Semester 2 Revision

NAME: TEACHER: Ms LeishmanLangley/CocksMs Le-RoddaMr 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 Answer8 Questions50 marks TOTAL:70 marks

Allowed Materials Scientific Calculator 2 pages (1 x A4 sheet) of revision notes Formulas  Area of a rectangle = l x w  Area of a parallelogram = b x h  Area of triangle = ½ x b x h  Area of a trapezium = ½ (a + b) x h  Area of circle = πr 2  Circumference = 2πr

Topics Trigonometry Trigonometry Shapes & Solids Shapes & Solids Graphs Graphs

Graphs Test A Test A Test B Test B

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

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.

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 = or C = 2πr Where r = radius (1/2 the diameter).

Area Is measured in square units e.g. mm 2, cm 2, m 2 or km 2 To calculate the area use the appropriate formula You need to be able identify shapes

Area rectangle triangle trapezium parallelogram circle

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 = πr 2 l = length w = width b = base length h = height r = radius a = side a length and b = side b length

Area rectangle triangle circle A = length x width A = ½ x base x height A = π x r 2

Area Area of parallelogram = b x h Area of parallelogram = b x h Area of trapezium = ½(a + b) x h Area of trapezium = ½(a + b) x h b h hab

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

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 A rectangular prism has 6 sides Each side is a rectangle Each side is a rectangle Each side has an equal and opposite side Each side has an equal and opposite side

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 A triangular prism has 5 sides The 2 ends are triangles The 2 ends are triangles The other 3 sides are rectangles The other 3 sides are rectangles

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 A circular prism (cylinder) has 3 sides The 2 ends are circles The 2 ends are circles The other side is a ????? The other side is a ????? h 2 x π x r

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

Trigonometry Hypotenuse Opposite Adjacent θ

Trigonometry Hypotenuse Opposite Adjacent θ Opposite Adjacent

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

Trigonometry 1 Sin θ Cos θ Cos θ θ

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

Trigonometry 5 5 x Sin θ 5 x Cos θ 5 x Cos θ θ

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

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

Trigonometry Tangent θ Adjacent = 1 Adjacent = 1 θ

Trigonometry 7 x Tan θ 7 θ

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

Trigonometry SOHCAHTOA

Trigonometry What if we want to find the angle ( θ)?

Trigonometry 6 x 30 o Example SOHCAHTOA

Trigonometry 6 x Example Use Sine

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

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

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

Trigonometry 10 9 x Example SOHCAHTOA

Trigonometry 10 9 x Example

Trigonometry 10 9 x Example

Trigonometry 10 9 x Example Sin x = 0.9 x = Sin

Trigonometry 10 9 x Example x = o

Trigonometry What if we want to find the hypotenuse (or adjacent)?

Trigonometry Things to remember: 1.Make sure your calculator is in DEG (degrees) mode 2.SOHCAHTOA 3.Which sides of the triangle are involved in the problem? 4.Each rule (Sin, Cos or Tan) can be used in 3 ways: To find one of the side lengths 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 length of the hypotenuse (Sin or Cos) or the adjacent (Tan, given the opposite) To find the angle (use inverse function on calculator) To find the angle (use inverse function on calculator)

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