Go over Final Exam, and class celebration party. All of our students have worked very hard and have made so much progress. I’m so proud of you! Have a great summer!

## Math 6A, Lesson 15, Final Exam Spring 2018, 6/10/2018

Final Exam Spring 2018, 6/10/2018

## Math 6A, Lesson 14, Spring 2018, 6/3/2018

**1. Perpendicular Bisectors and Angle Bisectors**

- Use of compass: center, radius, pin leg, and drawing leg
- To draw a circle
- To mark off or copy a line segment
- How to draw a
**perpendicular bisector of a line segment**? - Any point on the perpendicular bisector of a line segment is equidistant from the two end points of the segment.

**2. Angle Bisectors**

- A ray AZ divides <BAC into two equal angles, <BAZ and <CAZ. The ray is called
**the angle bisector**of <ABC - How to draw an angle bisector?
- Any point on the angle bisector of an angle is equidistant from the two sides of the angle.

**3. Class work**

- Construct/draw circles, triangles, angles, equal line segments
- construct /draw perpendicular bisectors of line segments
- construct/draw angle bisectors of angles

**4. Classification of Triangles**

- The number of equal sides in the triangle:
**scalene triangle**– no equal sides;**isosceles triangle**– two equal sides;**equilateral triangles**– three equal sides - The type of angles of the triangle:
**acute-angled triangle**– all angles are acute;**right-angled triangle**– one of the angles is a right angle;**obtuse-angled triangle**– one of the angles is an obtuse angle - Is an equilateral triangle also an isosceles triangle?
- Is it Possible to draw a triangle with more than one obtuse angle?
- Can a scalene triangle be an acute-angled, right-angled or obtuse-angled triangle?
- All the three angles in a scalene triangle are different size
- The angles opposite the equal sides of an isosceles triangle are equal
- All the three angles in an equilateral triangle are equal in size

**5. Quadrilaterals**

- A closed plane figure with four straight sides joined by four vertices is called a quadrilateral
- Vertices, diagonals
- Properties of special quadrilaterals
- Parallelogram: 2 pairs of parallel and equal opposite sides
- Rectangle: all angles are right angles
- Rhombus: all sides are equal, diagonals are perpendicular to each other
- Square: all sides are equal, all angles are right angles
- Trapezoid: 1 pair of parallel sides

**6. Home Work:**

**Handout:**- Two pages

**Workbook:**- Page 48-50: 12, 13, 14,15,16

## Math 6A, Lesson 13, Spring 2018, 5/20/2018

**1. Discount**

- Discount = Marked price – Selling price
- Percentage discount = ( Discount / Marked_price) x 100%
- Selling price = (100% – Discount %) x Marked_price

**2. Sales Tax and Income Tax**

- Tax = Tax_rate x Cost
- Income_tax = Tax_rate x Income
- Income: wage (hourly-paid), salary (annual basis)

**3. Compound Discount**

- Each successive discount is based on the price after the previous discount

**4. Points, Line and Planes**

- Point: has position; has no size
- Line: has an infinite number of points; has no width; can be determined by two points; can be straight or curved
- Ray: a part of a line with one endpoint
- Endpoint
- Line segment: a part of a line between two end points; has length
- Plane: a flat surface; has no thickness
- Parallel lines: two lines on the same plane do not intersect (meet or cut)
- Perpendicular (lines) to each other: two lines intersect at right angle
- Foot of the perpendicular

**5. Types of angles**

- Acute angle: angle < 90 degree
- Right angle: angle = 90 degree
- Obtuse angle: 90 degree < angle < 180 degree
- Reflex angle: 180 degree < angle < 360 degree

**6. Complementary, supplementary, and adjacent angles**

- Complementary angles: the sum of two angles is 90 degree
- Supplementary angles: the sum of two angels is 180 degree
- Adjacent angles: two angles share a common side and a common vertex but do not overlap

**7. Properties of Angles**

- The sum of adjacent angles on a straight line is 180 degree
- The sum of all angles at a point is 360 degree
- Vertically opposite angles: when two lines intersect, the vertically opposite angles are equal

**8. Home Work:**

**Handout:**- Three pages

**Workbook:**- Page 45: 1, 2, 3
- Page 46: 4, 5

## Math 6A, Lesson 12, Spring 2018, 5/13/2018

**1. Reverse Percentage**

- In a box, 15% of the balls are green. If there are 54 green balls, find the number of balls in the box.
- In the library, the fine for not returning a book on loan is 125% of the price of the book. If the fine for a book that was not returned was $90, find the price of the book.

