This article serves as a complete guide to JSS 2 mathematics students, covering all the important topics in the second term. Each section provides an easy-to-understand revision on the topic, along with likely questions to help you practice and prepare effectively.
1. Algebraic Expressions – Expansion and Simplification
Algebraic expressions are mathematical phrases involving numbers, variables, and operators. Understanding how to expand, simplify, and substitute these expressions is crucial.
Key Concepts:
- Expansion: This involves multiplying out terms in parentheses.
- Simplification: This means reducing an expression by combining like terms.
- Substitution: Replacing a variable with a specific number to find its value.
- LCM and HCF of algebraic terms: Least Common Multiple (LCM) and Highest Common Factor (HCF) are used to simplify expressions or solve problems.
Example:
- Expand and simplify: 3(x + 4) = 3x + 12.
- Find the LCM and HCF of 3x and 6x.
Likely Questions:
- Expand 2(x + 3).
- Simplify 4x + 3x – 2x.
- Substitute x = 2 in the expression 5x + 3.
- Find the LCM of 6x and 3x.
- Find the HCF of 4x and 6x.
- Expand (x + 2)(x + 3).
- Simplify 3a + 2b + 3a – 4b.
- Expand 5(x – 7).
- Substitute a = 3 and b = 5 in the expression 3a + 2b.
- Find the LCM of 4x² and 6x.
2. Algebraic Expressions – Quadratic Expressions and Factorization
Quadratic expressions are algebraic expressions where the highest power of the variable is squared (e.g., x²). Factorizing quadratic expressions means breaking them into simpler expressions.
Key Concepts:
- Expansion leading to quadratic expressions: Multiplying binomials to get a quadratic expression.
- Factorization of simple quadratic expressions: Breaking down quadratics like x² + 5x + 6 into (x + 2)(x + 3).
- Difference of two squares: The formula a² – b² = (a + b)(a – b).
- Algebraic fractions with monomial denominators: Simplifying fractions where the denominator is a monomial.
- Quantitative reasoning: Solving problems that involve interpreting and analyzing mathematical relationships.
Example:
- Factorize x² + 5x + 6 = (x + 2)(x + 3).
- Simplify (6x²) / (3x).
Likely Questions:
- Expand (x + 2)(x + 3).
- Factorize x² + 7x + 10.
- What is the difference of squares of 9x² – 16?
- Simplify the algebraic fraction (3x²) / (6x).
- Factorize x² – 16.
- Expand (x + 1)(x + 4).
- Factorize x² + 4x + 4.
- Solve the quadratic equation x² – 5x + 6 = 0.
- Simplify (4x²) / (2x).
- Factorize x² + 10x + 21.
3. Simple Linear Equations
Linear equations involve finding the value of an unknown variable. The goal is to isolate the variable by using inverse operations.
Key Concepts:
- Solving simple equations: Using operations to isolate the variable (e.g., x + 5 = 12).
- Solving equations involving brackets and fractions: Expanding or simplifying equations that include parentheses or fractions.
- Word problems leading to simple equations: Translating real-life problems into mathematical equations and solving.
Example:
- Solve for x in 2x + 4 = 10 by subtracting 4 from both sides, then dividing by 2.
Likely Questions:
- Solve for x: 3x – 5 = 10.
- Solve for y: 2(y + 3) = 16.
- Solve for z: 5z/2 = 15.
- Solve the equation 4(x – 2) = 12.
- Solve for x in 3x/5 = 12.
- Solve 2(x + 3) = 14.
- Solve for x: 7x – 2 = 20.
- Solve for y in (y/4) + 6 = 10.
- Translate the word problem “A number increased by 5 is equal to 12” into an equation.
- Solve for a: 2a + 6 = 18.
4. Linear Inequalities in One Variable
Inequalities are mathematical expressions that compare two values. Solving inequalities is similar to solving equations, but there are additional rules to follow when multiplying or dividing by negative numbers.
Key Concepts:
- Inequality symbols and meaning: Symbols like <, >, ≤, and ≥ show the relationship between two quantities.
- Solving linear inequalities: Use similar steps to solving equations, but reverse the inequality when multiplying or dividing by a negative number.
- Graphical representation: Represent solutions to inequalities on a number line.
- Word problems: Translate real-life situations into inequalities and solve.
Example:
- Solve x – 3 > 5 by adding 3 to both sides.
- Graph the solution to x ≥ 4 on the number line.
Likely Questions:
- Solve for x: x + 7 > 12.
- Solve for y: 3y – 4 < 8.
- Graph the solution to x < 5.
- Solve for z: 4z + 2 ≥ 14.
- Solve for p: -3p ≥ -9.
