ALGEBRA PART TWO
THE WEEKLY TESTS
term 2 week 10
term 2 week 11
term 2 week 12
term 3 week 1
Term 3 Week 2
In Algebra, we use symbols to represent numbers, operations, and formulas. It’s important to understand how these are arranged. It’s useful to be able to explain mathematical ideas using words. The curriculum is becoming more focused on students explaining and communicating their ideas in words. In fact, some achievement standards and not just in maths, offer literacy credits at L1 and L2. In mathematics these tend to be in statistics where students are expected to ask a question, come up with a plan to answer the question, graph and analyse data and end with a conclusion. That's a bit hard to do with numbers alone. In technology students are expected to write a report covering the technology development cycle that explains their product from the conception phase right through to the built item. However, it’s just as important to be able to use symbols—such as numbers (e.g. 8), letters (e.g. x or a), and signs (e.g. +,√). We often use 'a' or 'x' to represent some number in a mathematical calculation. Sometimes, we refer to the letters as variables because they can take on any value.
The multiplication and division symbols are not used a lot in algebra. They can be left out. For those that follow the Khan Academy tutorials you will notice that the times symbol has been replaced with a 'dot' in some cases. For example, 8 × x can be shown as 8x and a x b x c can be expressed as abc or a.b.c
In division, x ÷ 3 can be written as a fraction, x/3.
In division, x ÷ 3 can be written as a fraction, x/3.
literacy and symbols
Activity 1
In this activity you have to match the English phrase with the mathematical expression
1) a number with 5 add to it a) x/3
2) a number with 4 subtracted from it b) 2x +1
3) 6 times a number c) x - 4
4) a number divided by 3 d) x + 5
5) 2 added to 3 times a number e) 3x + 2
6) 4 more than a number f) 6x
7) 1 less than a number g) x + 4
8) 1 more than twice a number h) x - 1
Answers - 1d, 2c, 3f, 4a, 5e, 6g, 7h, 8b.
In this activity you have to match the English phrase with the mathematical expression
1) a number with 5 add to it a) x/3
2) a number with 4 subtracted from it b) 2x +1
3) 6 times a number c) x - 4
4) a number divided by 3 d) x + 5
5) 2 added to 3 times a number e) 3x + 2
6) 4 more than a number f) 6x
7) 1 less than a number g) x + 4
8) 1 more than twice a number h) x - 1
Answers - 1d, 2c, 3f, 4a, 5e, 6g, 7h, 8b.
Replace the symbols with their numerical value:
substitution
We have an equation, y = 2x + 5. If we are told that x is 3, what does y become?
Write out the equation again and replace the x with the 3, but be careful.
Write out the equation again and replace the x with the 3, but be careful.
y = 2(3) + 5
The brackets around the '3' are to help with the meaning that it is multiplied by the 2 in front of it. So:
y = 2 x 3 + 5 it is not y = 23 + 5!
Following the rules of BEDMAS we do the multiplication part first.
y = 6 + 5
= 11
Now try the next example only this time we will make x = 10. What is y now?
y = 2x + 5
y = 2(10) + 5
y = 2 x 10 + 5
y = 20 + 5
y = 25
With practice you can skip some of the steps in solving the equations. Now it's your turn.
Activity 2
Substitution. Lets pretend the value of x is 8. If that is true what would the following expressions become? (Remember, expressions don't have the equal sign (=). Also, 3x is the same as 3 times x, or 3 x x.
1) x - 6
2) 20 - x
3) x÷ 4
4) 5x
5) x ÷ 2
Answers: 1) 2, 2) 12, 3) 2, 4) 40, 5) 4
Now work out these equations. What would 'y' be if x was still 8. (Equations have the equals sign (=).
1) y = x + 2
2) y = 4x +1
3) y = 24 ÷ x
4) y = 7x - 1
5) y = 100 - 10x
Answers: 1) 10, 2) 33, 3) 3, 4) 55,20
Substitution. Lets pretend the value of x is 8. If that is true what would the following expressions become? (Remember, expressions don't have the equal sign (=). Also, 3x is the same as 3 times x, or 3 x x.
1) x - 6
2) 20 - x
3) x÷ 4
4) 5x
5) x ÷ 2
Answers: 1) 2, 2) 12, 3) 2, 4) 40, 5) 4
Now work out these equations. What would 'y' be if x was still 8. (Equations have the equals sign (=).
1) y = x + 2
2) y = 4x +1
3) y = 24 ÷ x
4) y = 7x - 1
5) y = 100 - 10x
Answers: 1) 10, 2) 33, 3) 3, 4) 55,20
more substitution
Activity 3
a, b and c are given the following values: a = 2, b = 5 and c = 10
Calculate the value of each expression:
1) a + b + c
2) c - a
3) c ÷ b
4) 3ab ÷ c
5) 2(a + c) - b
Answers: 1) 17, 2) 8, 3) 2, 4) 3, 5) 19
a, b and c are given the following values: a = 2, b = 5 and c = 10
Calculate the value of each expression:
1) a + b + c
2) c - a
3) c ÷ b
4) 3ab ÷ c
5) 2(a + c) - b
Answers: 1) 17, 2) 8, 3) 2, 4) 3, 5) 19