**2. Percentage increase**

**Increase**= Increased_value – Original_value- Percentage increase = (
**Increase**/**Original_value**) x 100% - Increased_value = (100% + Increase %) x Original_value

**3. Percentage decrease**

**Decrease**= Original_value – Decreased_value- Percentage decrease = (
**Decrease**/**Original_value**) x 100% - Decreased_value = (100% – Decrease %) x Original_value

**4. Home Work:**

**Handout:**- Three pages

**Workbook:**

- Page 40: 8, 9, 10, 11

## Math 6A, Lesson 11, Spring 2018, 5/6/2018

**1. Percentage: **a percentage is a fraction with 100 as the denominator

- Meaning of percentage: “per cent” means “by the hundred” or divided by one hundred. The term “percentage” is derived from the Latin
, meaning “per hundred”.*per centum*

38% = 38/100 = 0.38

100% = 100/100 = 1

0% = 0/100 = 0

- Decimals, percentages and fractions and how to express a number in each form
- Express one quantity as a percentage of another
- Compare quantities using percentage
- Word problems involving percentage

**2. Home Work:**

**Handout:****Two pages**

**Workbook:**

- Page 39: 1, 2, 3, 4, 5
- Page 40: 6, 7

## Math 6A, Lesson 10, Spring 2018, 4/29/2018

**Exam on ratio, rate, average rate, speed, uniform/constant speed and average speed, and Conversion of units.**

## Math 6A, Lesson 9, Spring 2018, 4/8/2018

**1. Average Rate**

Rate involves two quantities and it is usually expressed as one quantity per unit of another quantity.

$/oz, mile/gal, words/min, $/sq.ft, $/hour

**2. Speed, uniform/constant speed and average speed**

Speed = (distance traveled) / (time taken)

Average Speed = (Total distance traveled) / (total time taken)

**3. Conversion of units**

km/hr → m/s → miles/hr

$/inch → $/ft

$/ticket → euro/ticket

**4. Home Work:**

**Handout:****Three pages**

**Workbook:**

- Page 34: 5, 6, 7, 8, 9, 10
- Page 35: 11, 12, 13, 14, 15, 16, 17
- Page 36: 18, 19, 20, 21, 22

## Math 6A, Lesson 8, Spring 2018, 4/1/2018

**1. Ratio**

- Meaning of ratio – Given any two similar quantities, a and b, the ratio of a to b (denoted by a:b) is defined as a:b = a/b, where b != 0
- The quantities have to have same/similar unit.
- Simplification of ratios: a:b = (ma): (mb) = (a/m): (b/m), where m !=0

**2. Ratios of three quantities**: the ratio involving three quantities cannot be written as a fraction. However, it can be simplified by multiplying or dividing each term by the same constant. For example, a:b = 5:6, b:c = 8:11, find a:b:c. Recall LCM, we convert each ratio to an equivalent ratio where the new value of b is the LCM of the original values of b:

a:b = 5:6 = 5*4 : 6*4 = 20:**24**

b:c = 8:11 = 8*3 :11*3 = **24**:33

hence , a:b:c = 20:**24**:33

**3. Word problems involving ratios**

**4. Home Work:**

- Handout:
- two page

- Page 33:
- 1, 2, 3, 4

## Math 6A, Lesson 7, Spring 2018, 3/25/2018

**Continue on Chapter 5.4 Forming Linear Equations to Solve Problems**

**1. Midterm Exam: all about equations**

**2. Constructing/Forming Linear Equations to Solve Problems**

The steps involved in problem solving with linear equations are:

- Step 1. Read the question carefully and identify the unknown quantity
- Step 2. Use a letter to represent the unknown quantity (e.g. x)
- Step 3. Express other quantities in terms of x
- Step 4. Construct/Form an equation based on the given information
- Step 5. Solve the equation
- Step 6. Write down the answer statement

**3. Homework:**

- Redo the problems you got wrong in last two homework assignments