Math 6A, Lesson 16, Spring 2020, 6/21/2020

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Go over the Final Exam, and class celebration party – share your story and your thoughts.  All of our students have worked very hard and have made so much progress. I’m so proud of you! At this unprecedented time, we have had 14 ZOOM classes together with an almost perfect attendance rate! Your patience, resilience, self-motivated-learn and your humorous comments and laughter in the classroom, are the inspiration for me. I love you all!

Keep up your hard work! Have a great summer!

Math 6A, Lesson 15, Final Exam Spring 2020, 6/14/2020

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Final Exam Spring 2019, 6/9/2019. The exam will cover all the materials we have covered in Spring 2019 term, namely chapter 5 to chapter 8:

Math 6A, Lesson 14, Spring 2020, 6/6/2020

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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 2020, 5/31/2020

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1. Quiz about percentage (TBD)

2. Discount

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

3. Sales Tax and Income Tax

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

4. Compound Discount

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

5. 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

6. 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

7. 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

8. 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

9. Home Work:

  • Handout:
    • Three pages
  • Workbook:
    • Page 45: 1, 2, 3
    • Page 46: 4, 5

Math 6A, Lesson 12, Spring 2020, 5/17/2020

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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 ( End_value, or New_value) – Original_value
  • Percentage increase = ( IncreaseOriginal_value) x 100%
  • Increased_value = (100% + Increase %) x Original_value

3. Percentage decrease

  • Decrease = Original_value – Decreased_value ( End_value, or New_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 2020, 5/10/2020

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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 per centum, meaning “per hundred”.

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 2020, 5/3/2020

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

Math 6A, Lesson 9, Spring 2020, 4/26/2020

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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 2020, 4/19/2020

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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:
    • three pages
  • Page 33:
    • 1, 2, 3, 4

Math 6A, Lesson 7, Spring 2020, 4/5/2020

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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