Senior Secondary Education Curriculum Nigeria. Federal SS 3 General Mathematics Scheme of Work. Linear equations – Schemeofwork.com
GENERAL MATHEMATICS SS3 FIRST TERM
| WEEK | TOPIC / CONTENT | ACTIVITIES |
| 1 | MATRICES I i. Definition of matrix ii. Order and notation of matrix iii. Types of matrices (null, unit etc.) iv. Addition and subtraction of matrices v. Scalar multiplication of two by two matrices (2×2) and three by three (3×3) matrix | Teacher: Leads students to define a matrix. Leads students to understand the notations of matrices – identifies the different t types of matrices and performs the addition and subtraction operation – perform scalar multiplication of two by two matrices and three by three matrices. Students: Define matrix, identify matrix notation, identify different types of matrices, perform the operation of addition and subtraction of matrices. Perform the scalar multiplication of 2×2 and 3×3 matrices. Instructional Resources: Matrix charts, matrix addition charts, subtraction charts, determinant charts, computer assorted instructional material. |
| 2 | MATRICES II i. Transpose of a matrix ii. Determinant of a matrix (2×2) and (3×3) iii. Solution of simultaneous equations using determinant method (two equations in two unknown and three equations in three unknowns). iv. Inverse of 2 x2 matrix. | Teacher: Leads students to find transpose of a matrix by interchanging the rows with column -calculates the determinant of a matrix or matrices -applies determinant of matrices to solutions of simultaneous equations in two unknown and three unknowns Students: Find the transpose of a matrix and calculate the determinant of matrices. -applies determinant of matrices to solutions of simultaneous equations. Instructional Resources: Matrix charts, matrix additions charts, subtraction charts, determinant charts, computer assorted instructional material. |
| 3 | ARITHMETIC OF FINANCE i. Revision of simple interest ii. Compound interest including arithmetic of finance iii. Definition and calculation of depreciation iv. Definition and determination of annuity. | Teacher: Guides students to recall formula for calculating interest and derive the formula for computing compound interest and use of table in compound interest. Guides students to define and compute depreciation value of an item. Guides students to define and determine the annuity. Students: Calculate the simple interest and compound interest with the given formula. And table of logarithm in compound interest. Define and compute the value, compute the annuity. Instructional Resources: Charts, solution charts of logarithm on compound interest, solution chart on bond and debentures, solution charts of rate, taxes and value added tax. |
| 4 | ARITHMETIC OF FINANCE II i. Definition and computation of amortization. ii. Solving problems in capital market e.g. bonds and debentures, shares, rate, income tax and value added tax. | Teacher: Guides students to define and compute the amortization. Guides students to calculate interest on bonds and debentures, shares, rate, income tax and value added tax using logarithm table. Students: Compute amortization Calculate interest on bunds and debentures using logarithm table. Instructional Materials: Solution chart of logarithm on compound interest. Solution charts on logarithm on bond and debentures, logarithm table. Solution charts of rates, taxes and value added tax. (Excursion to stock exchange or inland revenue offices could be an added advantage. Stock exchange expect can also be invited to do simple calculations. |
| 5 | APPLICATION OF LINEAR AND QUADRATIC EQUATION i. Revision of solution of simultaneous linear equations and quadratic equations. ii. Word problem on linear equations. iii. Word problem on simultaneous linear equations. iv. Word problem on simultaneous equations one linear one quadratic v. Application to capital market. | Teacher: Displays chart of simple linear and quadratic equation. -revises the solution of simultaneous linear and quadratic equations. -guides students to discover how word problems can be interpreted into: linear, quadratic, simultaneous equation and quadratic equations one linear one quadratic. Students: Study the chart; solve the solution of simultaneous linear and quadratic equation. Use steps given by the teacher to solve word problems. Instructional Resources: Solution chart of simultaneous linear and quadratic equation. |
| 6 | TRIGONOMETRY i. Graph of trigonometric functions (sine and cosine graph for angles 0≤x≤ 360o) ii. Interpretation of graphs of trigonometric functions. | Teacher: Guides students to construct tables of values for sine and cosine. Plots graphs of sine and cosine for 0o≤x≤ 360o Interprets the graph and read out given values. Students: Construct table of values for 0o≤x≤ 360o. Plot the graphs of the tables of values. Interpret and read out given values. Instructional Resources: Graph board, graph books, pencil, ruler, broom stick/twine. (graph board and books mandatory) |
| 7 | SURFACE AREA AND VOLUME OF SPHERE i. Volume of a sphere ii. Surface area of a sphere iii. Volume of hemisphere (half of sphere) iv. Surface area of hemisphere. | Teacher: Brings cylinders, cone and spheres to the class. Determines the volume of a sphere practically by filling a cone and a cylinder with water/sand and then pouring them in the sphere. Notes the height of the cylinder and the diameter of the sphere. Leads students to find the volume of the sphere by formula and apply to solve problems. Brings a sphere to class and explain the concept of surface area, find the formula and solve problems. Students: Study the cylinder, cone and sphere. -participate in finding the volume of the sphere practically. -Find the formula for volume and apply it to solve problems Note the concept and find the surface area. Instructional Resources: Cylinder tin, sphere, cone, spherical globe etc. |
| 8 | THE EARTH AS A SPHERE i. Describe the earth as a sphere and identification of the line of longitude (meridian), latitude, equator, north pole and south pole, small circle and great circle. ii. Distance along the great circle iii. Radius of parallel of latitudes iv. Distance along the parallel of latitudes. v. Mathematical problems on earth as sphere. | Teacher: Guides students to revise the concepts of circles and spheres. Describes the earth a sphere. Brings skeletal and real globe to class. Leads students to identify the following North and South, Poles, Lines of longitudes and latitude, small circles and great circles, meridian and equator, parallel of latitude, radius of parallel of latitude. Radius of Earth, Deduce the formula for distance along great circle, distance along parallel of latitude. Leads students to solve problems on longitude and latitude. Students: Study the skeletal and the real globe;, participate in identification and locations. Solve given problems on longitude and latitude. Instructional Resources: Circles, spheres, real globe, skeletal globe, charts, charts of problems on longitude and latitude. |
