Lectures and Quick Notes(1.1)
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Chapter 1
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Lectures and Quick Notes(1.1
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Lectures and Notes 10 Videos

Section Introduction on Connecting English with Math & Graphing Lines

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Section Intro

Converting Word into Algebra for the basic Operations

example 1: Convert the following into algebra to expressions:

  • "+": 4 more than a number
  • "-": 4 less than a number
  • "\times": Three "times" a number
  • "of": Three of a number OR half of a number

See video for details

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Converting Word into Algebra for Sum Subtraction and Multiplication

Converting Words into Algebra Equation

A first example with percentage

example: 60\% of the school population is 300. What is the 100\% of the population?


See video for details


Solution:

500 is the population of the school.

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Converting Words into Algebra Equation

Converting words into Equations

example: Find a number when subtracted by 4 it's the same as when the number has been increased by 3 and then halved.


See video for steps


n = 11

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Converting Words into Equations ex1

How about division?

Typically here is what we do when we talk about division:

  • dividend รท divisor = quotient

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Converting Division word programs into Algebra Expressions

Modelling Cost of items

Jim is looking to buy a mixture of two coffee beans in StarCoffee. There are two different types of roast: Pike and Blonde. Jim is going to spend a total of \$24 on coffee beans. The Pike roast cost \$8/kg and the Blonde roast cost \$6/kg.

(a) Write an equation to represent Jim's purchases.

(b) Isolate the variable for the number of jellybeans in your equation.

(c) If Jim bought 250 g of Pike, how many grams of Blonde did he buy?

(d) If Jim bought 150 g Blonde, how many grams of Pike did he buy?


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Modelling Cost of items

Geometry Set Up Example

ex The length of a rectangle is 4 cm less than 3 times the width. The perimeter is 36 cm. Find the width and length.


Therefore, the width of the rectangle is 5.5 cm and the length of the rectangle is 12.5 cm.

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Geometry Set Up Example

ex Two consecutive numbers add up to 55. What are the two numbers?


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Consecutive Numbers

Graphing Lines

y = mx + b form

Ax + By = C

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Graphing Lines

Intersection of Lines

example: Find the intersection point between the two lines below.

  • \displaystyle y = \frac{1}{2}x -1
  • \displaystyle y = -\frac{3}{4}x + 6


The two lines share the point of intersection say (a, b).

Since (a, b) is on both lines they can be now written in terms of a and b in the following way.

  • \displaystyle b = \frac{1}{2}a -1
  • \displaystyle b = -\frac{3}{4}a + 6

Therefore,

\displaystyle \left(\frac{28}{5}, \frac{9}{5}\right)

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Intersection of Lines