DW RESOURCES DEMO

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DW RESOURCES DEMO

• The Authors
• Year 9
• Year 10
• NCEA Level 1
• NCEA Level 2
• Year 13 Calculus
• Year 13 Statistics
• How to contact us and Prices

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DW Resources Demo

• The following material has been put together by
  Chris Delisle and Helen Wiessing from Dargaville
  High School.
  
• We will give a small demonstration of sample
  lessons from Year 9 13.
  
• Years 11-13 have accompanying word documents
  which are sold to students.

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Some Advantages of Powerpoints

• Easily editable
• Ensures consistent teaching within department
• Gives Senior students lesson plans and
  requirements ahead of time so always prepared for
  lesson and can catch up when away.
  
• Allows teacher to do many more examples on
  board.
  
• Starter always ready to go as students walk into
  class

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Why our powerpoints?

• We are enjoying using them and making them.
• They are FULLY EDITABLE so you can tailor them to
  suit your school.
  
• Gives you a ready to go program.
• Schemes included
• Homework reviews for Years 9-11. Two levels in
  each year. Answers included.

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Our Weekly homework Reviews

• Ask questions up to and including current unit
• Includes previous years skills
• Designed to provide constant revision
• Has significantly improved our schools skills and
  exam results since beginning using them 4 years
  ago.
  
• 2 sets for each year level depending on ability
  level.
  
• Example of Non extension NCEA Level 1 next

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Year 9 Gold Folders (similar for Silver)
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3 Gold Unit 9 Geometry

• Lesson 1 Bearings/Protractors
• Lesson 2 Angle Rules
• Lesson 3 More angle rules
• Lesson 4 Angles in a triangle
• Lesson 5 ConstructionsPerpendicular Bisector

• Lesson 6/7/8 Rules of Parallel Lines (Extn Only)
• Lesson 9 Grid References
• Test Review

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Lesson 5 ConstructionsPerpendicular Bisector
Extend compass more than half way along the line
Place compass at A Draw an arc above and below th
e line Place compass at B Draw an arc above and
below the line Draw a line through the points whe
re the arcs intersect
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Bisect an Angle

• Put compass on vertex and make an arc on each
  arm.
  
• Keeping compass same size make arcs from arcs
  made in 1.
  
• Join Vertex to crossed arcs

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Make a 60 Degree angle
Since Equilateral Triangles have all 60 degree
angles, we think of creating an equilateral
triangle.

• Place compass at A and draw arc from B up to top
  of diagram
  
• Place compass at B and draw arc from A to top of
  diagram
  
• Connect from A to cross
• This is 60o angle

60o
A
B
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End Lesson 5

• Practice skills learned.
• Draw a line 15 cm long and construct a
  perpendicular bisector
  
• Draw a line 8 cm long and construct a 60 degree
  angle from it.
  
• Bisect the 60 degree angle from last construction.

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Year 10 Gold Folders (simliar Silver)
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Form 4 Midyear Exam Revision With Answers

• This will be a write on exam
• Use Blue or black pen only
• Do not use twink
• Graphs can be done in pencil
• SHOW ALL WORKING for full marks
• If you dont know question, leave it and move on.
  Come back to missed questions at end.

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Section A Number
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Section B Algebra
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3. Solving Equations
X37
X0
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4. Write coordinates of these points

• The number of girls in a class is 3 less
• than twice the number of boys. If there
• are 17 girls, how many boys are there?
• 6. The School Roll at Aotearoa High School
• is 757. There are 13 more boys than
• girls. Write an equation and solve it, to
• work out how many boys are on the
• roll.
• 7. A taxi company charges 2 per km, plus
• a 3 flagfall fee. A passenger pays
• 19. Write an equation and solve it for
• how far the distance travelled.

A B C D E F
(1,3) (1,-2) (-2,0) (-4,2) (-4,-2) (0,-4)
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• 9. A sequence is given by the rule Tn 4n-5
• What is the 15th term in sequence
• A term in sequence is 75, which term is this?

