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CSEC Mathematics (Grade 10) By Mr. King

Instructor Image Winsford King
15 Lessons
9 months
10 Student
Free
Enroll In This Course
IITAE Course UpdateCooperate CoursesGrade 10Secondary School Courses

CSEC Mathematics (Grade 10) By Mr. King

Instructor Image Winsford King
15 Lessons
9 months
10 Student
Free Enroll In This Course
Introduction

RATIONALE

The Caribbean society is an integral part of an ever-changing world. The impact of globalisation on most societies encourages this diverse Caribbean region to revisit the education and career opportunities of our current and future citizens. A common denominator of the Caribbean societies is to create among its citizens, a plethora of quality leadership with the acumen required to make meaningful projections and innovations for further development. Further, learning appropriate problem-solving techniques, inherent to the study of mathematics, is vital for such leaders. Mathematics promotes intellectual development, is utilitarian, and applicable to all disciplines. Additionally, its aesthetics and epistemological approaches provide solutions fit for any purpose. Therefore, Mathematics is the essential tool to empower people with the knowledge, competencies and attitudes which are precursors for this dynamic world.

AIMS

  1. make Mathematics relevant to the interests and experiences of students by helping them to recognise Mathematics in the local and global environment;
  2. help students appreciate the use of Mathematics as a form of communication;
  3. help students acquire a range of mathematical techniques and skills and to foster and maintain the awareness of the importance of accuracy;
  4. help students develop positive attitudes, such as open-mindedness, resourcefulness, persistence and a spirit of enquiry;
  5. prepare students for the use of Mathematics in further studies;
  6. help students foster a ‘spirit of collaboration’, with their peers and others within the wider community;
  7. help students apply the knowledge and skills acquired to solve problemsin everyday situations; and,
  8. integrate Information Communications, and Technology (ICT) tools and skills in the teaching and learning processes.

