Algebra Answers

If a1 is the first of n geometric means between a and b, show that a1^n+1=a^n b

Polynomial and rational functions can be used to model a wide variety of phenomena of science, technology, and everyday life.

Choose one of these sectors and give an example of a polynomial or rational function modeling a situation in that sector. [Hint: see the examples and exercises in the book.]

Go to www.desmos.com/calculator, write your equation, or function, and develop your explanation using the properties of graphs

Reflect on the concept of polynomial and rational functions. What concepts (only the names) did you need to accommodate these concepts in your mind? What are the simplest polynomial and rational function you can imagine? In your day to day, is there any occurring fact that can be interpreted as polynomial and rational functions? What strategy are you using to get the graph of polynomial and rational functions?

The purity of medicines is of concern for the industry, the regulator and the public. It is therefore import to regularly test the purity of medicinal compounds. A sample of paracetamol (acetaminophen) from a pharmaceutical manufacturer was analysed by dissolving 20.0mg of sample in 2ml of methyl alcohol and then bringing this solution to a total volume of 100ml with water. The sample was then analysed using a UV-Visible Spectrophotometer and the result compared with that of the same test performed on the same amount of a paracetamol standard known to be 100% pure. The test sample gave a reading of 0.0549 absorbance units while the standard gave a reading of 0.0558.

What is the quantity of paracetamol in the test sample and what is its percentage purity?

Discuss the steps that you can deploy in constructing number problems.

Jabu had a few marbles. Today he played and doubled his number of marbles. Then Thabo gave him three marbles for free. Jabu has 21 marbles now. How many did he have before he started playing? Solve this problem using a suitable model.

Modelling refers to the idea that learners build in their minds and play out with objects or in picture form on paper sometimes to solve problems. Give at least three benefits that you may achieve in your primary mathematics class by employing Modelling.

The photo is 120 mm×90 mm. It is enlarged to 360 mm ×270 mm. The elephant's tail in the smaller photo is 15 mm long. How long is its tail in the larger photo? Show your calculations.

Set up one example question (also provide solutions) which falls under the following.
Level 1:mathematical knowledge.
Level 2:routine procedures (in a real life context)
Level 3:complex procedures(in real life context)
Level 4:problem solving(in real life context?)