10. Complete following table. Then plot it on
a graph
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Section C Measurement
1. Find Perimeter and Area
a)
b)
10 m
10 m
P 32 m A 48 m2
P 31 cm A 77.5 cm2
c)
d)
P 28 cm A 39 cm2
P 36 cm A 72 cm2
2. How many m2 in a hectare?
10 000
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3. Find Volume of shape
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Section D Geometry Solve for x (Give reasons)
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• Draw a 6 cm long line. Use compass to bisect it
• Construct a 60 degree angle using a compass
• Bisect angle done in Question 3
• Draw Locus of points 3 cm from your line in 2.

3
4
60o
A
B
5
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NCEA Level 1 Folders (2 levels reviews included)
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Unit 5 Trigonometry
Starters

• Lesson 1 Trigonomic Ratios
• Lesson 2 Using Trigonometry to find sides
• Lesson 3 Applications of Trigonometry
• Lesson 45 Applications of Trigonometry 3D
• Lesson 6 Applications of Trigonometry
• Lesson 7 Similar Triangles

• Lesson 8 Practical Measuring
• Lesson 9 Vectors
• Lesson 10 Vectors and Bearings
• Lesson 11 Applications of Vectors
• Lesson 12 Vectors and Trig Applications
  Extension
  
• Lesson 13 Applications

Revision
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Trigonomic Ratios
Oopposite AAdjacent HHypotenuse
If we draw an angle and measure the lengths
indicated we find
If we shift tan this ratio it will give us the
angle
The ratio of sides of a right angled triangle is
the same for a given angle
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The ratio of sides of a right angled triangle is
the same for a given angle
We use this fact in trigonometry
We have Three Ratios we use
We label the sides with reference to the angle
Hypotenuse is always opposite the right angle
H
O
H
A
A
O
Adjacent side is beside (adjacent to) the angle
We can draw a line through the opposite angle to
the opposite side
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To find an angle

• Draw and label
• Write the formula
• Substitute
• Solve
• Units and Rounding
• Is answer reasonable

eg
5m
4m
O
H
A
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• Draw and label
• Write the formula
• Substitute
• Solve
• Units and Rounding
• Is answer reasonable

25cm
A
H
14cm
O
Run through labelling triangles
Ex 11.2 Q1 and recognition of
what to do with Q 2
Ie shift function
Ex 11.2 3-8
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• Draw and label
• Write the formula
• Substitute
• Solve
• Units and Rounding
• Is answer reasonable

15cm
23cm
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• Draw and label
• Write the formula
• Substitute
• Solve
• Units and Rounding
• Is answer reasonable

1.7m
43cm
5 Catley Ex 13.8 A
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End Lesson 1

• Ex 11.2 3-8

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Starter Lesson 8
3000m
63o
42o
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Answers Starter Lesson 8
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Answers Starter Lesson 8
x
y
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Calculator use Stats Mode in fx-9750G Plus
We will be doing an example of finding mean,
median, mode and quartiles of the following data
set 12, 14, 17, 20, 21, 21, 21, 26
Select Stats Mode Exe
Input Data Exe after each entry
If Data on screen select which list press F6
then F4 to Delete all
F6 to get this screen then F2 for CALC
F1 to say yes
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After Calc you do F6 Set but only need to do this
part once to set up
Make these settings then exit to get back
Press F1 1VAR
Scroll down to see all of these
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eg. Calculate the HV UQ Med LQ LV Range

IQR Mean Mode
for each of the following sets of values
a. 3, 7, 4, 5, 3, 6, 8, 3, 2, 3 b. 1
03, 107, 104, 105, 103, 106, 108, 103, 102, 103
c. 36 cm, 42 cm, 43 cm, 39 cm, 40 cm, 47 c
m, 49 cm and 72 cm.
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NCEA Level 2 Folders
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Unit 3 Graphs
Starters

• Lesson 7 Hyperbolae
• Lesson 8 Hyperbolae 2
• Lesson 9 Exponential Graphs
• Lesson 10 Logrithmic Graphs
• Lesson 11 12 Applications of Graphs
• Lesson 13 Writing Equations of Graphs
• Lesson 14 Writing Equations of Graphs 2
• Lesson 15 Features of Graphs
• Lesson 16 17 Merit Excellence Questions
• Lesson 18 Mock 2.2

• Revision
• Lesson 1 Parabolas in Factorised Form
• Lesson 2 Parabolas in Expanded Form
• Lesson 3 To Plot a Parabola by completing the
  square (Extn only)
  
