Week Seven - Mane 31st Mei

Today we continued preparation for your test on Thursday. I will be providing a revision session on Wednesday at interval for those of you who need extra help.

In order to prepare for the test you should:

• Read through all your notes in your exercise book - try to summarise this into one page of notes!
• Choose a few questions from each exercise (chapters 7, 8 and 9 in your homework book) and try them out to make sure you remember how to do them.
• Mark the work in your homework book and go back and do extra work on any topics where you got most questions wrong.

Good luck! Remember to also bring your clear-files in on Thursday.

Week Six - Paraire 28th Mei

Today we revised in preparation for our test which will now be on Thursday. Please make sure to bring your homework book on Monday.

Homework that was due on Friday: 9.06, 9.06 and all of 8.04

Week Six - Turei 25th Mei

Today we looked at finding the formula for a linear pattern. Linear patterns add the same number each time (this could be negative). All have a formula like dn + k where:

• d is the number we add each time (the difference)
• k would be the number if we went backwards in our pattern

Examples:

• 3, 5, 7, 9 (adds 2 each time so d is 2 and if we went backwards in the pattern we would get 9, 7, 5, 3, 1 so k is 1) ---> so the pattern rule is 2n + 1
• 2, 6, 10, 14 (adds 4 each time so d is 4 and if we went backwards in the pattern it would go 10, 6, 2, -2 so k is -2) ---> so the pattern rule is 4n - 2
• 99, 96, 93 (subtracts 3 each time so d is -3 and k is 102) ---> the rule is -3n + 102

Homework: 8.04

Week Six - Mane 24th Mei

Today we looked at patterns. We saw three ways to represent these:

• Using diagrams - these often show where patterns come from.
  
• Using a list of numbers such as 4, 7, 10, 13 ... Since we are adding 3 we know the next number should be 16
  
• Using a formula such as 3n + 1. A formula is the best of these as it can show us what comes next and what comes much much later.

For example we can use the formula to find the first 4 terms:

• When n=1 then 3n+1 = 3+1 = 4
• When n=2 then 3n+1 = 6+1 = 7
• When n=3 then 3n+1 = 9+1 = 10. These are the same numbers as the pattern above
• However with a formula we can also find when n=100 then 3n+1 = 300+1 = 301 which is the 100th number in the pattern.

Homework: 9.07

On Friday we will have the test. There will be a revision session at morning tea before it.

Week Five - Paraire 21st Mei

Today was our final day exploring factorising. We looked at factorising with a letter (or more than one letter) as our factor. Because we always choose the highest common factor we much choose the most letters possible. Examples:

• ab + ac = a(b + c)
• 2p + pq = p(2 + q)
• x^2 + 3x = x(x + 3) since x^2 is the same as x times x
• x^5 + 3x^4 = x^4 (x + 3) since x^4 is the highest power that is part of both terms

Homework: 9.06

Week Five - Taite 20th Mei

Today we looked at factorising by finding the highest common factor (HCF).

The HCF is a number that is the highest factor of both numbers. Example:

• factors of 4 are {1,2,4} since 4 = 1 x 4 and 2 x 2
• factors of 12 are {1,2,3,4,6,12} since 12 = 1 x 12 and 2 x 6 and 3 x 4
• So the HCF of 4 and 12 must be 4

To factorise we put the highest common factor first, and then find the missing parts.
e.g factorising 4x + 12 gives
4(x + 3) since 4 times x gives 4x and 4 times 3 gives 12.

For extra help with HCFs see homework exercise 1.02

Homework: 9.05 so 9.01 - 9.05 is due tomorrow.

Week Five - Turei 18th Mei

Today we looked at factorising. This is the opposite of expanding so it means putting an expression into brackets.

• The first step is to find a common factor - something that is the same for both parts of the expression. e.g for 2a + 2b it is 2
• We write this first then put a set of brackets. e.g. 2 ( )
• We fill in the space so that it makes the original expression e.g. to make 2a we need an a and to make 2b we need a b so in the brackets we have a + b
• The final answer is 2(a + b). We can check this is the same by expanding our brackets.

Homework: 9.04

Week Five - Mane 17th Mei

Today we looked at combining the skills of expanding and simplifying into one problem. In order to do this we take the following steps.

