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CSEC Mathematics (Grade 11) By Mr. King

Instructor Image Winsford King
12 Lessons
9 months
5 Student
Free
Enroll In This Course
IITAE Course UpdateIITAE Group CourseGrade 11Secondary School Courses

CSEC Mathematics (Grade 11) By Mr. King

Instructor Image Winsford King
12 Lessons
1 Quiz
9 months
5 Student
Free Enroll In This Course
Introduction

RATIONALE

The guiding principles of the Mathematics syllabus direct that Mathematics as taught in Caribbean schools should be relevant to the existing and anticipated needs of Caribbean society, related to the abilities and interests of Caribbean students and aligned with the philosophy of the educational system. These principles focus attention on the use of Mathematics as a problem solving tool, as well as on some of the fundamental concepts which help to unify Mathematics as a body of knowledge. The syllabus explains general and unifying concepts that facilitate the study of Mathematics as a coherent subject rather than as a set of unrelated topics.

Every citizen needs basic computational skills (addition, subtraction, multiplication and division) and the ability to use these mentally to solve everyday problems. All citizens should recognise the importance of accuracy in computation as the foundation for deductions and decisions based on the results. In addition, the citizen should have, where possible, a choice of mathematical techniques to be applied in a variety of situations. A ‘range of mathematical techniques’ is therefore, specified in recognition of the need to accommodate different levels of ability. Citizens need to use Mathematics in many forms of decision making: shopping, paying bills, budgeting and for the achievement of personal goals, critically evaluating advertisements, taxation, investing, commercial activities, banking, working with and using current technologies, measurements and understanding data in the media. Improving efficiency and skills in these matters will be beneficial to the community as well as to the individual.

The syllabus seeks to provide for the needs of specific mathematical techniques in the future careers of students, for example, in agriculture and in commercial and technical fields. By the end of the normal secondary school course, students should appreciate that the various branches of Mathematics are not rigidly segregated and that the approach to the solution of any problem is not necessarily unique.

This syllabus will contribute to the development of the Ideal Caribbean Person as articulated by the CARICOM Heads of Government in the following areas: “demonstrate multiple literacies, independent and critical thinking and innovative application of science and technology to problem solving. Such a person should also demonstrate a positive work attitude and value and display creative imagination and entrepreneurship”. In keeping with the UNESCO Pillars of Learning, on completion of this course the study, students will learn to do, learn to be and learn to transform themselves and society.

AIMS

This syllabus aims to:

  1. help students appreciate the use of mathematics as a form of communication;
  2. help students acquire a range of mathematical techniques and skills and to foster and maintain the awareness of the importance of accuracy;
  3. make Mathematics relevant to the interests and experiences of students by helping them to recognise Mathematics in their environment;
  4. cultivate the ability to apply mathematical knowledge to the solution of problems which are meaningful to students as citizens;
  5. help students cultivate the ability to think logically and critically;
  6. help students develop positive attitudes, such as open-mindedness, self-reliance, persistence and a spirit of enquiry;
  7. prepare students for the use of Mathematics in further studies;
  8. help students develop an appreciation of the wide application of Mathematics and its influence in the development and advancement of civilisation;
  9. help students become increasingly aware of the unifying structure of Mathematics

