JSS 3 Mathematics Second Term Full Web Book

A complete second-term mathematics learning page for JSS 3. Each topic is explained thoroughly with step-by-step examples, quick brain tests, external learning links, and a 30-question CBT quiz with corrections at the end.

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Second Term Scheme of Work

Scheme of Work Overview

The second term of JSS 3 Mathematics strengthens algebra, equations, graphs and data handling. The lessons are arranged to prepare learners for senior secondary mathematics and end-of-term assessment.

How to use this page: read each topic carefully, study the examples, answer the brain tests, and then attempt the full-term CBT quiz.

JSS 3 Mathematics Second Term Scheme of Work
Week	Topic	Core Content
1	Simultaneous Linear Equations	Solving two equations with two unknowns by substitution and elimination.
2	Factorization of Algebraic Expressions	Common factors, simple trinomials, difference of two squares.
3	Quadratic Expressions	Expanding, recognizing and factoring quadratic forms.
4	Inequalities	Solving and representing inequalities on a number line.
5	Graphs of Linear Equations	Plotting points, graphing straight lines and reading intercepts.
6	Variation	Direct and inverse variation with word problems.
7	Statistics and Data Interpretation	Mean, median, mode, range and data presentation.
8	Revision and Examination	General revision and assessment.

Topic 1

Simultaneous Linear Equations

Simultaneous equations are two equations that share the same unknowns. The solution is the pair of values that satisfies both equations at the same time. We can solve by substitution or elimination.

Substitution

Make one variable the subject and replace it in the other equation.

Elimination

Add or subtract equations to remove one variable.

Solution

The pair of values that satisfies both equations.

Worked examples

Example 1

Question: x + y = 10 and x - y = 2.

Step 1: Add the equations: 2x = 12.

Step 2: x = 6.

Step 3: Substitute into x + y = 10, so y = 4.

Example 2

Question: x + y = 8 and x = 5.

Step 1: Substitute x = 5 into the first equation.

Step 2: 5 + y = 8.

Step 3: y = 3.

Example 3

Question: 2x + y = 11 and x = 4.

Step 1: Substitute x = 4.

Step 2: 2(4) + y = 11.

Step 3: 8 + y = 11, so y = 3.

Example 4

Question: 3x + y = 14 and x - y = 4.

Step 1: From x - y = 4, write y = x - 4.

Step 2: Substitute into 3x + y = 14.

Step 3: 3x + x - 4 = 14, so 4x = 18 and x = 4.5.

Example 5

Question: 2x + y = 9 and x + y = 6.

Step 1: Subtract the second from the first.

Step 2: x = 3.

Step 3: Substitute into x + y = 6 to get y = 3.

Example 6

Question: x + 2y = 12 and x = 4.

Step 1: Substitute x = 4.

Step 2: 4 + 2y = 12.

Step 3: 2y = 8, so y = 4.

Quick Brain Tests

1. Two equations with same unknowns are called?

Simultaneous equations.

2. Method that removes a variable by adding/subtracting?

Elimination.

3. Method that replaces one variable with an expression?

Substitution.

4. If x + y = 10 and x - y = 2, x = ?

5. Same pair satisfies both equations?

Solution.

Topic 2

Factorization of Algebraic Expressions

Factorization means writing an algebraic expression as a product of simpler expressions. It is the reverse of expansion and is very important in algebra and equation solving.

Common factor

Factor that divides every term.

Difference of squares

a² - b² = (a - b)(a + b).

Trinomials

Expressions with three terms.

Worked examples

Example 1

Question: Factorize 6x + 12.

Step 1: Find the common factor 6.

Step 2: 6x + 12 = 6(x + 2).

Step 3: Answer: 6(x + 2).

Example 2

Question: Factorize 8a² + 4a.

Step 1: Common factor is 4a.

Step 2: 8a² + 4a = 4a(2a + 1).

Step 3: Answer: 4a(2a + 1).

Example 3

Question: Factorize x² + 5x.

Step 1: Common factor is x.

Step 2: x² + 5x = x(x + 5).

Step 3: Answer: x(x + 5).

Example 4

Question: Factorize x² - 9.

Step 1: Recognize difference of squares.

Step 2: x² - 9 = x² - 3².

Step 3: Answer: (x - 3)(x + 3).

Example 5

Question: Factorize 9y² - 16.

Step 1: Recognize difference of squares.

Step 2: 9y² - 16 = (3y)² - 4².

Step 3: Answer: (3y - 4)(3y + 4).

