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Summary of topics, outcomes and their relevance:

1. Functions – linear, quadratic, exponential, rational
Outcome Relevance
10.1.1 Relationships between variables in terms of graphical, verbal and symbolic representations of functions (tables, graphs, words and formulae). Functions form a core part of learners’ mathematical understanding and reasoning processes in algebra. This is also an excellent opportunity for contextual mathematical modelling questions.
10.1.2 Generating graphs and generalising effects of parameters of vertical shifts and stretches and reflections about the x-axis.
10.1.3 Problem solving and graph work involving prescribed functions.
2. Number Patterns, Sequences and Series
Outcome Relevance
10.2.1 Number patterns with constant difference. Much of mathematics revolves around the identification of patterns.
3. Finance, Growth and Decay
Outcome Relevance
10.3.1 Use simple and compound growth formulae. The mathematics of finance is very relevant to daily and long-term financial decisions learners will need to make in terms of investing, taking loans, saving and understanding exchange rates and their influence more globally.
10.3.2 Implications of fluctuating exchange rates.
4. Algebra
Outcome Relevance
10.4.1 Identifying and converting forms of rational numbers.Working with simple surds that are not rational. Algebra provides the basis for mathematics learners to move from numerical calculations to generalising operations, simplifying expressions, solving equations and using graphs and inequalities in solving contextual problems.
10.4.2 Working with laws of integral exponents.Establish between which two integers a simple surd lies.Appropriately rounding off real numbers.
10.4.3 Manipulating and simplifying algebraic expressions (including multiplication and factorisation).
10.4.4 Solving linear, quadratic and exponential equations.Solving linear inequalities in one and two variables algebraically and graphically.
5. Differential Calculus
Outcome Relevance
10.5.1 Investigate average rate of change between two independent values of a function. The central aspect of rate of change to differential calculus is a basis to further understanding of limits, gradients and calculations and formulae necessary for work in engineering fields, e.g. designing roads, bridges etc.
6. Probability
Outcome Relevance
10.6.1 Compare relative frequency and theoretical probability.Use Venn diagrams to solve probability problems.Mutually exclusive and complementary events.Identity for any two events A and B. This topic is helpful in developing good logical reasoning in learners and for educating them in terms of real-life issues such as gambling and the possible pitfalls thereof.
7. Euclidean Geometry and Measurement
Outcome Relevance
10.7.1 Investigate, form and try to prove conjectures about properties of special triangles, quadrilaterals and other polygons.Disprove false conjectures using counter-examples.Investigate alternative definitions of various polygons. The thinking processes and mathematical skills of proving conjectures and identifying false conjectures is more the relevance here than the actual content studied. The surface area and volume content studied in real-life contexts of designing kitchens, tiling and painting rooms, designing packages, etc. is relevant to the current and future lives of learners.
10.7.2 Solve problems involving surface area and volumes of solids and combinations thereof.
8. Trigonometry
Outcome Relevance
10.8.1 Definitions of trig functions.Derive values for special angles.Take note of names for reciprocal functions. Trigonometry has several uses within society, including within navigation, music, geographical locations and building design and construction.
10.8.2 Solve problems in 2 dimensions.
10.8.3 Extend definition of basic trig functions to all four quadrants and know graphs of these functions.
10.8.4 Investigate and know the effects of a and q on the graphs of basic trig functions.
9. Analytical Geometry
Outcome Relevance
10.9.1 Represent geometric figures on a Cartesian coordinate system.For any two points, derive and apply formula for calculating distance, gradient of line segment and coordinates of mid-point. This section provides a further application point for learners’ algebraic and trigonometric interaction with the Cartesian plane. Artists and design and layout industries often draw on the content and thought processes of this mathematical topic.
10. Statistics
Outcome Relevance
10.10.1 Collect, organise and interpret univariate numerical data to determine mean, median, mode, percentiles, quartiles, deciles, interquartile and semi-interquartile range. Citizens are daily confronted with interpreting data presented from the media. Often this data may be biased or misrepresented within a certain context. In any type of research, data collection and handling is a core feature. This topic also educates learners to become more socially and politically educated with regards to the media.
10.10.2 Identify possible sources of bias and errors in measurements.

Mathematics educators also need to ensure that the following important specific aims and general principles are applied in mathematics activities across all grades:

  • Calculators should only be used to perform standard numerical computations and verify calculations done by hand.
  • Real-life problems should be incorporated into all sections to keep mathematical modelling as an important focal point of the curriculum.
  • Investigations give learners the opportunity to develop their ability to be more methodical, to generalise and to make and justify and/or prove conjectures.
  • Appropriate approximation and rounding skills should be taught and continuously included and encouraged in activities.
  • The history of mathematics should be incorporated into projects and tasks where possible, to illustrate the human aspect and developing nature of mathematics.
  • Contextual problems should include issues relating to health, social, economic, cultural, scientific, political and environmental issues where possible.
  • Conceptual understanding of when and why should also feature in problem types.
  • Mixed ability teaching requires educators to challenge able learners and provide remedial support where necessary.
  • Misconceptions exposed by assessment need to be dealt with and rectified by questions designed by educators.
  • Problem solving and cognitive development should be central to all mathematics teaching and learning so that learners can apply the knowledge effectively.

Questions & Answers

how do they get the third part x = (32)5/4
kinnecy Reply
can someone help me with some logarithmic and exponential equations.
Jeffrey Reply
sure. what is your question?
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
I'm not sure why it wrote it the other way
I got X =-6
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
Commplementary angles
Idrissa Reply
im all ears I need to learn
right! what he said ⤴⤴⤴
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
Kevin Reply
a perfect square v²+2v+_
Dearan Reply
kkk nice
Abdirahman Reply
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
Kim Reply
or infinite solutions?
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Embra Reply
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
Nancy Reply
rolling four fair dice and getting an even number an all four dice
ramon Reply
Kristine 2*2*2=8
Bridget Reply
Differences Between Laspeyres and Paasche Indices
Emedobi Reply
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
Mary Reply
is it 3×y ?
Joan Reply
J, combine like terms 7x-4y
Bridget Reply
how do you translate this in Algebraic Expressions
linda Reply
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
Crystal Reply
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
Chris Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
types of nano material
abeetha Reply
I start with an easy one. carbon nanotubes woven into a long filament like a string
many many of nanotubes
what is the k.e before it land
what is the function of carbon nanotubes?
I'm interested in nanotube
what is nanomaterials​ and their applications of sensors.
Ramkumar Reply
what is nano technology
Sravani Reply
what is system testing?
preparation of nanomaterial
Victor Reply
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
Himanshu Reply
good afternoon madam
what is system testing
what is the application of nanotechnology?
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
anybody can imagine what will be happen after 100 years from now in nano tech world
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
silver nanoparticles could handle the job?
not now but maybe in future only AgNP maybe any other nanomaterials
I'm interested in Nanotube
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
can nanotechnology change the direction of the face of the world
Prasenjit Reply
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
Ali Reply
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
bamidele Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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Source:  OpenStax, Mathematics grade 10 teachers' guide - siyavula webbooks. OpenStax CNX. Aug 10, 2011 Download for free at http://cnx.org/content/col11341/1.1
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