1 m .𝑚2=−1m2=−1.Parallel Lines (l ∥∥ m) Mid-point of the segment AB M (𝑥1+𝑥2/2),(𝑦1+𝑦2/2) Slope of the line (𝑦 2 −𝑦1)/(𝑥 2 - 𝑥1)=𝑟𝑖𝑠𝑒/𝑟𝑢𝑛
Area of a triangles A=1/2bh The angles inside a triangle add up to? 180 degrees equilateral triangle These triangles have three equal sides, and all three angles are 60 ∘ Isosceles An isosceles triangle has two equal sides. The "base" angles (the ones opposite the two sides) are equal (see the 45∘ triangle above). Area of a Circle A=π𝑟 2 Circumference of a Circle C =2π𝑟 The angles of a circle adds up too? 360 Area of a rectangle A=lw Area of a Parallelogram A=bh
A=l*w Angle of a parallelogram Regular polygons are n-sided figures with all sides equal and all angles equal. The sum of the inside angles of an n-sided regular polygon is(𝑛−2).180∘ Area of a trapezoid: A=1/2h(b1+b2) Volume of a rectangular/right prism V=bh Surface value of a rectangular/ right prism 𝑆𝐴=𝑝ℎ+2𝐵SA=ph+2B Surface Area of a cylinder: SA=2πrh+2πr² Volume of a cylinder V=πr²h Surface Area of a Cone SA=πrt+πr² Volume of a Cone V=1/3πr²h Surface Area of a Sphere
Middle value in the list (which must be sorted) Example: median of{3,10,9,27,50}=10{3,10,9,27,50}= Example: median of{3,9,10,27}=(9+10)/2=9. Average 𝑠𝑢𝑚 𝑜𝑓 𝑡𝑒𝑟𝑚𝑠/𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑒𝑟𝑚𝑠 Average speed 𝑡𝑜𝑡𝑎𝑙 𝑑𝑖𝑠𝑡𝑎𝑛𝑐𝑒/𝑡𝑜𝑡𝑎𝑙 𝑡𝑖𝑚𝑒 Probability 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑑𝑒𝑠𝑖𝑟𝑒𝑑 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠/ 𝑛𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑡𝑜𝑡𝑎𝑙 𝑜𝑢𝑡𝑐𝑜𝑚𝑒𝑠 Simple Interest The charge for borrowing money or the return for lending it.Interest = principal × rate × time (𝐼=prt) Multiplying Two Powers of the SAME Base When the bases are the same, you find the new power by just adding the exponents (𝑥^𝑎*𝑥^𝑏=𝑥^(𝑎+𝑏)) Powers of Powers
For power of a power: you multiply the exponents.(𝑥^𝑎)^𝑏=𝑥^(𝑎𝑏) Dividing Powers 𝑥^𝑎/𝑥^𝑏=𝑥^𝑎^(𝑥−𝑏)=𝑥^(𝑎−𝑏) The Zero Exponent Anything to the 0 power is 1. 𝑥^0= 1