Example 6

Question: Factorize x² + 7x + 12.

Step 1: Find two numbers that multiply to 12 and add to 7.

Step 2: The numbers are 3 and 4.

Step 3: Answer: (x + 3)(x + 4).

Quick Brain Tests

1. Common factor of 10x and 15x?

5x.

2. x² - 25 factorized?

(x - 5)(x + 5).

3. Factorize x² + 6x?

x(x + 6).

4. Factorization is reverse of?

Expansion.

5. x² + 5x + 6 factorized?

(x + 2)(x + 3).

Topic 3

Quadratic Expressions

Quadratic expressions contain a squared term, a linear term and a constant. They often appear in factorization, expansion and equation solving.

Form

ax² + bx + c.

Expansion

Multiply brackets carefully.

Factorization

Break into two brackets where possible.

Worked examples

Example 1

Question: Expand (x + 2)(x + 3).

Step 1: x × x = x².

Step 2: Outer and inner terms: 3x + 2x.

Step 3: Final answer: x² + 5x + 6.

Example 2

Question: Expand (x - 4)(x + 1).

Step 1: Multiply x by x and then by 1.

Step 2: Multiply -4 by x and by 1.

Step 3: Answer: x² - 3x - 4.

Example 3

Question: Factorize x² + 5x + 6.

Step 1: Find two numbers that multiply to 6 and add to 5.

Step 2: 2 and 3 fit.

Step 3: Answer: (x + 2)(x + 3).

Example 4

Question: Factorize x² + 7x + 12.

Step 1: Find numbers that multiply to 12 and add to 7.

Step 2: 3 and 4 fit.

Step 3: Answer: (x + 3)(x + 4).

Example 5

Question: Factorize x² - x - 6.

Step 1: Find numbers that multiply to -6 and add to -1.

Step 2: -3 and 2 fit.

Step 3: Answer: (x - 3)(x + 2).

Example 6

Question: Expand (2x + 1)(x + 5).

Step 1: Multiply 2x by x and 5.

Step 2: Multiply 1 by x and 5.

Step 3: Answer: 2x² + 11x + 5.

Quick Brain Tests

1. General form of quadratic expression?

ax² + bx + c.

2. Expand (x + 1)(x + 1)?

x² + 2x + 1.

3. x² + 6x + 9 factorized?

(x + 3)².

4. Difference of squares formula?

a² - b² = (a - b)(a + b).

5. A quadratic has highest power?

Topic 4

Inequalities

Inequalities compare quantities that are not necessarily equal. They use symbols such as <, >, ≤ and ≥. Solutions are often represented on a number line.

Less than

Greater than

Number line

Shows the set of values that satisfy the inequality.

Worked examples

Example 1

Question: Solve x > 3.

Step 1: Any number greater than 3 works.

Step 2: Show it on a number line with an open circle at 3.

Step 3: Answer: x is greater than 3.

Example 2

Question: Solve x ≤ 5.

Step 1: Any number less than or equal to 5 works.

Step 2: Use a closed circle at 5.

Step 3: Answer: x ≤ 5.

Example 3

Question: Solve x + 2 < 7.

Step 1: Subtract 2 from both sides.

Step 2: x < 5.

Step 3: Answer: x < 5.

Example 4

Question: Solve 3x ≥ 12.

Step 1: Divide both sides by 3.

Step 2: x ≥ 4.

Step 3: Answer: x ≥ 4.

Example 5

Question: Solve x - 4 ≥ 1.

Step 1: Add 4 to both sides.

Step 2: x ≥ 5.

Step 3: Answer: x ≥ 5.

Example 6

Question: Solve 2x + 1 < 9.

Step 1: Subtract 1 from both sides: 2x < 8.

Step 2: Divide by 2.

Step 3: Answer: x < 4.

Quick Brain Tests

1. Symbol for less than?

2. x ≥ 2 means?

x is 2 or more.

3. Open circle on number line means?

The value is not included.

4. Closed circle means?

The value is included.

5. x < 0 is?

Negative values only.

Topic 5

Graphs of Linear Equations

Graphs of linear equations are straight-line graphs. They help show the relationship between variables and are useful for interpreting patterns and predictions.

Linear graph

A straight line graph.

Intercept

Where the graph crosses an axis.

Coordinates

Points written as (x, y).

Worked examples

Example 1

Question: Find the intercept of y = 2x + 3 on the y-axis.

Step 1: At x = 0, y = 3.

Step 2: The graph crosses the y-axis at 3.

