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.3 - Draw graphs of logarithmic functions using an appropriate technology and by hand, and interpret them.

Suggested placement

Semester 1, Week 7 (Week 7 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.292: 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
• exemplars - p.292: a stacked fraction, matrix, vector or other two-dimensional construct is flattened by the text layer; all visible parts require comparison with the rendered page

Curriculum reference

NaCCA curriculum document, p. 292

Exemplars (from the NaCCA curriculum)

Collaborative Learning, Experiential Learning, Problem-based Learning, Project-Based Learning and Talk for Learning
Activity: Graphs of Logarithmic Functions
Using Talk for Learning Approaches, Problem-based Approaches, Project-based, experiential, Experiential Learning (use of ICT tools) and collaborative learning approaches, learners construct graphs of logarithms and describe the behaviour of the graph when a restriction/ condition is imposed.
Learners recognise that any relation of a non-linear form 𝑦 = 𝑎 % , where 𝑥 and 𝑦 are variables and 𝑎 being constant can be reduced to a linear form 𝑦 = 𝑚 + 𝑐, by first taking the logarithm of both sides of the relation, then applying the addition and the power rule, rearrange and compare with 𝑦 = 𝑚 + 𝑐
Example Draw the graphs by hand, then photograph or scan your graph; use GeoGebra to create the graph; then insert a screenshot.
Imagine that you are asked to graph 𝑙6(𝑥 + 3) − 2. How does this graph compare to the graph of 𝑙6(𝑥)?
The table presents the value of two related variables 𝑎 and 𝑏, as obtained in an experiment: 𝑎 1 2 3 4 5 𝑏 3 10 51 190 760
If it is true that 𝑎 and 𝑏 are connected by a scientific law given by 𝑏 = 𝑘 & , where c and k are constants,
- Plot a suitable graph and verify that the law is valid.
- Use your graph to estimate
- the values of 𝑐 and 𝑘 correct to one decimal place
- the value of 𝑏 when 𝑎 = 3.5 (Hint: take the log to the base 10 of both sides and proceed).
Teaching and Learning Resources:
- Graph paper
- Ruler
- A scientific calculator
Assessment (2.1.1.AS.3). The document marks these depth-of-knowledge levels for this indicator: Level 4 Extended critical thinking and reasoning.