• Lesson 4 Scale Factors and Parabolas
• Lesson 5 Cubics
• Lesson 6 Circles

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Lesson 7 Hyperbolae
Hyperbolae exist in the form xynumber
Or

• Coordinates of a point multiply to give the same
  number
  
• Hyperbolae have 2 distinct branches
• They are NOT continuous graphs
• They get very close to the x and y axis but they
  never touch
  
• The x and y axis are asymptotes
• If the number is negative the graph is reflected
  in the x axis
  

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The bigger the number gets the further away from
the origin the graph gets
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To plot say What do I times 1 by to make 8?
Answer 8 so (1,8) What do I times 2 by to
make 8? Answer 4 so (2,4) What do I times 3 b
y to make 8? Answer not a whole number What d
o I times 4 by to make 8? Answer 2 so (4,2)
What do I times 1/2 by to make 8? Answer 16
so (1/2,16) etc
Use table mode in graphics Calculator
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Hyperbolae can be translated on the grid like
parabolas
1) Vertical Translation
The 4 moves the hyperbola up 4 units
The horizontal asymptote is now y4 instead of
the x axis To plot find the asymptote then pre
tend it is the x axis and plot
You can put y0 to find the x intercept. Or G-
solve (root) on the calc
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2) Horizontal translation
The -4 in the brackets moves the parabola right ?
to 4 units The vertical asymptote is now x4
instead of the y axis To plot find the asympt
ote then pretend it is the y axis and plot
You can put x0 to find the y intercept. Or G-
solve on the calc
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3) Vertical and Horizontal translation
This is a graph translated up 2 and
left 1

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7 Calculus folders
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7 Calculus Unit 5 Conics

• Lesson 1 Coordinate Geometry Revision
• Lesson 2 Parallels and Perpendiculars
• Lesson 3 Distance Formula Applications
• Lesson 4 Translation of Curves
• Lesson 5 Circles
• Lesson 67 Graphs
• Lesson 8 Ellipses
• Lesson 9 Parabolas

• Lesson 10 Hyperbolae
• Lesson 11 Applications
• Lesson 12 Parametric Equations of Straight Lines
  and Circles
  
• Lesson 13 Parametric equations Ellipses and
  Parabolas
  
• Lesson 14 Parametric equations of Hyperbolae
• Lesson 15 Parameters
• Lesson 16 Parameters 2

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Lesson 3 Distance between two points
We can find the distance between two points by
Pythagoras
From example
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Distance Formula Applications
2) Distance between 2 points
From sheet
Remember
a variation on Pythagoras-be aware of 3,4,5
5,12,13 7,24,25 triangles
A locus is the path traced by a point
A straight line is the shortest distance between
two points
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Eg 5 Find the locus of the point P(x,y) which
moves so that it is always 5 units from the origin
(x,y)
(0,0)
5units
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6 Find the equation of the locus of the point
which moves so that it is equidistant from the p
oints (5,1) and (1,-9)

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(5,1)
(1,-9)
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Eg 7 Find the locus of the point P (x,y) which
moves so that the sum of the distances from (-1,
0) and (1,0) is 4
(x,y)
b
a
(1,0)
( )2 (
)2
(-1,0)
( )2 ( )2
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Students often request things
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Eg Ex 11.2 6
y
x
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Eg Ex 37.6 1
If a barge is to pass under a bridge then if we
look at the coordinates of the corners, the y
coordinate must be less than the one obtained
from the equation of the bridge
If not, this is what happens
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Chapter 22 Linear Programming

• Lesson 1 Linear programming
• Lesson 2 Intersection of linear inequalities.
• Lesson 3 Words Problems
• Lesson 4 Linear programming
• Lesson 5 Linear programming - Applications

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Lesson 1 Linear Programming
We are going to look at a set of constraints on
some variables. From these we are going to look
to find a maximum or minimum of an expression
that falls within these constraints.
These constraints are conditions or restrictions
we put on the variables. For example we must
operate between 10 and 40 degrees Celsius.
(0l life applications like maximizing profits given
resource constraints. We will also do some
questions without application just for practice.
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Recall Inequations
Inequations are like equations except they have
and inequality

Same rules as solve except
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Graphing Inequalities

• First graph the boundary line. That means
  graph the y type first then worry about the
  inequality.
  
