Chapter 4 Equations and Formulae

Warm Up If p = -2, q = 3 and r = 4, find ▫p + 5qpr – 7q

Holly is studying overseas and makes a lot of calls back home. She is comparing two different mobile phone plans, both of which give free local calls, but which charge international calls at different rates. Plan A costs €25 for the monthly access fee and international calls are billed at 17 cents per minute. Plan B costs only €10 for the monthly access fee but international calls are billed at 23 cents per minute Things to think about: ▫Can you write a formula for each plan that connects total cost €C with the number of minutes m used on international calls per month? ▫Use the formula to find the total cost for each plan if Holly’s international calls total  150 minutes per month300 minutes per month ▫Find the values of m such that the cost of each plan is the same. ▫What advice would you give Holly regarding her choice of plans?

Vocabulary to Know Expression-variables and numbers but no = ▫Simplify or Evaluate Equation- variables and numbers but with = ▫Solve Formula- connects the values of variables

Linear Equation Form ax + b = 0, highest exponent = 1 Solve: 8 – 4x = -2

Fractions! Say What?!

Another One

More than one variable Solve: 4(2x + 5) -3(x – 2) = 16

Another Solve: 4x – 3 = 3x + 7

And Another Solve: 5 – 3(-1 + x) = x CD begin p. 96 #1a – c, #3a, b DP you will also do #4, but not yet.

Expand it and solve it.

DP Do the others and include p. 97 #1

Get rid of fractions!

Again

Warm Up!

What’s different?

Another

Warm Up!

Solve: 4.6x – 8.9 = 7.2 Equation must be set equal to zero first. Press Math button and arrow down and select Solver. Type in equation. Place cursor on “x =“ Press Alpha then Enter

How can this be used? It’s good to know when you DON’T have the skills to solve the equation. Use it to check answers.

Solving Graphically

Examples When w grams of weight are placed on a spring balance, the scale reads R mm. The reading is given by the rule R = 0.4w + 5 ▫R = 27R = 42

Try These! P. 100 #1, 2, 4-6

4E: TLW problem solve with linear equations.

Steps to Guide You 1.Decide what’s unknown and label with variables 2.What operations do you need to use? 3.Write an equation. 4.Solve it. 5.Write it in a sentence complete with label. 6.Check it.

When a number is doubled and then subtracted from 3, the result is -17. Find the number.

When a certain number is trebled then decreased by 1, the result is twice as much as 5 more than the number. What’s the number?

Using a box to organize. Malikah’s mom is presently four times as old as Malikah. In 6 year’s time her mom will be 3 times as old as Malikah is then. How old is Malikah now? ▫Need to write equation for the same year. NowIn 6 years Malikah Mom

Carl has only 20¢ coins and 50¢ coins in his wallet. He has 3 more 50¢ coins than 20¢, and their total value is $2.90. How many 20¢ coins does Carl have?

You’re on your own, unless you’re nice to me. P #1-10, CD skip #3 and 7

3F TLW substitute values into formulas. Formulas connect two or more variables to each other. What are some formulas you know?

Time For You to Shine P. 104 #1-8

4G: TLW rearrange formulas. You can rearrange formulas to make equivalent formula that is easier to work with.

Volume of a Cone

It’s like solving an equation for a variable. Make y the subject of 3x – 7y = 22

Make x the subject of 7x + 3y = d

Rearrangement and Substitution

Try These Now! P, 107 #1-4

4H TLW solve simultaneous equations. There are many ways to solve simultaneous equations and we will look at a few. You need to find a solution that must be true for all the equations at the same time What does the solution represent graphically?

Solving with a GDC (Polysmlt 2)

Graphical Method and the GDC

Algebraic Methods-Substitution

Example

Elimination Equations are in ax + by = c format Get one set of variables with the same size and opposite signs ▫Add them together

Example Look for variables with opposi signtes or the same coefficient

Time to Solve 4H.3 p. 111 #1-2 a-c only 4H.4 p. 112 #2-4 Check with GDC!

4I: TLW problem solve using simultaneous equations.

Steps to Help You Solve 1.What unknowns represent x and y? 2.Two variables = 2 equations 3.Solve it. 4.Check it. 5.Write your answer in a sentence with labels.

Find two numbers which have a sum of 37 and a difference of 11.

Try These P. 113 #1 and 2

Two adults’ tickets and three children’s tickets to a baseball match cost $45, while 3 adults’ and 4 children’s tickets cost $64. Find the cost of each type of ticket.

Assignment CD p.114 #3-6 DP p. 114 #3-10 ▫Remember: Distance = Rate * Time

Factoring Quadratics

How To… These numbers should multiply to c and add to b.

Examples

The Youngberg Method

4J: TLW solve quadratic equations.

Example

Try These 4J.1 p. 116 #1a-d, 2a-c, h (DP only)

The Null Factor Law

The Null Facto Law If a*b = 0, then a = 0 or b = 0 Must factor quadratic Set each factor = zero ▫Example: 3x(x – 5) = 0

Example (x – 4)(3x + 7) Assignment: p J.2 #1-2

Quadratics and the GDC

Example 3(x-1) + x(x +2) =3 ▫What’s wrong with this picture?

Try These 4J.3 p.118 #3 CD a and b; DP a, b, d

Example

Graphing for Solutions

Quadratic Formula

Example

Try These P.121 CD #1a-f DP #1, 2a, b Final assignment: CD p. 121 #1 g-I DP p. 120 #7, p.121 #1g-i, 2c-f

4K: TLW problem solve with quadratics.

Process Transfer words into an equation Solve it Do you have reasonable solutions? Write answer in a sentence with labels

Two integers differ by 12 and the sum of their squares is 74. Find the integers.

Assignment CD p.123 #6-8 DP p.123 #1-8

Assignment CD p.123 #9, 10, 11 DP p. 123 #9-14