Math 6A, Lesson 16, Spring 2018, 6/17/2018

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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!

Spring2018

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

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Final Exam Spring 2018, 6/10/2018

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

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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 2018, 5/20/2018

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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

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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 – 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

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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 2018, 4/29/2018

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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 2018, 4/8/2018

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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 2018, 4/1/2018

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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:
    • two page
  • Page 33:
    • 1, 2, 3, 4

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

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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