| 9 | CO-ORDINATE GEOMETRY I i. Identification of Cartesian rectangular coordinate (x, y). ii. Drawing and interpretation of linear graph iii. Distance between two points iv. Mid- point of line joining two points v. Practical application of coordinate geometry. | Teacher: Leads students to understand the relative positions of a point in the (x-y) plane. The abscissa (x-axis), ordinate (y-axis) and origin (O) of x-y plane. -plots linear graph win the (x-y) plane -determines the distance between two coordinate points -calculates2 the midpoint of the line joining two points. Students: Plot linear graph in the x-y plane. Determine the length and midpoint of a line using the coordinate system. Instructional Resources: Graph board, graph books, and coordinate graph charts. Graph board line, mathematical instrument. |
| 10 | COORDINATE GEOMETRY II 1. Gradient of a straight line and y-intercept. 2. Equation of a straight line 3. Angle between two intersecting lines 4. Condition for parallel line and perpendicular line 5. Practical application of coordinate geometry. | Teacher: Leads students to define gradient and intercept of lines and determine them -writes equation of a straight line. -calculates the angle between two intersecting straight lines -leads students to appreciate the application of linear graphs to real life situation. Students: Define and determine gradient and intercepts. -write the equation of a straight line and calculate the angle between the intersection of two straight lines. -apply the concept of linear graphs to real life situation. Instructional Resources: Graph board, graph books, graph charts etc. |
| 11 | DIFFERENTIATION I 1. Meaning of differentiation 2. Differentiation from first principle 3. Technique of differentiation (General rule) 4. Standard derivative 5. Differentiation of polynomials 6. Rules of differentiation (sum and difference) 7. Differentiation of trigonometrically functions. | Teacher: Leads students to define differentiation and explain the meaning of derived function, -Differentiates functions from first principles for functions like y=x, y=x2, y=x3, y = x2+5x+7, etc. -interprets the standard derivatives of some basic functions. -solves problems on differentiation using the sum and difference rule. Students: Define and explain the differentiation and the meaning of derived function -perform differentiation from first principles -apply the rules of differentiation. Instructional Resources: Standard derivative charts, computer assisted instructional materials. |
| 12 | DIFFERENTIATION II 1. Rule of differentiation of sum, difference product, quotient and function- of- function (composite function) 2. Application of differentiation in determining maximum and minimum point. Acceleration, velocity and rate of change. | Teacher: Leads students to solve problems on differentiation using the rules of differentiation i) d (u+v) = du + dv dx dx dx ii) d (u-v) = du – dv dx dx dx iii) d (uv) = vdu + udv dx dx dx iv) d ( u ) = vdu – udv dx v dx dx v2 v) If y = Un dy = dy x du dx du dx e.g. If y = (3x2+5)6 let 3x2 + 5; du = 6x dx y = u6; du = 6x dx dy = dy x du dx du dx = 6(3x2 + 5)5 x 6x Students: Apply the rules of differentiation to solve related problems. -apply differentiation in solving life problems and in capital market issues. Instructional Resources: Standard derivative charts, computer assisted instructional materials. |
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| 14 | Examinations | Examinations |
GENERAL MATHEMATICS SS3 SECOND TERM
| WEEK | TOPIC / CONTENT | ACTIVITIES |
| 1 | INTEGRATION I 1. Integration as anti-differentiation 2. Techniques of integration (standard intergral) 3. Integration of algebraic functions 4. Special integrals 5. Integration by substitution | Teacher: Guides students to understand that integration is the reverse of differentiation. Leads students to integral functions using (a) Substitution method, (b) integration by parts (c) Integration by partial fractions. Students: Perform differentiation of a function and integrate the same function to show the reversed forms of differentiations and interpretation. Leads students to integrate functions using Substitution methodIntegration by partial fractions. Instructional Resources: Integration charts, standard integral charts etc. |
| 2 | INTEGRATION II i. Integration of trigonometric functions ii. Integration by part iii. Integration by partial fraction iv. Application of integration – the use of Simpson’s rule to find area under the curve. v. Integration of exponential function. | Teacher: Guides students to integrate trigonometric functions like sine, cosine, and tangents. Leads students to integrate functions using i. Substitution method ii. Integration by part iii. Integration by partial functions. Students: Solve problems on integration using: -substitution method -integration by part method -integration by partial functions method -should apply integration to real life situation and capital market issues. Instructional Resources: Integration charts, standard integral charts etc. |
| 3 | LOGARITHMS ai) Revision of law of indices ii) Revision of the use of logarithm table to calculate logarithm of numbers bi) Theory of logarithm ii) Rules connecting logarithm Log(pq) = log p – log q Log (p/q) = log p – log q Logaxn = nlogax etc. | Teacher: Brings the logarithm rules chart and solution chart of logarithm to the classroom Guides students to revise the use of logarithm rules. – revises the use of logarithm table in problems involving calculations Students: Study the two charts. Deduce laws of logarithm especially Log10 (pq) = log10 p + log10 q Log10 (p/q) = log10 p – log10q Log10pn = nlog10p Verify logarithm laws with simple exercise. Revise the use of logarithm table to solve problems involving calculations. Instructional Resources: Logarithm law chart, solution chart of logarithm, logarithm table. |
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| 5 | Examinations | Examinations |