Lessons

Section 1 - REVISION
8 Topics
  • Writing numbers in Scientific Notation or Standard Form
  • Solving Linear Equations
  • Finding the hypotenuse of a right triangle using Pythagoras Theorem
  • Finding the other sides of a right angle triangle using Pythagoras Theorem
  • Finding mean, mode and median
  • Sequences
  • Finding percentage profit or loss
  • Finding percentage of a quantity
Section - Practice exercises
7 Topics
  • Lesson on fractions and Algebra
  • Sequences
  • Functions and graphs
  • Statistics and Sequences
  • Transformation
  • Transformation Two
  • Vectors and Circles - Assignment Four
SECTION 2 – NUMBER THEORY AND COMPUTATION GENERAL OBJECTIVES
19 Topics
  • Lesson 1 – Distinguish among sets of numbers
  • Lesson 2 – Compute powers of real numbers of the form 𝓍 𝑎 , where 𝑎 ∈ ℚ
  • Lesson 3 – Evaluate numerical expressions using any of the four basic operations on real numbers
  • Lesson 4 – Convert among fractions, per cents and decimals
  • Lesson 5 – List the set of factors and multiples of a given integer
  • Lesson 6 – Compute the H.C.F. or L.C.M. of two or more positive integers
  • Lesson 7 – State the value of a digit of a numeral in a given base
  • Lesson 8 – Convert from one set of units to another
  • Lesson 9 – Express a value to a given number of a) significant figures and b) decimal places
  • Lesson 10 – Use properties of numbers and operations in computational tasks
  • Lesson 11 – Write any rational number in scientific notation
  • Lesson 12 – Calculate any fraction or percentage of a given quantity
  • Lesson 13 – Express one quantity as a fraction or percentage of another
  • Lesson 14 – Compare quantities
  • Lesson 15 – Order a set of real numbers
  • Lesson 16 – Compute terms of a sequence given a rule
  • Lesson 17 – Derive an appropriate rule given the terms of a sequence
  • Lesson 18 – Divide a quantity in a given ratio
  • Lesson 19 – Solve problems involving concepts in number theory and computation
SECTION 1 – CONSUMER ARITHMETIC
10 Topics
  • Lesson 1 – Calculate a) discount, b) sales tax, c) profit and d) loss
  • Lesson 2 – Calculate a) percentage profit and b) percentage loss
  • Lesson 3 – Express a profit, loss, discount, markup and purchase tax, as a percentage of some value
  • Lesson 4 – Solve problems involving marked price, selling price, cost price, profit, loss or discount
  • Lesson 5 – Solve problems involving payments by instalments as in the case of hire purchase and mortgages
  • Lesson 6 – Solve problems involving simple interest
  • Lesson 7 – Solve problems involving compound interest
  • Lesson 8 – Solve problems involving appreciation and depreciation
  • Lesson 9 – Solve problems involving measures and money
  • Lesson 10 – Solve problems involving a) rates and taxes, b) utilities, c) invoices and shopping bills, d) salaries and wages and e) insurance and investments
SECTION 3 – SETS
8 Topics
  • Lesson 1 – Explain concepts relating to sets
  • Lesson 2 – Represent a set in various forms
  • Lesson 3 – List subsets of a given set
  • Lesson 4 – Determine elements in intersections, unions and complements of sets
  • Lesson 5 – Describe relationships among sets using set notation and symbols
  • Lesson 6 – Draw Venn diagrams to represent relationships among sets
  • Lesson 7 – Use Venn diagrams to represent the relationships among sets
  • Lesson 8 – Solve problems in Number Theory, Algebra and Geometry using concepts in Set Theory
SECTION 4 – MEASUREMENT
14 Topics
  • Lesson 1 – Convert units of length, mass, area, volume, capacity
  • Lesson 2 – Use the appropriate SI unit of measure for area, volume, capacity, mass, temperature and time (24-hour clock) and other derived quantities
  • Lesson 3 – Determine the perimeter of a plane shape
  • Lesson 4 – Calculate the length of an arc of a circle
  • Lesson 5 – Estimate the area of plane shapes
  • Lesson 6 – Calculate the area of polygons and circles
  • Lesson 7 – Calculate the area of a sector of a circle