Lessons

COORDINATE GEOMETRY

FINDING GRADIENT, MIDPOINT AND LENGTH OF A LINE
- - -
Finding equation of a line
- - -
REVISION
49 Topics
  • Standard Form
  • Linear Equations
  • Finding the hypotenuse of a right triangle using Pythagoras Theorem
  • Finding the other sides of a right angle triangle using Pythagoras Theorem
  • Pythagoras Theorem practice
  • Substition
  • Linear Equations practice
  • Transformation one
  • Transformation Two
  • Trigonometry one
  • Pythagoras theorem four
  • Mean Mode Median one
  • Trigonometry three
  • Pythagoras five
  • Trigonometry four
  • Bar chart and pie chart
  • Histogram and Frequency Polygon
  • Cumulative Frequency curve
  • Finding mean from grouped data
  • Solving word problems
  • Solving word problems two
  • Solving word problems three
  • Constructing angles one
  • Constructing triangles one
  • Formulae - area of triangle
  • Relations and Functions
  • Inverse functions one
  • Inverse functions two
  • Inverse functions three
  • Composite function one
  • Composite function two
  • Composite function three
  • Parallel lines one
  • Bar chart pie chart two
  • Speed and distance one
  • Speed and distance two
  • pythagoras six
  • Pie chart one
  • Pie chart two
  • Mean from frequency table one
  • Mean three
  • Interpreting tables one
  • Plotting graphs one
  • Plotting graphs two
  • Plotting graphs three
  • Plotting graphs five
  • Plotting graphs six
  • Plotting graphs seven
  • linear equations four
Section 1 -Miscellaneous Section
31 Topics
  • Finding length of the hypotenuse and the length of another side in a right angle triangle
  • Pythagoras theorem practice
  • finding the sides in a right angle triangle using trigonometry
  • 27/4 finding the sides in a right angle triangle using trigonometry practice
  • finding the angles in a right angle triangle using trigonometry
  • finding the angles in a right angle triangle using trigonometry
  • Bar Chart, Pie chart and Frequency table
  • constructing histograms and frequency polygons
  • Finding mean from grouped data
  • Statistics one
  • plotting cumulative frequency curves
  • Mean Mode and Median
  • Solving word problems
  • Solving word problems two
  • Solving word problems three
  • Constructing angles
  • Constructing triangles
  • 2/6 Finding area of triangle
  • 4/6 Construction and Statistics
  • 8/6 Relations and functions
  • Finding inverse function
  • 15/6 Finding inverse function two
  • Finding inverse function three
  • Finding composite function
  • 22/6 Finding composite function two
  • composite function three
  • The Cosine rule
  • The sine rule
  • Change of Subject
  • Finding angles of elevation and depression
  • Explain basic concepts associated with relations
SECTION 2 – RELATIONS, FUNCTIONS AND GRAPHS
14 Topics
  • Explain basic concepts associated with relations
  • Represent a relation in various ways
  • State the characteristics that define a function
  • Use functional notation
  • Distinguish between a relation and a function
  • Evaluate a function 𝑓(𝑥) at a given value of x
  • Draw graphs of linear functions
  • Represent the solution of linear inequalities in one variable using a) set notation, b) the number line and c) graph
  • Derive the composition of functions
  • State the relationship between a function and its inverse
  • Derive the inverse of a function
  • 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
  • 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'ml
  • 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
Section 3 - SBA work
- - -
SECTION 4 – VECTORS AND MATRICES
13 Topics
  • Explain concepts associated with vectors
  • Simplify expressions involving vectors
  • Write the position vector of a point 𝑃(𝑎, 𝑏) as 𝑂𝑃⃗= (𝑎/𝑏) where 𝑂 is the origin (0,0)
  • Determine the magnitude of a vector
  • Determine the direction of a vector
  • Use vectors to solve problems in geometry
  • Explain basic concepts associated with matrices
  • Solve problems involving matrix operations
  • Evaluate the determinant of a ‘2 x 2’ matrix
  • Define the multiplicative inverse of a non-singular square matrix
  • Obtain the inverse of a nonsingular ‘2 x 2’ matrix
  • Use matrices to solve simple problems in Arithmetic, Algebra and Geometry
  • Solving simultaneous equations using matrices
Section 5 - Relations functions Graphs Two
9 Topics
  • Determine the intercepts of the graph of linear functions
  • Determine the gradient of a straight line
  • Determine the equation of a straight line
  • Solve problems involving the gradient of parallel and perpendicular lines
  • Determine from co-ordinates on a line segment a) the length and b) the co-ordinates of the midpoint
  • Solve a pair of simultaneous linear equations in two unknowns graphically
  • Draw a graph to represent a linear inequality in two variables
  • interpret graphs of functions
  • Solve problems involving graphs of linear and non-linear functions
SECTION 6 – NUMBER THEORY AND COMPUTATION GENERAL OBJECTIVES
19 Topics
  • Distinguish among sets of numbers
  • Compute powers of real numbers of the form 𝓍 𝑎 , where 𝑎 ∈ ℚ
  • Evaluate numerical expressions using any of the four basic operations on real numbers
  • Convert among fractions, per cents and decimals
  • List the set of factors and multiples of a given integer
  • Compute the H.C.F. or L.C.M. of two or more positive integers
  • State the value of a digit of a numeral in a given base
  • Convert from one set of units to another
  • Express a value to a given number of a) significant figures and b) decimal places
  • Use properties of numbers and operations in computational tasks
  • Write any rational number in scientific notation
