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Semester 2 Revision

Semester 2 Revision. NAME: TEACHER: Ms Leishman Langley/Cocks Ms Le-Rodda Mr Sinniah (please circle your teacher’s name) GISBORNE SECONDARY COLLEGE Year 9 Maths Semester Two Examination 2012 Reading Time: 10 minutes Writing Time: 60 minutes

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Semester 2 Revision

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  1. Semester 2 Revision

  2. NAME: • TEACHER: Ms Leishman Langley/Cocks Ms Le-Rodda Mr Sinniah • (please circle your teacher’s name) GISBORNE SECONDARY COLLEGE Year 9 Maths Semester Two Examination 2012 Reading Time: 10 minutes Writing Time: 60 minutes Section A: Multiple Choice 20 Questions 20 marks Section B: Short Answer 8 Questions 50 marks TOTAL: 70 marks

  3. Allowed Materials • Scientific Calculator • 2 pages (1 x A4 sheet) of revision notes

  4. Topics • Trigonometry • Shapes & Solids • Graphs

  5. Graphs • Test A • Test B

  6. Shapes & Solids Perimeter The distance around the outside of a shape Area The space inside a 2-dimensional (flat) shape Volume The space inside a 3-dimensional solid

  7. Perimeter Is measured in linear units e.g. mm, cm, m or km To calculate the perimeter, find the length of all sides then add them together. The perimeter of a circle is called the circumference.

  8. Circumference The rule for finding the circumference of a circle is: C = π x d Where d = diameter (the width of the circle) and π = 3.142 or C = 2πr Where r = radius (1/2 the diameter).

  9. Area Is measured in square units e.g. mm2, cm2, m2 or km2 To calculate the area use the appropriate formula You need to be able identify shapes

  10. Area rectangle triangle trapezium parallelogram circle

  11. Area Area of a rectangle = l x w Area of triangle = ½ x b x h Area of a parallelogram = b x h Area of a trapezium = ½ (a + b) x h Area of circle = πr2 l = length w = width b = base length h = height r = radius a = side a length and b = side b length

  12. Area rectangle A = length x width triangle A = ½ x base x height A = πx r2 circle

  13. Area • Area of parallelogram = b x h • Area of trapezium = ½(a + b) x h h h b a b

  14. Prisms A prism is a 3-dimensional solid that has congruent ends

  15. Surface area of a prism The total surface area of a prism is the sum of the area of each side. • A rectangular prism has 6 sides • Each side is a rectangle • Each side has an equal and opposite side

  16. Surface area of a prism The total surface area of a prism is the sum of the area of each side. • A triangular prism has 5 sides • The 2 ends are triangles • The other 3 sides are rectangles

  17. Surface area of a prism The total surface area of a prism is the sum of the area of each side. • A circular prism (cylinder) has 3 sides • The 2 ends are circles • The other side is a ????? h 2 x π x r

  18. Volume of a prism Volume of a prism = area of the base x height base base height height

  19. Trigonometry Hypotenuse Opposite θ Adjacent

  20. Trigonometry Hypotenuse Opposite Adjacent θ Opposite Adjacent

  21. Trigonometry Length of opposite = sine θ Hypotenuse = 1 Opposite θ Length of adjacent = cosine θ Adjacent

  22. Trigonometry 1 Sin θ θ Cos θ

  23. Trigonometry Length of opposite = 5 x sine θ 5 θ Length of adjacent = 5 x cosine θ

  24. Trigonometry 5 5 x Sin θ θ 5 x Cos θ

  25. Trigonometry So Length of opposite = length of hypotenuse x Sin θ and Length of adjacent = length of hypotenuse x Cos θ

  26. Trigonometry Opposite = Hypotenuse x Sin θ Adjacent = Hypotenuse x Cos θ

  27. Trigonometry Tangent θ θ Adjacent = 1

  28. Trigonometry 7 x Tan θ θ 7

  29. Trigonometry Opposite = Hypotenuse x Sin θ Adjacent = Hypotenuse x Cos θ Opposite = Adjacent x Tan θ Sin θ = Cos θ= Tan θ =

  30. Trigonometry SOHCAHTOA Sin θ = Cos θ= Tan θ =

  31. Trigonometry What if we want to find the angle (θ)? Sin θ = Cos θ= Tan θ = θ = Sin-1 θ = Cos-1 θ = Tan-1

  32. Trigonometry Example 6 x 30o SOHCAHTOA

  33. Trigonometry Example 6 x 30o Use Sine

  34. Trigonometry Example 6 x 30o Opposite = hypotenuse x Sin θ

  35. Trigonometry Example 6 x 30o x = 6 x Sin 30o

  36. Trigonometry Example 6 x 30o x = 6 x 0.5 x = 3

  37. Trigonometry Example 10 9 x SOHCAHTOA

  38. Trigonometry Example 10 9 x Sin θ =

  39. Trigonometry Example 10 9 x Sin x =

  40. Trigonometry Example 10 9 x Sin x = 0.9 x = Sin-1 0.9

  41. Trigonometry Example 10 9 x x = 64.16o

  42. Trigonometry What if we want to find the hypotenuse (or adjacent)? Sin θ = Cos θ= Tan θ = Hyp = Hyp = Adj =

  43. Trigonometry Things to remember: • Make sure your calculator is in DEG (degrees) mode • SOHCAHTOA • Which sides of the triangle are involved in the problem? • Each rule (Sin, Cos or Tan) can be used in 3 ways: • To find one of the side lengths • To find the length of the hypotenuse (Sin or Cos) or the adjacent (Tan, given the opposite) • To find the angle (use inverse function on calculator)

  44. The End • Remember to bring to the exam: • 1 page (back and front of revision notes) • Pens, pencils, eraser, ruler • Scientific calculator (ipods & phones not allowed) GOODLUCK!

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