  • Lesson 8 – Calculate the area of a triangle given two sides and the angle they form
  • Lesson 9 – Calculate the area of a segment of a circle
  • Lesson 10 – Calculate the surface area of solids
  • Lesson 11 – Calculate the volume of solids
  • Lesson 12 – Solve problems involving the relations among time, distance and speed
  • Lesson 13 – Estimate the margin of error for a given measurement
  • Lesson 15 – Solve problems involving measurement
SECTION 5 – STATISTICS
14 Topics
  • Lesson 1 – Differentiate between sample and population attributes
  • Lesson 2 – Construct a frequency table for a given set of data
  • Lesson 3 – Determine class features for a given set of data
  • Lesson 4 – Construct statistical diagrams
  • Lesson 5 – Determine measures of central tendency for raw, ungrouped and grouped data
  • Lesson 6 – Determine when it is most appropriate to use the mean, median and mode as the average for a set of data
  • Lesson 7 – Determine the measures of dispersion (spread) for raw, ungrouped and grouped data
  • Lesson 8 – Use standard deviation to compare sets of data
  • Lesson 9 – Draw cumulative frequency curve (Ogive)
  • Lesson 10 – Analyse statistical diagrams
  • Lesson 11 – Determine the proportion or percentage of the sample above or below a given value from raw data, frequency table or cumulative frequency curve
  • Lesson 12 – Identify the sample space for simple experiment
  • Lesson 13 – Determine experimental and theoretical probabilities of simple events
  • Lesson 14 – Determine experimental and theoretical probabilities of simple events
SECTION 6 – ALGEBRA
21 Topics
  • Lesson 1 – Use symbols to represent numbers, operations, variables and relations
  • Lesson 2 – Translate between algebraic symbols and worded expressions
  • Lesson 3 – Evaluate arithmetic operations involving directed numbers
  • Lesson 4 – Simplify algebraic expressions using the four basic operations
  • Lesson 5 – Substitute numbers for variables in algebraic expressions
  • Lesson 6 – Evaluate expressions involving binary operations (other than the four basic operations)
  • Lesson 7 – Apply the distributive law to factorise or expand algebraic expressions
  • Lesson 8 – Simplify algebraic fractions
  • Lesson 9 – Use the laws of indices to manipulate expressions with integral indices
  • Lesson 10 – Solve linear equations in one unknown
  • Lesson 11 – Solve simultaneous linear equations, in two unknowns, algebraically
  • Lesson 12 – Solve a simple linear inequality in one unknown
  • Lesson 13 – Change the subject of formulae
  • Lesson 14 – Factorise algebraic expressions
  • Lesson 15 – Rewrite a quadratic expression in the form 𝑎(𝑥 + ℎ)2 +k
  • Lesson 16 – Solve quadratic equations algebraically
  • Lesson 17 – Solve word problems
  • Lesson 18 – Solve a pair of equations in two variables when one equation is quadratic or nonlinear and the other linear
  • Lesson 19 – Prove two algebraic expressions to be identical
  • Lesson 20 – Represent direct and inverse variation symbolically
  • Lesson 21 – Solve problems involving direct variation and inverse variation
SECTION 7 – RELATIONS, FUNCTIONS AND GRAPHS
26 Topics
  • Lesson 1 – Explain basic concepts associated with relations
  • Lesson 2 – Represent a relation in various ways
  • Lesson 3 – State the characteristics that define a function
  • Lesson 4 – Use functional notation
  • Lesson 5 – Distinguish between a relation and a function
  • Lesson 6 – Draw graphs of linear functions
  • Lesson 7 – Determine the intercepts of the graph of linear functions
  • Lesson 8 – Determine the gradient of a straight line
  • Lesson 9 – Determine the equation of a straight line
  • Lesson 10 – Solve problems involving the gradient of parallel and perpendicular lines
  • Lesson 11 – Determine from co-ordinates on a line segment a) the length and b) the co-ordinates of the midpoint
  • Lesson 12 – Solve a pair of simultaneous linear equations in two unknowns graphically
  • Lesson 13 – Represent the solution of linear inequalities in one variable using a) set notation, b) the number line and c) graph
