Graph of a function. Algebraic representation of geometrical relationships. Trigonometric ratios of negative angles. Curve trigonometry including continuity and limit of a function as well as gradient of a curve as an introduction to calculus (differentiation). Differentiation from first principle, differentiation of linear and polynomial functions as well as the composite function rules. Quadratic polynomials, inequalities and the roots of quadratic equations. Parabola and the concept of locus.
The core content of year 11 maths starts with a review of previous years’ maths curriculums; basic arithmetic and algebra topics:
Quadratic and simultaneous equations.
Plane geometry will involve the re-visitation of congruent triangles and an expansion on Pythagoras’ theorem including its converse.
Also in Year 11 maths, algebra and geometry topics will be intertwined when studying locus and constructing graphs of functions. Trigonometric ratios will be used to totally solve triangles.
Differentiation in calculus will be introduced with the idea of continuity and the limit of a function as they are related to curves as well as tangent and secants of curves. Methods of differentiation will then be taught including differentiating from the first principle and differentiation using rules. Apart from differentiating polynomials, quadratic polynomials will be studied on their own including graphs and roots of quadratic functions as well as quadratic inequalities.
Calculus is a perennial challenge for year 11 maths students. This year, grappling with one arm of it, differentiation, will present particular difficulties for students. Polynomials will also prove tricky especially when studied within differentiation and separately in quadratic expressions.
At the end of this year, students should be able to compute and solve all kinds of basic algebra problems. They must, likewise, be adept at solving triangles and at using the Pythagoras’ theorem. Trigonometric ratios are key topics to grasp for this class too. Most importantly, a good understanding of the principles of differentiation is absolutely essential for higher calculus in the next year. Finally, students must, at the end of year 11 maths, be capable of solving quadratic polynomial equations as well as constructing graphs of quadratic functions and solving quadratic inequalities.
More importantly than the rest, your child must understand and be able to use differentiation in year 11. Apart from that, trigonometric ratios and quadratic polynomials are core concepts to be fully understood.
Should you get a tutor for your child, encourage a concentration in calculus, polynomials and trigonometric ratios. When differentiating functions, let the child start with differentiating from the first principle before moving onto the rules; this way, they can fully understand the underlying transformation of calculus rather than relying on rote and formulae.
Calculus, more often than not, looms large in the mind of a year 11 maths student. The fear of calculus in many ways slow some students from learning the topic. Since year 11 is close to the end of high school, preparation for final assessments may not allow a lot of time to fully tackle the core topics this year.
Again, the importance of algebra must be stressed. If you child is not completely comfortable with reasonbably complex algebraic manipulations it will make mastering topics like calculus nearly impossible.
Help your child prepare for final assessment as much as you can. This is a good year to get a tutor for him/her in maths. Quite a number of very important new topics are introduced in year 11 maths and it is important that your child master them irrespective of other preparations that need be made for the next year.
You should also stress regular revision and general good study habits. The sheer volume of content this year makes success challenging. Success becomes more about effective study habits and exam preparation techniques rather than just “getting” the math. Many students are caught off-guard at exam time because of the increased pace of learning and increasingly difficult content – it is truly hard to manage.
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