1. Re-write the equation using a multiplication symbol right before the brackets. e.g 7(p + 2) - 4p = 7 x (p + 2) - 4p
2. Find the part that needs expanding. Shown in bold here: 7 x (p + 2) - 4p
3. Expand as usual, while leaving the rest the same: 7p + 14 - 4p
4. Simplify using like terms: 3p + 14

Homework: 9.03

Remember your lines if you need them.

Week Four - Paraire 14th Mei

Today we finished off and marked our mini-test. Everything in this test had been covered at school so if you got any questions wrong you need to revise more :)

Then we looked at expanding equations. Examples:

• 2(x + y) = 2x + 2y
• 3(x - 4) = 3x - 12
• p(2q - 8) = 2pq - 8p
• 2x(5x - 9) = 10x^2 -18x

Homework: 9.01 & 9.02

Week Four - Taite 13th Mei

Today we revised what we have studied in algebra so far and completed a mini-test.

Homework: 1.09

Week Four - Turei 11th Mei

Today we extended our power rules from Monday, to allow for terms which have coefficients (numbers out the front).

• When we multiply we add powers, and we multiply the numbers out the front.

e.g 4a^2 x 3a^5 = 12a^7

• When we divide we subtract powers, and we simplify the numbers like a fraction on a calculator
  

e.g. 12a^7/4a^4 = 3a^3

• When there are brackets we multiply each power with the one outside, and we calculate the number to the power of the outside power.

e.g. (3a^3 b)^2 = 9a^6 b^2

Homework: 8.07

Week Four - Mane 10th Mei

Today we looked at four important rules for working with powers in algebra. These are:

1. When we multiply we add powers e.g a^2 x a^5 = a^7
2. When we divide we subtract powers e.g. a^7/a^4 = a^3
3. When there are brackets we multiply each power with the one outside e.g. (a^3 b)^2 = a^6 b^2
4. Anything to the power of zero is one e.g. x^0 = 1 and (24x^79 y^33)^0 = 1

Homework: 8.06

Week Three - Paraire 7th Mei

Today we looked at simplifying products of algebraic terms. A product is a series of letters and number multiplied together. There are three steps in order to simplify these:

1. Multiply all the numbers e.g. 3a x 4 = 12a
2. Follow this with the letters in alphabetical order e.g. 6b x 2a x c = 12abc
3. For more than one of the same letter use a power e.g. b x b x b x b = b^4

These can all be combined e.g. 3q x p x 4q = 12pq^2

Homework: 8.01 & 8.05
Other homework from last week: 1.10, 7.05, 8.02 & 8.03

Week Three - Taite 6th Mei

Today we looked at simplifying algebraic expressions by adding and subtracting like terms. To do this we looked at the parts of an algebraic term: the coefficient, the unknown/variable and the power/exponent. For example in the term 3x^2:

• 3 is the coefficient (the number out the front)
• x is the unknown or variable
• 2 is the power or exponent

Like terms have the same power and exponent. Examples of like terms are 3x & 5x, 2ab & 2ba, and 3x^2 and -x^2. Examples of terms that are not like terms are 3p & 3q, 2x & 5 and 4x^2 and 7x.

To add and subtract we group like terms and remember that the sign belongs to the term following it

• e.g. 2x + 3x + 4y - y = 5x + 3y
• e.g. 3a + 2 - 7a + 12 = -4a + 14

Homework: 8.02 & 8.03
Also due Friday: 1.10 & 7.05

Week Three - Turei 4th Mei

Today we were interrupted by a fire alarm so we continued with our work using formulae.

Homework: 1.10

Week Three - Mane 3rd Mei

Today we looked at using algebraic formulas. These are useful in science, maths, economics, and many other subjects.

In a formula each letter represents some information. It is important to know what each bit means. For example in A = 1/2 b x h, A represents the are of a triangle, b represents the base length of the triangle, and h represents the height in the triangle.

We follow certain steps when we use formulas. Question - what was the velocity of a car if it traveled 300km in 4 hours?

1. Write out the formula e.g. v=d/t
2. Work out what each letter means - v = velocity, d = distance, t = time
3. Substitute into the formula d = 300, t =4 so v =300/4
4. Calculate and give units if needed v = 75km/h

Homework: 7.05