Mathematical review 1 Mathematical review Algebra 2 Mathematical

Mathematical review 1

Mathematical review Algebra 2

Mathematical review Algebra Involves the solving of a mathematical equation 3

Mathematical review Algebra Involves the solving of a mathematical equation 3+ 6 = X 4

Mathematical review Algebra Involves the solving of a mathematical equation 3+ 6 = X 9=X 5

Mathematical review Algebra Involves the solving of a mathematical equation 6 + X = 21 6

Mathematical review Algebra Involves the solving of a mathematical equation 6 + X = 21 How many numbers are in this equation? 7

Mathematical review Algebra 5 + 7 X + 13 = -10 How many numbers are in this equation? 8

Mathematical review Algebra 12 + 8 X/3 + 15 = 9 How many numbers are in this equation? 9

Mathematical review Algebra Solve the following mathematical equation 6 + X = 21 solve for X 10

Mathematical review Algebra Involves the solving of a mathematical equation 6 + X = 21 solve for X 1 st isolate X 11

Mathematical review Algebra Involves the solving of a mathematical equation 6 + X = 21 solve for X X = 21 -6 12

Mathematical review Algebra Involves the solving of a mathematical equation 6 + X = 21 solve for X X = 21 -6 X = 15 13

Mathematical review Algebra Involves the solving of a mathematical equation 6 + 8 + 2 X = 18 1 st isolate the number containing the variable 14

Mathematical review Algebra Involves the solving of a mathematical equation 6 + 8 + 2 X = 18 1 st isolate the number containing the variable 2 nd isolate the variable within the number 3 rd solve the equation 15

Mathematical review Algebra Involves the solving of a mathematical equation 6 + 8 + 2 X = 18 -6 + 6 -8 +8 +2 X =18 -6 -8 2 X = 4 2 X/2 = 4/2 X=2 16

Mathematical review Algebra Involves the solving of a mathematical equation d= 10 m v = 10 m/s t= 3 sec solve for a(accleration) d = vt + ½ at 2 17

Mathematical review Algebra Involves the solving of a mathematical equation d= 10 m v = 10 m/s d = vt + ½ at 2 10 m = 10 m/s(3 s) + ½ a(3 s)2 t= 3 sec 10 m = 30 m + ½ a(9 s 2) solve for a(acceleration) 10 m-30 m = 30 m-30 m + a 4. 5 s 2 -20 m =a 4. 5 s 2 -20 m/4. 5 s 2 = a -4. 4 m/s 2 = a a = -4. 4 m/s 2 18

Mathematical review Algebra Involves the solving of a mathematical equation a 2 b + c = 24 solve for a; if b= 2 and c = 6 19

Mathematical review Algebra Involves the solving of a mathematical equation a 2 b + c = 24 solve for a; if b= 2 and c = 6 1 st Isolate a 20

Mathematical review Algebra Involves the solving of a mathematical equation a 2 b + c = 24 solve for a; if b= 2 and c = 6 a 2 b + c -c = 24 -c a 2 b = 24 – c a 2 b/b = (24 –c)/b a 2 = (24 –c)/b a = 21

Mathematical review Algebra Involves the solving of a mathematical equation a 2 b + c = 24 solve for a; if b= 2 and c = 6 a 2 b + c -c = 24 -c a 2 b = 24 – c a 2 b/b = (24 –c)/b a 2 = (24 –c)/b a = Plug in known values and solve 22

Mathematical review Algebra Involves the solving of a mathematical equation a 2 b + c = 24 solve for a; if b= 2 and c = 6 a 2 b + c -c = 24 -c a 2 b = 24 – c a 2 b/b = (24 –c)/b a 2 = (24 –c)/b a = = =3 23

Mathematical review Trigonometry 24

Mathematical review Trigonometry Sin Cos Tan 25

Mathematical review Trigonometry Sin θ = opp/hyp = a/c Cos θ = adj/hyp = b/c c a θ Tan θ = opp/adj = a/b a = 3, c = 9, b θ=? 26

Mathematical review Trigonometry Sin θ = opp/hyp = a/c Cos θ = adj/hyp = b/c c a θ Tan θ = opp/adj = a/b b a = 3, c = 9, θ=? Sin = opp/hyp = 27

Mathematical review Trigonometry Sin θ = opp/hyp = a/c Cos θ = adj/hyp = b/c c a θ Tan θ = opp/adj = a/b b a = 3, c = 9, θ=? Sin θ = opp/hyp = a/c = 3/9= 0. 333 28

Mathematical review Trigonometry Sin θ = opp/hyp = a/c Cos θ = adj/hyp = b/c c a θ Tan θ = opp/adj = a/b b Sin θ = 0. 333 Sin-1 0. 333 = θ 29

Mathematical review Trigonometry Sin θ = opp/hyp = a/c Cos θ = adj/hyp = b/c c a θ Tan θ = opp/adj = a/b Sin θ = 0. 333 Sin-1 0. 333 = θ b Sin-1 0. 333 = 19 o 30

Mathematical review Trigonometry Sin = opp/hyp = a/c c a Cos = adj/hyp = b/c b Tan = opp/adj = a/b 31

Mathematical review Trigonometry Sin = opp/hyp = a/c c a Cos = adj/hyp = b/c b Tan = opp/adj = a/b 32

Scientific Notation • Scientific notation is the expression of a number in the “power of 10” v 36, 900 3. 69 x 104 ü allows a number to expressed in significant digits by using the correct significant digits in the coefficient ü eliminates the need to write multiple zeros Know how to add, subtract, multiply, and divide numbers expressed in scientific notation 33

1 -4 Measurement and Uncertainty; Significant Figures The number of significant figures is the number of reliably known digits in a number. It is usually possible to tell the number of significant figures by the way the number is written: 23. 21 cm has 4 significant figures 0. 062 cm has 2 significant figures (the initial zeroes don’t count) 80 km is ambiguous – it could have 1 or 2 significant figures. If it has 3, it should be written 80. 0 km.

1 -4 Measurement and Uncertainty; Significant Figures When multiplying or dividing numbers, the result has as many significant figures as the number used in the calculation with the fewest significant figures. Example: 11. 3 cm x 6. 8 cm = 77 cm When adding or subtracting, the answer is no more accurate than the least accurate number used.