  • Calculate any fraction or percentage of a given quantity
  • Express one quantity as a fraction or percentage of another
  • Compare quantities
  • Order a set of real numbers
  • Compute terms of a sequence given a rule
  • Derive an appropriate rule given the terms of a sequence
  • Divide a quantity in a given ratio
  • Solve problems involving concepts in number theory and computation
SECTION 7 – CONSUMER ARITHMETIC
9 Topics
  • Calculate a) discount, b) sales tax, c) profit and d) loss
  • Express a profit, loss, discount, markup and purchase tax, as a percentage of some value
  • Solve problems involving marked price, selling price, cost price, profit, loss or discount
  • Solve problems involving payments by instalments as in the case of hire purchase and mortgages
  • Solve problems involving simple interest
  • Solve problems involving compound interest
  • Solve problems involving appreciation and depreciation
  • Solve problems involving measures and money
  • Solve problems involving a) rates and taxes, b) utilities, c) invoices and shopping bills, d) salaries and wages and e) insurance and investments
SECTION 8 – SETS
8 Topics
  • Explain concepts relating to sets
  • Represent a set in various forms
  • List subsets of a given set
  • Determine elements in intersections, unions and complements of sets
  • Describe relationships among sets using set notation and symbols
  • Draw Venn diagrams to represent relationships among sets
  • Use Venn diagrams to represent the relationships among sets
  • Solve problems in Number Theory, Algebra and Geometry using concepts in Set Theory
SECTION 9 – MEASUREMENT
15 Topics
  • Convert units of length, mass, area, volume, capacity
  • Use the appropriate SI unit of measure for area, volume, capacity, mass, temperature and time (24-hour clock) and other derived quantities
  • Determine the perimeter of a plane shape
  • Calculate the length of an arc of a circle
  • Estimate the area of plane shapes
  • Calculate the area of polygons and circles
  • Calculate the area of a sector of a circle
  • Calculate the area of a triangle given two sides and the angle they form
  • Calculate the area of a segment of a circle
  • Calculate the surface area of solids
  • Calculate the volume of solids
  • Solve problems involving the relations among time, distance and speed
  • Estimate the margin of error for a given measurement
  • Use scales and scale drawings to determine distances and areas
  • Solve problems involving measurement
SECTION 10 – STATISTICS
14 Topics
  • Differentiate between sample and population attributes
  • Construct a frequency table for a given set of data
  • Determine class features for a given set of data
  • Construct statistical diagrams
  • Determine measures of central tendency for raw, ungrouped and grouped data
  • Determine when it is most appropriate to use the mean, median and mode as the average for a set of data
  • Determine the measures of dispersion (spread) for raw, ungrouped and grouped data
  • Use standard deviation to compare sets of data
  • Draw cumulative frequency curve (Ogive)
  • Analyse statistical diagrams
  • Determine the proportion or percentage of the sample above or below a given value from raw data, frequency table or cumulative frequency curve
  • Identify the sample space for simple experiment
  • Determine experimental and theoretical probabilities of simple events
  • Determine experimental and theoretical probabilities of simple events
SECTION 11 – ALGEBRA
18 Topics
  • Use symbols to represent numbers, operations, variables and relations
  • Translate between algebraic symbols and worded expressions
  • Evaluate arithmetic operations involving directed numbers
  • Simplify algebraic expressions using the four basic operations
  • Substitute numbers for variables in algebraic expressions
  • Evaluate expressions involving binary operations (other than the four basic operations)
  • Apply the distributive law to factorise or expand algebraic expressions
  • Simplify algebraic fractions
  • Use the laws of indices to manipulate expressions with integral indices
  • Solve linear equations in one unknown
  • Solve simultaneous linear equations, in two unknowns, algebraically
  • Change the subject of formulae
  • Factorise algebraic expressions
  • Solve quadratic equations algebraically
  • Solve word problems
  • Prove two algebraic expressions to be identical
  • Represent direct and inverse variation symbolically
  • Solve problems involving direct variation and inverse variation
SECTION 12 – GEOMETRY AND TRIGONOMETRY
17 Topics
  • Explain concepts relating to geometry
  • Draw and measure angles and line segments accurately using appropriate instruments
  • Construct lines, angles, and polygons using appropriate instruments
  • Identify the type(s) of symmetry possessed by a given plane figure
  • 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
  • Identify the type(s) of symmetry possessed by a given plane figure
  • Represent translations in a plane using vector
  • 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
  • State the relationship between an object and its image in the plane under geometric transformations
  • Describe a transformation given an object and its image
  • Locate the image of an object under a combination of transformations
  • Use Pythagoras’ theorem to solve problems
  • Define the trigonometric ratios of acute angles in a right triangle
  • Relate objects in the physical world to geometric objects
  • Apply the trigonometric ratios to solve problems
  • Use the sine and cosine rules to solve problems involving triangles
  • Solve problems involving bearings

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