  • Lesson 14 – Draw a graph to represent a linear inequality in two variables
  • Lesson 15 – Use linear programming techniques to graphically solve problems involving two variables
  • Lesson 16 – Derive the composition of functions
  • Lesson 17 – State the relationship between a function and its inverse
  • Lesson 18 – Derive the inverse of a function
  • Lesson 19 – Evaluate a function 𝑓(𝑥) at a given value of x
  • Lesson 20 – Draw and use the graph of a quadratic function to identify its features b) an element of the domain that has given image, b) the image of a give element in the domain, c) the maximum or minimum value of the function and d) the equation of the axis of symmetry
  • Lesson 21 – Interpret the graph of a quadratic function to determine a) the interval of the domain for which elements of the range may be greater than or less than a given point, b) an estimate of the value of the gradient at a given point and c) intercepts of the function
  • Lesson 22 – Determine the equation of the axis of symmetry and the maximum or minimum value of a quadratic function expressed in the form 𝑎(𝑥 + ℎ)2 +k
  • Lesson 23 – Sketch the graph of a quadratic function expressed in the form 𝑦 = 𝑎(𝑥 + ℎ)2 + 𝑘 and determine the number of roots
  • Lesson 24 – Draw graphs of non-linear functions
  • Lesson 25 – interpret graphs of functions
  • Lesson 26 – Solve problems involving graphs of linear and non-linear functions
SECTION 8 – GEOMETRY AND TRIGONOMETRY
17 Topics
  • Lesson 1 – Explain concepts relating to geometry
  • Lesson 2 – Draw and measure angles and line segments accurately using appropriate instruments
  • Lesson 3 – Construct lines, angles, and polygons using appropriate instruments
  • Lesson 4 – Identify the type(s) of symmetry possessed by a given plane figure
  • Lesson 5 – Solve geometric problems using properties of a) lines, angles and polygons, b) congruent triangles, c) similar figures, d) faces, edges and vertices of solids and e) classes of solids
  • Lesson 6 – Identify the type(s) of symmetry possessed by a given plane figure
  • Lesson 7 – Represent translations in a plane using vector
  • Lesson 8 – Determine and represent the location of a) the image of an object under a transformation; and b) an object given the image under a transformation
  • Lesson 9 – State the relationship between an object and its image in the plane under geometric transformations
  • Lesson 10 – Describe a transformation given an object and its image
  • Lesson 11 – Locate the image of an object under a combination of transformations
  • Lesson 12 – Use Pythagoras’ theorem to solve problems
  • Lesson 13 – Define the trigonometric ratios of acute angles in a right triangle
  • Lesson 14 – Relate objects in the physical world to geometric objects
  • Lesson 15 – Apply the trigonometric ratios to solve problems
  • Lesson 16 – Use the sine and cosine rules to solve problems involving triangles
  • Lesson 17 – Solve problems involving bearings
SECTION 9 – VECTORS AND MATRICES
13 Topics
  • Lesson 1 – Explain concepts associated with vectors
  • Lesson 2 – Simplify expressions involving vectors
  • Lesson 3 – Write the position vector of a point 𝑃(𝑎, 𝑏) as 𝑂𝑃⃗= (𝑎/𝑏) where 𝑂 is the origin (0,0)
  • Lesson 4 – Determine the magnitude of a vector
  • Lesson 5 – Determine the direction of a vector
  • Lesson 6 – Use vectors to solve problems in geometry
  • Lesson 7 – Explain basic concepts associated with matrices
  • Lesson 8 – Solve problems involving matrix operations
  • Lesson 9 – Evaluate the determinant of a ‘2 x 2’ matrix
  • Lesson 10 – Define the multiplicative inverse of a non-singular square matrix
  • Lesson 11 – Obtain the inverse of a nonsingular ‘2 x 2’ matrix
  • Lesson 12 – Determine a ‘2 x 2’ matrix associated with a specified transformation
  • Lesson 13 – Use matrices to solve simple problems in Arithmetic, Algebra and Geometry
TRIAL EXAMINATION
1 Quiz
  • GRADE 11 TRIAL EXAMINATION

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