Application of Algebra

Curriculum details

Strand

Modelling with Algebra (Strand 1)

Sub-strand

Application of Algebra (1.1)

Content standard

2.1.1.CS.3 - Demonstrate understanding of the laws and properties of indices and apply the ideas to solve problems. 2.1.1.LO.1 Investigate De Morgan's law on sets algebraically and graphically, formulate and solve real life problems up to three sets. 2.1.1.LO.2 Model sequence recursively and explicitly, and establish the relationship between the two forms, as well as solve real life problems involving linear and exponential sequences and series. 2.1.1.LO.3 Apply indices and logarithms to solve real life problems, including logarithms with different bases, and sketch and interpret logarithmic functions. 2.1.1.LO.4 Formulate and derive appropriate strategies to solve quadratic inequalities. 2.1.1.LO.5 Graph systems of given inequality and identify the region that provides the feasible solution and apply it to real life situations. 2.1.1.LO.6 Determine the set of values for which a rational function is defined and resolve rational functions into partial fractions. 2.1.1.LO.7 Multiply matrices, determine the inverse of a 2 x 2 matrix, find the determinant up to a 3 x 3 matrix and represent matrices in linear transformations.

Indicator

2.1.1.LI.11 - Resolve rational functions into partial fractions, specifically quadratic denominators and improper rational functions.

Suggested placement

Semester 1, Week 14 (Week 14 of the year)

Our suggestion, laid out in curriculum order across three terms of twelve weeks. NaCCA does not fix the week, so follow your school's scheme of learning.

Source document note

The official curriculum document has a fault in this entry, so the curriculum text above is transcribed exactly as printed:

• exemplars - p.316: adjacent duplicated CambriaMath characters were collapsed, but this PDF also maps some equation glyphs to the wrong letter or operator; verify every mathematical expression in this row against the rendered page

Curriculum reference

NaCCA curriculum document, p. 316

Exemplars (from the NaCCA curriculum)

Activity1: Working with Partial Fractions
Collaborative Learning, Experiential Learning, Whole class discussion, Talk for Learning Approaches and Problem-based Learning
Learners work in groups/pairs to revise processes for resolving rational functions containing linear factors and or repeated factors as denominators. Learners revise resolving rational functions whose denominator is made up of linear factors and repeated factors using different strategies:
Examples Split 5(𝑥 + 2) into partial fractions. (𝑥 + 1)(𝑥 + 6)
0 * ) Split into partial fractions. (0 $ !)(0*!) !
Activity 2: Improper Rational functions and functions with irreducible quadratic factors.
Collaborative Learning, Experiential Learning, Whole class discussion, Talk for learning Approaches and Problem-based learning:
Work with a partner: One of the pairs decomposes the irrational function into partial terms whiles the other composes the fractions back into a single unit. Learners recognise that a rational function with the denominator containing irreducible quadratic factors is resolved using the process: 𝑎 − 𝑏 𝐴 + 𝐵 = ) 𝑎 + 𝑏 + 𝑐 𝑎 + 𝑏 + 𝑐 )
Example .0 Express (0 ! $0$!)(0*)) as the sum of its partial fractions. Reverse the process to verify your answer.
Solution: .0 .(!*)0) !( = 7(0 ! + 7(0*)) (0 ! $0$!)(0*)) $0$!)

 0 ! $,0 _ ) Express (0*!)(0 ! $!) in partial fractions.
Learners recognise that an improper rational function is resolved by first reducing it to a proper rational function:
)0 ! $ ! Example: Resolve (0*!)(0$)) in partial fractions. Reverse the process to verify your answer.
Solution: )0 ! $ ! ! " = 2 + (0*!) − (0$)) (0*!)(0$))
Teaching and Learning Resources:
- Graph paper
- Ruler
- A scientific calculator
Assessment (2.1.1.AS.11). The document marks these depth-of-knowledge levels for this indicator: Level 2 Skills of conceptual understanding.