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Sig Figs The smallest number of decimal places in the question is the number of decimal places in the answers (WHEN – OR +). The smallest number of significant figures in the measurements is the number of significant figures in the outcome (WHEN X OR /). 8000 = assume it is one significant figure unless it has a measurement. Machine to nearest unit then 8000 has 4 sig figs Machine to nearest thousand then 8000 has 1 sig fig Scientific Notation 8000 to 4 sig figs = 8.000 x 103 8000 to 1 sig figs = 8 x 103 ¼ (0.25 = 2 sig figs) + 0.1234 = 0.3734 = 0.37 to 2 decimal places

Formulas RECTANGLE V = 1wh A = 2lw + 2lh + 2wh CUBE V= e3 A = 6e3

CYLINDER V = πr2h A = 2πr2 + 2πrh S = 2πrh

CONE V = 1/3 πr2h A = πr2 + πrs S = πrs

PRISM V = Bh S = ph

PYRAMID V = 1/3 bh S = ½ ps SPHERE V = 4/3 πr3 S = 4πr2

Geometry

coincide for an equilateral triangle, otherwise they may not be the same

Heroes Formula

S = ½ (a + b + c) A = √ s ( s−a ) ( s− b )(s−c)

Pythagoras Theorem

Quadrilaterals

C2 = a 2 + b 2

a = ½ h (a + b)

Circles

A = πr2 C = 2πr = π (2r) = (πd) π=

c d

c = distance around the diameter

d = distance across circle

If r = 1, c = 2π, the proportions of 2π can be used to measure the size of angles

360 = 2π radius 180 = ½ (2π) 50 = 50/360 (2π) = 0.8727 radians (4 decimal places) Irregular Areas TRAPEZOIDAL RULE

A = ½ (1st + 2 middles + last) HEROS Half the perimeter. SIMPSONS A = h / 3 (1st + 4 odds + 2 evens + last)

Trapezoidal Rule Six strips – can be odd or even

A = ½ h (a0 + a1) + ½ h (a1 + a2) + ½ h (a2 + a3) + ½ h (a3 + a4) + ½ h (a4 + a5) +

½ h (a5 + a6) A = ½ h (a0 +2a1 + 2a2 + 2a3 + 2a4 + 2a5 + a6) A = ½ (1st + 2 middles + last) Simpsons Rule  

Number of strips must be even – odd number of measurements The tops are joined by quadratic functions instead of straight lines

For 6 Strips A = h / 3 (a0 + 4a1 + 2a2 + 4a3 + 2a4 + 4a5 + a6) A = h / 3 (1st + 4 odds + 2 evens + last) 1st and last

N 0 1 2 3 4 5 6 7 8 9 10 =

Odds

Evens

0 4.8 5.7 10.5 15.2 18.5 18.8 17.9 11.3 8.8 3.1 3.1

60.5

51

H = 1.5 between each A = 1.5 / 3 (3.1 + 4 x (60.5) + 2x (51.0) = 173.55 = 174 km2 Solid Geometric Figures Trimeated Cone (frustum) volume is the difference between the volume of the whole cone minus the volume of the smaller cone. Prism and right solid – 3D objects with vertical sides Cylinder V = (area of base) x height V = πr2 x height

Area Using Heroes Formula Angle B = 67 C2 = a2 + b2 C = 90.5 + 38.4 C = 98.3cm Perimeter = a + b + c = 227.2cm

S = ½ (a + b + c) = ½ perimeter = ½ (227.2) = 113.6

A=

113.6 − 98.3 113.6 113.6 −90.5) ( 113.6 −38.4) ¿ ( √

= 1737.999 rec = 1740 cm 2 to three sig figs

tan = +180 cos = -360 sin = -180 tan-1 (1.574) = 57.57 degrees OR = 180 + 57.57 = 237.7 A = 49.67 c = 0.8253 Cos 49.7 = b/ 0.8253 b = 0.8253 x cos (49.67) b = 0.5341 a = 0/0.8253 = sin (49.67) x 0.8523 = 0.6292

Given sin theta = 5/13, find cos theta and cot theta. Sin theta = 5/13 = sin-1(5/13) = 22.61 cos theta = cos (22.62) = 0.923 cot theta = 1/tan theta = 1/tan (22.62) = 2.400 Important

B = 40.33

Sin theta = 0.998

= sin (0.998) = 88.85 = 88.85 – 180 = 91.15...