- Solve 5x – 2 < 18.
- Solve for x: -2x + 3 > 5.
- Graph the solution to y ≤ 6.
- Solve the inequality x – 4 > 8.
- Write the inequality for “A number is less than 5 but greater than 2.”
5. Graphs – Cartesian Plane
The Cartesian plane is a two-dimensional grid used to plot points and graph equations. Understanding how to plot points and draw graphs is essential in mathematics.
Key Concepts:
- Constructing a Cartesian plane: Draw two perpendicular lines (x-axis and y-axis) to create a grid.
- Ordered pairs and coordinates: Points on the plane are represented as (x, y).
- Plotting points: Identify the coordinates of a point and mark it on the plane.
- Graphs of linear equations: Draw a line that represents a linear equation.
Example:
- Plot the point (3, 4) on the Cartesian plane.
- Graph the equation y = 2x + 1.
Likely Questions:
- Plot the point (2, 5) on a Cartesian plane.
- Plot the points (4, 2) and (1, 3).
- Graph the linear equation y = x + 3.
- Plot the point (0, 0) on the Cartesian plane.
- Draw the graph of y = 2x.
- Identify the coordinates of the point where the line intersects the y-axis.
- Plot the equation y = -x.
- Graph the equation y = x + 4.
- Find the slope of the line passing through (1, 2) and (3, 4).
- Plot the points (1, 2), (2, 3), and (3, 4).
6. Graphs – Interpreting Information on Graphs
Understanding how to interpret data from graphs is crucial. This section covers the different types of graphs, their meanings, and how to apply them to real-life scenarios.
Key Concepts:
- Gradient: The slope or steepness of a line.
- Vertical and horizontal lines: Vertical lines have no slope, while horizontal lines have a slope of zero.
- Intercepts with axes: Points where the graph crosses the x-axis or y-axis.
- Real-life graphs: Distance-time graphs, velocity-time graphs, and more.
Example:
- Interpret the gradient of a line on a distance-time graph.
- Understand a velocity-time graph to determine the speed of an object.
Likely Questions:
- What is the gradient of the line in the graph?
- Identify the intercepts of the line y = 2x + 5.
- Describe the graph of a constant speed (distance-time graph).
- What does the slope of a velocity-time graph represent?
- Identify the horizontal line on the graph.
- Interpret the information in a travel graph.
- Describe the graph of an object at rest (distance-time graph).
- What does the gradient of a distance-time graph show?
- Identify the vertical line on the graph.
- Solve a word problem based on a given velocity-time graph.
7. Plane Figures – Properties of Quadrilaterals
Plane figures include shapes like quadrilaterals, triangles, and circles. Knowing their properties is important in geometry.
Key Concepts:
- Properties of quadrilaterals: Parallelogram, rhombus, and kite.
- Area formulas: Areas of circles, quadrilaterals, and triangles.
- Pythagorean Theorem: Relation in right-angled triangles (a² + b² = c²).
Example:
- Calculate the area of a parallelogram: Area = base × height.
- Use the Pythagorean theorem to find the length of the hypotenuse.
Likely Questions:
- What are the properties of a parallelogram?
- Find the area of a triangle with base 5 cm and height 4 cm.
- Use the Pythagorean theorem to find the hypotenuse of a right triangle with sides 3 cm and 4 cm.
- What are the properties of a rhombus?
- Calculate the area of a circle with a radius of 7 cm.
- Find the area of a rectangle with length 8 cm and width 6 cm.
- What is the difference between a rhombus and a kite?
- Calculate the perimeter of a kite with side lengths 6 cm and 8 cm.
- Solve for the missing side in a right-angled triangle using the Pythagorean theorem.
- What are the properties of a kite?
8. Scale Drawing and Patterns
Scale drawings involve representing objects in reduced or enlarged sizes using a specific ratio. Understanding how to apply this concept helps solve real-world problems, such as drawing maps or designing structures.
Key Concepts:
- Scale drawing: A drawing that uses a specific ratio to represent real-life dimensions.
- Applications of scale drawing: Solving problems related to maps and building designs.
Example:
- Draw a house with a scale of 1:100 (1 unit in the drawing equals 100 units in real life).
Likely Questions:
- What is a scale drawing?
- Draw a rectangle with a scale of 1:50.
- Solve a map-related problem using scale.
- What is the scale of a map that represents 1 cm as 10 km?
- Apply scale drawing to solve a building design problem.
- Draw a circle with a scale of 1:200.
- What is the purpose of using scale in drawings?
- Solve a problem using a scale of 1:10.
- Calculate the area of a room using scale drawing.
- Explain the importance of scale drawing in architecture.