Step 3: Answer: y-intercept = 3.

Example 2

Question: Plot points for y = x + 1 when x = 0, 1, 2.

Step 1: Find y values: 1, 2, 3.

Step 2: Plot (0,1), (1,2), (2,3).

Step 3: Join the points to get a straight line.

Example 3

Question: What is the slope of y = 3x + 2?

Step 1: The slope is the coefficient of x.

Step 2: The coefficient is 3.

Step 3: Answer: 3.

Example 4

Question: What is the x-intercept of y = x - 4?

Step 1: Set y = 0.

Step 2: 0 = x - 4, so x = 4.

Step 3: Answer: 4.

Example 5

Question: Plot (2, 5).

Step 1: Move 2 units right.

Step 2: Move 5 units up.

Step 3: The point is (2, 5).

Example 6

Question: Is y = 4x + 1 linear?

Step 1: Check the power of x.

Step 2: The power is 1, so it is linear.

Step 3: Answer: yes.

Quick Brain Tests

1. Straight-line graph?

Linear graph.

2. y-intercept of y = x + 5?

3. Slope of y = 2x + 1?

4. Point format?

(x, y).

5. When x = 0, we find?

y-intercept.

Topic 6

Variation

Variation describes how one quantity changes in relation to another. Direct and inverse variation are common in algebra and real-life word problems.

Direct

y = kx.

Inverse

y = k/x.

Constant

A fixed value linking the variables.

Worked examples

Example 1

Question: If y varies directly as x and y = 6 when x = 2, find k.

Step 1: Use y = kx.

Step 2: 6 = 2k.

Step 3: k = 3.

Example 2

Question: If y = 15 when x = 5, find y when x = 8.

Step 1: Find k: 15 = 5k, so k = 3.

Step 2: y = 3x.

Step 3: y = 24.

Example 3

Question: If y varies inversely as x and y = 4 when x = 3, find k.

Step 1: Use y = k/x.

Step 2: 4 = k/3.

Step 3: k = 12.

Example 4

Question: If y = 10 when x = 2 in inverse variation, find y when x = 5.

Step 1: Find k: 10 = k/2, so k = 20.

Step 2: y = 20/5.

Step 3: y = 4.

Example 5

Question: State the kind of variation when p = kq.

Step 1: Compare the formula with direct variation.

Step 2: It matches y = kx form.

Step 3: Answer: direct variation.

Example 6

Question: If a car's speed and travel time for fixed distance are related, what type of variation is this?

Step 1: As speed increases, time decreases.

Step 2: That is inverse variation.

Step 3: Answer: inverse variation.

Quick Brain Tests

1. Direct variation formula?

y = kx.

2. Inverse variation formula?

y = k/x.

3. If y increases as x increases?

Direct variation.

4. If y decreases as x increases?

Inverse variation.

5. k is called?

Constant of variation.

Topic 7

Statistics and Data Interpretation

Statistics helps us collect, organize, present and interpret data. It is useful for understanding patterns, comparing groups and making informed decisions from information.

Mean

Add values and divide by number of values.

Median

The middle value in ordered data.

Range

Highest value minus lowest value.

Worked examples

Example 1

Question: Find the mode of 2, 3, 3, 4, 5.

Step 1: Count the repeats.

Step 2: 3 appears most often.

Step 3: Answer: 3.

Example 2

Question: Find the median of 2, 4, 6, 8, 10.

Step 1: Arrange in order.

Step 2: Choose the middle value.

Step 3: Answer: 6.

Example 3

Question: Find the mean of 2, 4, 6.

Step 1: Add: 2 + 4 + 6 = 12.

Step 2: Divide by 3.

Step 3: Answer: 4.

Example 4

Question: Find the range of 2, 5, 7, 10.

Step 1: Highest value = 10.

Step 2: Lowest value = 2.

Step 3: Range = 8.

Example 5

Question: Why do we use tables in statistics?

Step 1: Tables arrange data neatly.

Step 2: They make comparison easy.

Step 3: Answer: to present data clearly.

Example 6

Question: Name one method of collecting data.

Step 1: Recall common methods.

Step 2: Questionnaire is one method.

Step 3: Answer: questionnaire.

Quick Brain Tests

1. Most frequent value?

Mode.

2. Middle value?

Median.

3. Average value?

Mean.

4. Highest minus lowest?

Range.

5. Data collection tool?

Questionnaire.

External Resources

CBT Practice Test

30 questions | Timed quiz | Corrections appear after submission.

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