# GRADE 12 / YEAR 13 AS MATHEMATICS M1 COURSE SYLLABUS 2020-2021

# Course Outline

## Overview

The Math Syllabus at GEMS Wesgreen International Secondary School aims to support students to develop their ability to calculate fluently, to reason and solve problems through application of knowledge and transferable skills. Throughout the year we recover and extend objectives as the focus is on securing an understanding in the subject by developing a greater depth.

## Learning Outcomes

The aims of all subjects state what a teacher may expect to teach and what a student may expect to experience and learn. These aims suggest how the student may be changed by the learning experience.

The aims of the Math Syllabus are to encourage and enable students to:

- become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately.
- reason mathematically by following a line of enquiry, conjecturing relationships and generalizations, and developing an argument, justification or proof using mathematical language
- can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

## Unit Overviews

### Term 1

**Unit 1 – ****Forces and equilibrium**

**Approximate length: 3 weeks **

In this unit the children will develop their idea of forces and different types of forces as possible and types of situations in which they might be present.

Specific CIE Objectives Covered:

- identify the forces acting in a given situation, e.g. by drawing a force diagram
- understand the vector nature of force, and find and use components and resultants; calculations are always required, not approximate solutions by scale drawing
- use the principle that, when a particle is in equilibrium, the vector sum of the forces acting is zero, or equivalently, that the sum of the components in any direction is zero; solutions by resolving are usually expected, but equivalent methods (e.g. triangle of forces, Lami’s Theorem, where suitable) are also acceptable; these other methods are not required knowledge, and will not be referred to in questions • understand that a contact force between two surfaces can be represented by two components, the normal component and the frictional component
- use the model of a ‘smooth’ contact, and understand the limitations of this model
- understand the concepts of limiting friction and limiting equilibrium, recall the definition of coefficient of friction, and use the relationship F = μR or F ≤ μR, as appropriate; terminology such as ‘about to slip’ may be used to mean ‘in limiting equilibrium’ in questions
- use Newton’s third law, e.g. the force exerted by a particle on the ground is equal and opposite to the force exerted by the ground on the particle

**Unit 2 – Kinematics of motion in a straight line**

**Approximate length: 4 weeks **

In this unit the children will reiterate the difference between scalar and vector quantities and that in one dimension, the direction of a vector will determine whether you use a positive or negative sign. They will develop te understanding and application that negative speed or distance is incorrect and a negative acceleration is equivalent to a positive deceleration.

Specific CIE Objectives Covered:

- understand the concepts of distance and speed as scalar quantities, and of displacement, velocity and acceleration as vector quantities; restricted to motion in one dimension only; the term ‘deceleration’ may sometimes be used in the context of decreasing speed
- sketch and interpret displacement–time graphs and velocity–time graphs, and in particular appreciate that: the area under a velocity–time graph represents displacement, the gradient of a displacement–time graph represents velocity, the gradient of a velocity-time graph represents acceleration
- use differentiation and integration with respect to time to solve simple problems concerning displacement, velocity and acceleration; calculus required is restricted to techniques from the content for Paper 1: Pure Mathematics 1
- use appropriate formulae for motion with constant acceleration in a straight line; questions may involve setting up more than one equation, using information about the motion of different particles

**Unit 3 –Momentum**

**Approximate length: 3 weeks **

In this unit the children will be introduced to the concept of linear momentum (p) as the product of the mass (m) and the velocity (v) of a particle and that momentum is a vector quantity that acts in the direction of motion of the particle.

Specific CIE Objectives Covered:

- use the definition of linear momentum and show understanding of its vector nature; for motion in one dimension only
- use conservation of linear momentum to solve problems that may be modelled as the direct impact of two bodies; including direct impact of two bodies where the bodies coalesce on impact; knowledge of impulse and the coefficient of restitution is not required

**Term 2**

**Programme of Study**

**Programme of Study**

## Blended Learning

Throughout this year there will be blended learning. All students whether face to face or learning from home will have the opportunity to access all the lessons and resources. Students will use Phoenix and myimaths. Each lesson begins with a set of clearly stated objectives and an explanation of its place in the overall CIE AS/A level syllabus. Effective learning is encouraged through frequent activities and self-assessment questions.

Links for solving past papers and links related to concepts covered to reinforce classroom learning followed will be available to students. Students will have access to worksheets with progression of difficulty, online assessments, tasks/open ended questions and fun activities through online platforms.

## Assessment

**Formative: **Throughout the units, the children will complete graded work, quizzes and problem solving activities which allows the teacher to assess the students’ attainment and inform their planning. For each unit the students complete written quizzes, online quizzes as well as Chapter- wise tests (Topic Tests). Quizzes are taken based on 1-chapter assessment, where Tests are combined as per the requirement i.e. 2 to 3 chapters/topics – sections. This allows us to see progress across the units and align our planning.

**Summative: **At the end of each term we complete internal and standardized tests. This allows us to measure the students’ progress throughout the term and year. End of term 2 they have CIE format exam for Mechanics. This is practice / preparation for their final CIE examinations. At the end of one year course, students appear for their final CIE examination for Syllabus - Cambridge CIE® Mathematics 9709.