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Year 10 mathematics in Victoria

Here’s a list of topics covered in the Year 10 mathematics curriculum within the State of Victoria, Australia. This list might be out of date, or it might be missing some topics. I’m happy to add other topics as I become aware of them. The pedagogy contents in this post are based on Lynch and Parr [1] and Swan et al. [2].

Algebraic simplification

1. Simplifying expressions involving addition and subtraction. For example,
1. $5x + 7x = 12x$
2. $2x^2 + 3y - 5x^2 + y = -3x^2 + 4y$
2. Simplifying algebraic expressions using the distributive law $a(b + c) = ab + ac$
1. the binomial expansion $(a + b) (c + d) = a(c + d) + b(c + d) = ac + ad + bc + bd$
2. difference of two squares $(a + b) (a - b) = a^2 - b^2$
3. perfect squares $(a + b)^2 = a^2 + 2ab + b^2$ and $(a - b)^2 = a^2 - 2ab + b^2$
3. Simplifying rational expressions
1. addition of rational expressions $\displaystyle \frac{a}{b} + \frac{c}{d} = \frac{ad}{bd} + \frac{bc}{bd} = \frac{ad + bc} {bd}$
2. subtraction of rational expressions $\displaystyle \frac{a}{b} - \frac{c}{d} = \frac{ad}{bd} - \frac{bc}{bd} = \frac{ad - bc} {bd}$
3. multiplication of rational expressions $\displaystyle \frac{a}{b} \times \frac{c}{d} = \frac{ac}{bd}$
4. division of rational expressions $\displaystyle \frac{a}{b} \div \frac{c}{d} = \frac{a}{b} \times \frac{d}{c} = \frac{ad}{bc}$

Surds and indices

1. Simplifying expressions involving surds
1. addition of surds $a\sqrt{b} + c\sqrt{b} = (a + c) \sqrt{b}$
2. subtraction of surds $a\sqrt{b} - c\sqrt{b} = (a - c) \sqrt{b}$
3. multiplication of surds $a\sqrt{b} \times c\sqrt{d} = ac \sqrt{bd}$
4. division of surds $a\sqrt{b} \div c\sqrt{d} = {\displaystyle\frac{a}{c} \sqrt{\frac{b}{d}}}$
5. rationalizing the denominator $\displaystyle \frac{a}{\sqrt{b}} = \frac{a}{\sqrt{b}} \times \frac{\sqrt{b}}{\sqrt{b}} = \frac{a\sqrt{b}}{b}$
2. Index form
1. addition of indices $a^m \times a^n = a^{m + n}$
2. subtraction of indices $a^m \div a^n = a^{m - n}$
3. multiplication of indices $(a^m)^n = a^{mn}$
4. negative indices $\displaystyle \frac{1}{a^n} = a^{-n}$ for $n \neq 0$
5. standard form $a_1 a_2 a_3 \cdots a_n = a_1 . a_2 a_3 \cdots a_n \times 10^{n-1}$, for example, $12345 = 1.2345 \times 10^4$
6. $n$-th root $\displaystyle \sqrt[n]{a} = a^{\frac{1}{n}}$

Factorization
Factorizing using the distributive law $a(b + c) = ab + ac$

1. the binomial expansion $(a + b) (c + d) = a(c + d) + b(c + d) = ac + ad + bc + bd$
2. difference of two squares $(a + b) (a - b) = a^2 - b^2$
3. perfect squares $(a + b)^2 = a^2 + 2ab + b^2$ and $(a - b)^2 = a^2 - 2ab + b^2$

Problem solving using graphs of functions
Here’s a list of the graphs of some elementary functions. Problem solving questions should involve visualization of such graphs.

Linear function.

Cubic function.

Sine function.

Cosine function.

Logarithmic function.

Length and area

1. length
1. unit conversion in the metric system
2. Unit conversion in the metric system.

3. Pythagoras’ Theorem: If $a$, $b$ and $c$ are the lengths of the three sides of a right-angled triangle with $c$ being the length of the hypotenuse, then $c^2 = a^2 + b^2$.
4. Pythagoras' Theorem.

5. distance between two points — given two points $A = (x_1, y_1)$ and $B = (x_2, y_2)$, the distance between $A$ and $B$ is given by $\sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}$.
6. the perimeter of geometric figures
2. areas of common plane figures
1. square — $\text{Area} = a^2$

Area of a square.

2. rectangle — $\text{Area} = w \times h$

Area of a rectangle.

3. parallelogram — $\text{Area} = b \times h$

Area of a parallelogram.

4. triangle — $\text{Area} = \frac{1}{2} b h$

Area of a triangle.

5. trapezium — $\text{Area} = \frac{1}{2} (a + b)h$

Area of a trapezium.

6. circle — $\text{Area} = \pi r^2$

Area of a circle.

Descriptive statistics

1. mean, median, mode
2. graphical, diagrammatical emphasis

Trigonometry

1. deducing values of angles
2. the SOHCAHTOA rules:

• SOH: Sine is Opposite over Hypotenuse
• CAH: Cosine is Adjacent over Hypotenuse
• TOA: Tangent is Opposite over Adjacent
3. graphical, diagrammatical emphasis

References

1. B. J. Lynch and R. E. Parr. Maths 10. Longman Sorrett, 2nd edition, 1982.
2. K. Swan, R. Adamson, M. Cocking, D. Adams, and S. Ferguson, editors. Nelson Maths 10: VELS Edition. Thomson Nelson, 2007.