Comprehensive Guide on "SS 2 Scheme of Work for Mathematics (Second Term)

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SS 2 Scheme of Work for Second Term

Week(s)	Topic(s)	Content
1	Revision	Overview of the previous term’s work to refresh students’ understanding and ensure readiness for new topics.
2	Straight Line: Gradient of Straight Line and Curve	Gradient of a straight line, gradient of a curve, drawing tangents to a curve, and understanding the slope-intercept form.
3	Inequalities	Revision of linear inequalities in one variable, solutions of inequalities in two variables, combined inequalities, and range of values.
4	Graphs of Linear Inequalities	Graphing linear inequalities in two variables, determining maximum and minimum values of simultaneous linear inequalities.
5	Applications of Linear Inequalities and Programming	Application of linear inequalities in real life, introduction to linear programming and its practical uses.
6	Algebraic Fractions	Simplification of algebraic fractions, operations on algebraic fractions, equations involving fractions, and understanding undefined fractions.
7	Review of First Half Term and Periodic Test	A thorough revision of the topics covered in the first half of the term, followed by a periodic test to assess students’ understanding.
8	Fractions (Continued)	Substitution in fractions, simultaneous equations involving fractions, and deeper work with algebraic fractions.
9	Logic	Simple and compound statements, logical operations and truth tables, conditional statements, and indirect proofs.
10	Chord Properties of Circles	Perpendicular bisector of a chord, distance of equal chords from the center of the circle, and angles subtended by two equal chords.
11	Circle Theorems	Angle properties of circles, angle subtended by an arc at the center is twice the one subtended at the circumference, angle in the same segment, and opposite angle of a cyclic quadrilateral.
12-13	Revision and Exams	Final revision and practice, leading up to exams to solidify understanding and ensure readiness.

Detailed Explanations for Each Topic

Week 1: Revision

This week focuses on refreshing the content from the previous term. This revision ensures that students have a solid understanding of the foundational concepts required for the new term’s topics.

Examples:
1. Review the key equations and functions from last term.
2. Discuss the importance of graphing functions.
3. Refresh concepts related to solving quadratic equations.
4. Revisit algebraic simplifications.
5. Go over geometric shapes and their properties.
6. Reinforce problem-solving strategies.

Week 2: Straight Line – Gradient of Straight Line and Curve

Gradient of a Straight Line: The gradient (or slope) of a straight line refers to the steepness of the line, which can be found using the formula:
$x\text{Gradient} = \frac{\text{Change in } y}{\text{Change in } x}$ The gradient of a straight line shows the rate of change of $y$ with respect to $x$ .
Gradient of a Curve: For curves, the gradient changes at different points. The slope at a specific point on a curve is the derivative of the function at that point.
Drawing Tangents to a Curve: A tangent to a curve is a straight line that touches the curve at exactly one point. The gradient of the tangent equals the gradient of the curve at that point.
Examples:
1. Find the gradient of the line passing through the points (1, 2) and (3, 4).
2. Determine the gradient of the curve $y = x^2$ at $x = 2$ .
3. Draw the tangent to the curve $y = x^3$ at $x = 1$ .
4. Solve for the equation of a line with a gradient of 2 that passes through (0, 5).
5. Calculate the slope of a line given two points: (2, 3) and (5, 6).
6. Apply the concept of tangents to solve real-world problems in velocity and acceleration.

Week 3: Inequalities

Linear Inequalities in One Variable: An inequality in one variable has a solution set that can be expressed on a number line. For example, $x + 3 > 5$ .
Inequalities in Two Variables: These inequalities describe a region in the coordinate plane. For example, $y > 2 x + 1$ represents a region above the line $y = 2 x + 1$ .
Combined Inequalities: Solving inequalities involving multiple conditions, such as $\leq x < 5$ , involves finding the values that satisfy both conditions.
Range of Values: The solution set of an inequality defines the range of values that the variable can take.
Examples:
1. Solve $3 x - 5 < 10$ .
2. Graph the inequality $\leq 2x + 1$ .
3. Find the solution set for $\geq 7$ and $x < 5$ .
4. Solve and graph the inequality $y > 3 x + 4$ .
5. Determine the combined solution set for $2 x - 1 > 4$ and $\leq 3$ .
6. Solve $\leq x + 3 \leq 5$ and graph the solution.

Week 4: Graphs of Linear Inequalities

This week focuses on visualizing inequalities. Linear inequalities in two variables are graphed as shaded regions in the coordinate plane. The solution to a system of linear inequalities is the overlapping region of their graphs.

Examples:
1. Graph $\geq 2x + 1$ .
2. Graph the inequality $y < - x + 4$ .
3. Solve and graph the system of inequalities: $\geq x + 3 \quad \text{and} \quad y < 2x – 1$
4. Find the maximum and minimum values of $y$ for the system $\leq 2x + 1$ and $\geq x – 3$ .
5. Apply graphing linear inequalities to find the feasible region for a business optimization problem.
6. Graph a system of three inequalities and identify the feasible region.

Week 5: Applications of Linear Inequalities and Linear Programming

Applications: Linear inequalities are used in real-life scenarios such as budgeting, production limits, and optimization problems.
Linear Programming: This is a mathematical method used to find the best outcome in a given mathematical model. Linear programming problems typically involve maximizing or minimizing a linear objective function subject to linear constraints.
Examples:
1. Maximize profit with constraints on resources.
2. Determine the best allocation of funds between multiple projects using linear programming.
3. Apply linear inequalities to solve supply and demand problems.
4. Use inequalities to model diet problems where the goal is to minimize cost while meeting nutritional requirements.
5. Apply linear programming to solve manufacturing problems with multiple constraints.
6. Solve an optimization problem in business using linear programming.

Week 6: Algebraic Fractions

Simplification of Algebraic Fractions: Simplifying fractions involves reducing them to their simplest form by canceling common factors.
Operations on Algebraic Fractions: This includes addition, subtraction, multiplication, and division of fractions involving algebraic expressions.
Equations Involving Fractions: Solving equations that involve fractions, including finding the value of variables in fractional equations.
Undefined Fractions: A fraction is undefined when the denominator equals zero, which leads to expressions such as $1x−2\frac{1}{x – 2}$ , where $x = 2$ makes the fraction undefined.
Examples:
1. Simplify $2x+4x+2\frac{2x + 4}{x + 2}$ .
2. Solve $1x+3=5\frac{1}{x} + 3 = 5$ .
3. Multiply the fractions $3×4×2×5\frac{3x}{4} \times \frac{2x}{5}$ .
4. Solve $3x−2=6\frac{3}{x – 2} = 6$ .
5. Simplify $x2+4x+4×2+2x\frac{x^2 + 4x + 4}{x^2 + 2x}$ .
6. Determine when $yx+1\frac{y}{x + 1}$ is undefined.

Conclusion

The SS 2 Scheme of Work for Second Term covers essential topics in mathematics that will not only prepare students for their exams but also provide valuable real-life problem-solving skills. With detailed explanations, step-by-step examples, and practical applications, this guide ensures students gain a deep understanding of each concept.

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