Automotive service technician, food and beverage management, heating technician, heavy duty and commercial mechanics, and resort management programs

2. Radicals. 3

4. Review and Test 4

5. Pythagorean Theorem. 5

6. Make a Table and Graph. 6

7. Construction Geometry. 7

8. Review and Test. 7

9. Applications. 8

10. Trigonometry – Tangent 10

11. Trigonometry Sine and Cosine. 12

12. Review and Test. 13

Lesson 1.

Averages and Reading Graphs.

In this lesson you will learn to find averages and solve problems involving averages. You will also review material on interpreting graphs.

	Answers and Notes
Find the mean of: 5, 5, 7, 10, 15	8.4
Find the median of: 5, 5, 7, 10, 15	7
Find the mode of: 5, 5, 7, 10, 15	5

Bar graphs	know how to make these and how to read information from these
Line Graphs
Pie graphs (circle)

Line Graph

1. What is the average speed at 50m?

2.5 m/s

Lesson 2.

Radicals

In this lesson we look at the square root of a number () as well as the square root of algebraic expressions.

	Answers and Notes
	5 8 13 9 4 15 3 2 1 7 12 14
	x x³ x⁶
	6x 7x³ 9x⁶
	x/7

After completing the material you should be able to simplify expressions like:

and

13x⁶ 2x¹⁰/15

Lesson 3.

Scientific Notation

This is a short but important topic. Scientific notation is a good way to write very large or very small numbers. After this lesson you will do a practice review lesson and a quiz on all of the topic covered so far from Part I and Part II.

	Answers and Notes
Convert to scientific notation: 783,000,000 = 0.00052 =	7.83 x 10⁸ 5.2 x 10^-4
Convert to decimal notation: 2.8 x 10⁷= 3.91 x 10 ^–4 =	28 000 000 0.000391

After completing the material you should be able to

Convert to a decimal 7.8 x 10 ^–5 = 0.0078

Convert to scientific notation 0.0379 = 3.79 x 10^-2

Lesson 4.

Review and Test

Answers: (1) 1.46 (2) –8, 90, 23, -11 (3) 7 (4) $4.50 (5) (6) 11 (7) $3.50, $7, $14 (8) 17, 19, 21 (9) –1 (10) 12.86 cm (11) 8.4% (12) 30.3% (13) 44 (14) 84.78 m³ (15) 31.4 m (16) 54° (17) 87° (19) 130.625 kg (20) 70 cm (21) 9x⁶, x³/12 (22) 0.0000915, 5.2 x 10^-4

After completing the review —write a quiz based on the review.

Lesson 5.

Pythagorean Theorem.

In this lesson you will learn to use the Pythagorean theorem to calculate the missing side of a right triangle.

	Answers and Notes
	note that the legs are on one side of the equation and the hypotenuse the other
	c = 13
	b = 12

After completing the material you should be able to find the missing side of the following:

(1) a = 4 (2) x = 25 (3) x = Ö3 = 1.73

Lesson 6.

Make a Table and Graph.

In this lesson you will learn how to make a table of values from an equation and to use the table to plot points on a graph. A good knowledge of the x-y coordinates is important. Reading and making graphs are important aspects of most trades.

	Answers and Notes
Ordered pair
Coordinate
Quadrant
Origin
x-axis and y-axis
Make a table and graph y=3x+2 For a lesson on this see: http://www.purplemath.com/modules/graphlin.htm

After completing the material you should be able to make a table and graph an equation like: y = 4x – 5

Lesson 7.

Construction Geometry.

Trades that require measurement rely on construction geometry. You will be expected to perform the following using only a straight edge and compass: bisect an angle; bisect a line segment; construct a right angle; construct perpendicular lines; construct parallel lines

Go to http://www.nas.com/~kunkel/construction/whatis.htm and read about the rules governing constructions.

Go to http://www.nas.com/~kunkel/construction/reference.htm and learn to do construction # 1 to 7. ( a print version of this is available)

Lesson 8.

Review and Test.

A review of all of the material covered in the intermediate level to date is provided here. You should complete this review, check your work and then sit the test.

Answers: (1) 32 (2) 14, -32, 19, -12 (3) 4 (4) $49.70 (5) (6) 4 (7) 2, 4, 12 (8) 26, 28, 30 (9) –11 (10) 1.67 m (11) 20 % (12) 24 (13) 15 (14) 565.2 m³ (15) 3 cm (16) 50° (17) 150° (19) 8.34 g (20) ~86 (21) 12x⁴, x³/9 (22) 0.00314, 3.24 x 10⁵ (24) 13.2

Lesson 9.

Applications.

You are taking mathematics because your trade requires you to solve some problems. One of the most useful parts of mathematics is the topic of applications that help us with our work. The aim of this lesson is to provide you with some tools that you can use in solving problems within your trade.

	Answers and Notes
An algebraic expression for:
One job takes five times as long as another	5t
Pump B lifts one-quarter as much water as pump A	B = A/4 or A = 4B
We have ten times as many washers as bolts	W = 10B
A 15m pipe is divided into two parts	x and 15 - x
increased by more than combined, together total of sum added to	all mean add
decreased by minus, less difference between/of less than, fewer than	all mean subtract
of times, multiplied by product of increased/decreased by a factor of (this type can involve both addition or subtraction and multiplication!)	all mean multiply
per, a out of ratio of, quotient of percent (divide by 100)	divide
is, are, was, were, will be gives, yields sold for	this is where the equal sign goes

After completing the material you should be able to translate the following into symbols:

The length of a football field is 30 yards more than its width. Express the length of the field in terms of its width w.

L = w + 30

Twenty gallons of crude oil were poured into two containers of different size. Express the amount of crude oil poured into the smaller container in terms of the amount g poured into the larger container

smaller = 20 - g

Lesson 10.

Trigonometry – Tangent

There are three trigonometric ratios: tangent, sine and cosine. We begin with tangent because the majority of problems can be solved with this ratio. A review of Pythagoras and right triangle properties is necessary.

Answers and Notes

Find side X:

tan 76 = x/80

x = 80 tan 76

= 321

Find side X:

tan 76 = 50/x

x = 50/tan 76

= 50/4.0108

= 12.5

Find angle X

tan x = 20/80 = 0.25

x = tan^-1 (0.25)

= 14.04

After completing the material you should be able to do the following: draw appropriate triangles; set up your trig equations; and solve the equations.

The angle of the sun is 21°. How long is the shadow of this 25m high totem pole?

65 m

Earlier that day when the sun’s angle was 52° the shadow of this tree was 63m. How high is the tree?

81 m

This tree cast a shadow of 75m and when it came down it measured 45m. What was the angle of the sun?

31°

Lesson 11.

Trigonometry Sine and Cosine.

The other two commonly used trigonometric functions are sine and cosine.

Answers and Notes

sin A = 70/250 = 0.28

cos A = 240/250 = 0.96

After completing the material you should be able to do MAP 360 page 632 # 6 to 8.

Lesson 12.

Review and Test.

A review of all of the material for the intermediate level is provided here. You should complete this review, check your work and then sit the test.