• If the Inequality is , we graph the line as a
  solid line
  
• If the Inequality is the line is not to
  be included so we used a dashed line.
  
• Now use a test point on either side of the line
  and see if this satisfies the inequality. If it
  does shade in that side of the line. If the test
  point does not satisfy inequality, shade in other
  side of line.
• To confuse things later we will shade out the
  side we dont want.

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Graphing Inequalities Example 1
Graph the inequality y2x 1 First, graph the bo
undary line y 2x 1 (Dashed since )
Now try a test point (0,0) to see if it satisfies
equation. 02(0)1 01 False Since it do
es not satisfy, we shade the other side of line
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Graphing Inequalities Example 2
Graph the inequality y -2x 3
First, graph the boundary line y -2x 3 (Solid
since )
Now try a test point (0,0) to see if it satisfies
equation. 0-2(0)3 0 3 True Since it does sa
tisfy, we shade this side
Test point does not have to be (0,0) it just is
easy. If (0,0) is on line pick a new test point.
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End Lesson 1

• Exercise 22.1 odd

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Lesson 2 Intersection of Linear inequalities.
We are now going to graph a set of linear
inequalities and look for a region (area) common
to all three. As mentioned earlier we are now goi
ng to shade out the regions we dont want so
the region we do want is the only part left
clean, without shading. Otherwise you would be lo
oking for overlap of three or more shadings.
This gets very messy. The most important thing is
to again draw in the Boundary lines. We also
want the intersection of the boundary lines to be
clear. These intersections are just solving a
system of linear equations, two equations at a
time.
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Intersection of linear inequalities Example 1
Find the region defined by
Solid Solid dashed
First Boundary lines
Now try a test point (0,0) to see if it satisfies
equation 1 0 2(0)4 0 4 True Since it does
satisfy, we shade out other side side
Now try a test point (0,0) to see if it satisfies
equation 2 0 0 -2 0 -2 True Since it does
satisfy, we shade out other side side
We want xpoint)
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Intersection of linear inequalities Example 1
(cont)
Find the region defined by
So any point that is not shaded satisfies all
three conditions. Note since boundary x2 is not
shaded we can get close to x2 line but not touch.
The lines intersect at (-2,0) (2,8) and (2, -4)
Easy to solve just using two lines at a time and
substituting. These points of intersection will b
ecome very important soon.
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Intersection of linear inequalities Example 2
Find the region defined by
Dashed Dashed Solid Solid
First Boundary lines
We cant use test point (0,0) for the first two
equations as on the line.
Use test point (1,1)
Equation 1 10, true, shade other side
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Intersection of linear inequalities Example 2
(cont)
Find the region defined by
Dashed Dashed Solid Solid
First Boundary lines
We cant use test point (0,0) for the first two
equations as on the line.
Use test point (1,1)
Equation 2 10, true, shade other side
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Intersection of linear inequalities Example 2
(cont)
Find the region defined by
Dashed Dashed Solid Solid
First Boundary lines
We cant use test point (0,0) for the first two
equations as on the line.
Use test point (1,1)
Equation 3 113, true, shade other side
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Intersection of linear inequalities Example 2
(cont)
Find the region defined by
Dashed Dashed Solid Solid
First Boundary lines
We cant use test point (0,0) for the first two
equations as on the line.
Use test point (1,1)
Equation 4 117, true, shade other side
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Intersection of linear inequalities Example 2
(end)
Find the region defined by
Here it is easier to see. Sometimes you are asked
for the integer coordinates that satisfy the
system. Watch you are not allowed on dashed lines
!
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Graphics Calculator Notes

• Calculator can shade for you pick type for
  etc.
  
• Calculator will not do xby hand anyway)
  
• Use calculator to find intersections of 2 lines
  at a time.

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How to contact us and Prices

• Chris Delisle chris_at_dwresources.co.nz
• Helen Wiessing helen_at_dwresources.co.nz
• Call Dargaville High School [phone]
• Pricing Depends on school size.
• 600-1000 students 200 per year level
• 1000-1500 students 250 per year level
• 1500-2000 students 300 per year level
• 2000 students 350 per year level
• 50 per level continued access which includes
  updates each year.
  
• Note Calculus and Statistics are considered
  different levels for charging purposes