Foundation Mathematics

1017SCG

Week 1


Foundation Mathematics


Welcome!

Convenor: Juan Carlos Ponce Campuzano


Lecture (two hours)

  • Choice of lecture:
    • [Recommended] Live lecture on-campus.
    • Pre-recorded lecture (not run live).

  • Format of lecture:
    • Introduce the content for the week.
    • Worked examples.



Workshop (two hours) 📝

  • Format of workshop:
    • Collaborate with other students.
    • Work through workshop questions.
    • Opportunity to ask questions.
    • Receive individualised help.
    • Marks for engagement with workshop.



Assumed Knowledge

No assumed knowledge from senior high school mathematics.

Orientation Week (0-Week) Revision:

  • Understanding of the basic operations.
  • Working with negative numbers.
  • Working with fractions.
  • Converting between fractions, decimals and percentages.
  • Rounding decimals.

👉 Resources available in Learning@Griffith


Resources available on Learning@Griffith

  • No textbook required and no reading list.
  • Lecture videos (pre-recorded).
  • Weekly summary sheet.
  • Workshops Questions (and solutions).
  • Numbas (online practice environment).



Assessment

  • Foundation Mathematics is non-graded course.
  • Non-graded pass (NGP) or non-graded fail (NGF).


  • Workshop Engagement (20%) - Weekly.
  • Progress Test 1 (20%) - Week 4.
  • Progress Test 2 (30%) - Week 8.
  • Progress Test 3 (30%) - Week 12.


  • Minimum of 65% overall required for a non-graded pass (NGP).

Need help?

  1. Workshop. 📝
  2. Revision sessions/Drop-in Session/Study Sessions.
  3. Microsoft Teams.
  4. Email (for personal and confidential matters).




Required Resources

Scientific Calculator (graphics calculators and programmable calculators cannot be used during assessment).

  1. Campus Bookshop.
  2. Officeworks.
  3. Big W.

Reliable internet connection (or use Griffith WiFi). 🛜



Workload (10-12 hours per week for 10CP course)

Activity Approx time
Lecture 2 hours
Workshop 2 hours
Complete workshop questions 2 hours
Re-watch video 1 hours
Numbas (online environment) 2 hours
Revision/Study for assessment 1 hours
Total hours   = 10

Mathematics
∞

Topics for Week 1


  • Order of Operations.
  • Index Laws.
  • Scientific Notation.

Let's begin!

🚀

Order of Operations

When we solve a mathematical expression, we can't just work from left to right. We follow a specific order known as BIDMAS:

  • Brackets
  • Indices (exponents or powers)
  • Division and Multiplication (left to right)
  • Addition and Subtraction (left to right)

Question: How would you do this operation?

$3 + 12 \times 3 ÷ 2$


Let's solve it using BIDMAS

$3 + 12 \times 3 ÷ 2$

Step 1: Multiplication and Division come first, left to right:

$12 \times 3 = 36,$ and then $36 ÷ 2 = 18$

Step 2: Now add 3:

$3 + 18 = 21$

✅ Final answer: $21$



What if? 🤔

$3 + 12 \times 3 ÷ 2$


$3 + 12 \times 3 ÷ 2 = 21$ $3 + 12 \times 3 ÷ 2 = 22.5 $
✅ ❌

Always follow the order of operations!


Practice Examples 📝

Try solving these using the correct order of operations:

  1. \( 4 + 6 \times 2 \)
  2. \( (4 + 6) \times 2 \)
  3. \( 3^2 + 5 \times 2 \)
  4. \( (8 + 4) ÷ 2^2 \)
  5. \( 20 - 3 \times (2 + 1) \)


Scientific Notation

Scientific notation is a way of writing very large or very small numbers in a more compact form.

  • We write numbers as a number between 1 and 10 multiplied by a power of 10.
  • The power tells us how many places to move the decimal point.
  • Positive powers are used for large numbers.
  • Negative powers are used for small numbers.


Scientific Notation

Scientific notation is a way of writing very large or very small numbers in a more compact form.

  • We write numbers as a number between 1 and 10 multiplied by a power of 10.
  • The power tells us how many places to move the decimal point.
  • Positive powers are used for large numbers.
  • Negative powers are used for small numbers.

Format: $\;a \times 10^n \;$ where $1 \leq a \lt 10$


Large Numbers in Scientific Notation

Convert the following to scientific notation:

  • \( 5,200\)
  • \(300,000,000\)
  • \( 92,000\)



Small Numbers in Scientific Notation

Convert the following to scientific notation:

  • \( 0.004\)
  • \( 0.000072 \)
  • \( 0.09 \)



Try It Yourself 📝

Write the following in scientific notation:

  1. $47,000$
  2. $0.00056$
  3. $6,300,000$
  4. $0.0089$



Index Laws

Index laws (or exponent rules) help us simplify expressions involving powers of the same base.

$ \ds \left(\frac{2a^2b}{b^3}\right)^3 ÷ \left(\frac{16a^5}{ab^7}\right)^2 $

😬

Index Laws

Index laws (or exponent rules) help us simplify expressions involving powers of the same base.

$ \ds \frac{b^8}{32a^2} $

😃

Index Laws

Multiplying:

\( \Large a^m \times a^n \) \( \Large \,= a^{m+n} \)






Index Laws

Dividing:

\(\Large \dfrac{a^m}{a^n} \) \( \Large \,= a^{m-n} \)





Index Laws

Power of a power:

\(\Large \left(a^m\right)^n \) \( \Large \, = a^{m \times n} \)






Index Laws

Power of a product:

\(\Large \left(ab\right)^n \) \( \Large \, = a^n b^n \)






Index Laws

Zero index:

\(\Large a^0 \) \( \Large \, = 1 \) \( \Large \quad (a \neq 0) \)






Index Laws

Negative index:

\(\Large a^{-n} \) \( \Large \, = \dfrac{1}{a^n} \)





Index Laws

Rational power:

\(\Large a^{\frac{1}{n}} \) \( \Large \, = \sqrt[n]{a} \)

 

\( \Large a^{\frac{m}{n}} \) \( \Large \, = \sqrt[n]{a^m} \)




Index Laws

  • Multiplying: \( a^m \times a^n = a^{m+n} \)
  • Dividing: \( \dfrac{a^m}{a^n} = a^{m-n} \)
  • Power of a power: \( \left(a^m\right)^n = a^{m \times n} \)
  • Power of a product: \( \left(ab\right)^n = a^n b^n \)
  • Zero index: \( a^0 = 1 \quad (a \neq 0) \)
  • Negative index: \( a^{-n} = \dfrac{1}{a^n} \)
Extra:
$\large a^{\frac{1}{n}} = \sqrt[n]{a}$

Examples: Multiply and Divide

  • \( x^3 \times x^4 \)
  • \(\dfrac{y^5}{y^2} \)
  • \( 2^3 \times 2^2 \)



Power of a Power / Product

  • \(\left(x^2\right)^3 \)
  • \(\left(3a^2\right)^2 \)
  • \(\left(2x^3\right)^2 \)



Zero and Negative Indices

  • \(a^0 = 1 \) (as long as \( a \neq 0 \))

     

  • \( a^{-n} = \dfrac{1}{a^n} \)

     

  • $a^{\frac{1}{n}}=\sqrt[n]{a}$


Try These 📝

  1. \( x^5 \times x^3 \)
  2. \( \dfrac{a^6}{a^2} \)
  3. \( \left(b^4\right)^2 \)
  4. \( \sqrt[4]{y^2} \)
  5. \( 5^0 + 3^{-1} \)


Credits