SSS 1 Revision and Examination for Further Mathematics – Second Term - Edujects: Easy Learning, Confident Teaching, Project Solutions

This article provides a detailed revision of the key topics in the second term Mathematics syllabus for SSS 1 students. Each week covers essential concepts, followed by example questions to help students prepare for exams.

Week 1: Revision

This week focuses on revisiting the foundational topics covered earlier in the term. A solid understanding of these topics is essential before moving to more advanced concepts.

Key Areas:

Basic Arithmetic: Addition, subtraction, multiplication, and division of numbers.
Fractions and Decimals: Simplification of fractions, converting fractions to decimals and vice versa.
Percentages: Calculating percentages, percentage increase or decrease.
Algebraic Expressions: Simplifying and solving basic algebraic equations.

Example Questions:

Simplify 3/4 + 5/8.
Convert 0.75 to a fraction.
Find 20% of 150.
Solve for x: 3x + 5 = 20.
What is 3/5 of 100?
Simplify 5a + 3a.
Convert 25% to a decimal.
Solve for x: x – 7 = 12.
Add 3/5 and 4/10.
Subtract 2/3 from 5/6.

Week 2: Functions

In this week, students will learn about functions, a crucial concept in mathematics. A function relates one set of values to another.

Key Points:

Definition of a Function: A relation where every input has exactly one output.
Domain and Range: Domain refers to the set of all possible inputs, and range is the set of possible outputs.
Function Notation: Using symbols like f(x) to represent a function.
Linear Functions: Functions of the form f(x) = mx + b, where m is the slope and b is the y-intercept.

Example Questions:

What is the range of the function f(x) = 2x + 3 for x = 1, 2, and 3?
If f(x) = 5x – 2, find f(3).
What is the domain of the function f(x) = x^2 + 1?
Solve for x if f(x) = 4x + 6 and f(x) = 18.
Identify the slope and y-intercept of the linear function f(x) = 2x + 4.
Find the value of f(5) if f(x) = x^2 – 3x.
What does it mean for a relation to be a function?
Graph the function f(x) = x + 2.
What is the value of f(0) for f(x) = 3x – 1?
How do you determine the domain and range of a function?

Week 3: Sequence and Series

This week delves into sequences and series, important concepts in understanding patterns in mathematics.

Key Points:

Sequence: A list of numbers arranged in a specific order, such as arithmetic or geometric sequences.
Arithmetic Sequence: A sequence where the difference between consecutive terms is constant.
Geometric Sequence: A sequence where each term is found by multiplying the previous term by a fixed number.
Series: The sum of the terms in a sequence.

Example Questions:

Write the first five terms of the arithmetic sequence where the first term is 3 and the common difference is 4.
Find the nth term of the geometric sequence 2, 6, 18, 54, …
What is the sum of the first 10 terms of the arithmetic sequence 5, 8, 11, …?
Write the general term for the geometric sequence 5, 10, 20, 40, …
Find the sum of the first 5 terms of the series 3 + 6 + 9 + …
What is the common difference of the arithmetic sequence 7, 10, 13, 16, …?
Calculate the 10th term of the geometric sequence 3, 9, 27, 81, …
What is the sum of the first 6 terms in the sequence 2, 4, 8, 16, …?
Find the general form for the nth term of the sequence 1, 4, 7, 10, …
Calculate the sum of the first 5 terms of the arithmetic series 3, 6, 9, 12, …

Week 4: Sequence and Series (Continued)

This week continues with deeper exploration into sequences and series, focusing on more advanced topics such as summation formulas.

Key Points:

Sum of Arithmetic Series: Formula to calculate the sum of an arithmetic series: $Sn=n2(a1+an)S_n = \frac{n}{2} (a_1 + a_n)$ , where $a_1$ is the first term, $a_n$ is the nth term, and $n$ is the number of terms.
Sum of Geometric Series: Formula for sum of geometric series: $Sn=a1(1−rn)1−rS_n = \frac{a_1 (1 – r^n)}{1 – r}$ for $\neq 1$ , where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the number of terms.

Example Questions:

Find the sum of the first 10 terms of the arithmetic sequence 1, 4, 7, 10, …
Calculate the sum of the first 8 terms of the geometric series 2, 6, 18, 54, …
What is the 12th term in the arithmetic sequence 5, 10, 15, 20, …?
Find the sum of the first 5 terms in the series 3, 6, 9, 12, …
Calculate the 8th term in the geometric sequence 1, 3, 9, 27, …
Determine the sum of the first 15 terms of the arithmetic sequence 10, 20, 30, 40, …
Use the formula to find the sum of the first 6 terms of the geometric sequence 5, 15, 45, …
Find the sum of the first 7 terms of the sequence 2, 4, 8, 16, …
What is the common ratio of the geometric sequence 2, 6, 18, 54, …?
Calculate the sum of the first 4 terms of the series 4, 8, 12, 16, …

Week 5: Linear Inequalities

This week covers linear inequalities, which involve inequalities rather than equations.

Key Points:

Linear Inequality: An inequality that involves a linear function. For example, $2 x + 3 < 7$ .
Graphing Inequalities: Understanding how to graph the solution of linear inequalities on a number line.
Solving Linear Inequalities: Methods for solving inequalities and finding the solution set.

Example Questions:

Solve the inequality $2 x - 3 > 5$ .
Graph the solution of $\leq 10$ on a number line.
Solve $\geq 2x + 7$ .
Write the solution set for $x - 2 < 4$ .
Solve $4 x - 1 > 3 x + 2$ .
Graph the solution to $\geq 2$ .
Solve the inequality $5 x + 3 < 18$ .
What is the solution to $\leq 15$ ?
Solve for x in $6 x - 5 > 10$ .
Graph $\geq 5$ on a number line.

Week 6: Linear Inequalities (Continued)

This week continues with solving more complex linear inequalities.

Key Points:

Compound Inequalities: Inequalities involving two or more simple inequalities combined, like $x - 2 > 4$ and $x + 3 < 10$ .
Interval Notation: Using intervals to express the solution of inequalities.

Example Questions:

Solve the compound inequality $3 x - 5 > 4$ and $\leq 7$ .
Write the solution set for $x > 2$ and $\leq 5$ using interval notation.
Solve for x in $\geq 4$ and $x + 1 < 6$ .
Solve the inequality $x - 4 > 3$ or $x + 2 < 5$ .
Graph the solution of $\leq 8$ and $x - 1 > 3$ on a number line.
Solve $\leq 3$ and $2 x - 4 > 6$ .
Express the solution of $\leq x < 5$ in interval notation.
Solve $x - 2 > 6$ or $\leq 10$ .
Graph $\geq 5$ and $x - 4 < 1$ .
Solve for x in $x + 3 > 8$ and $\leq 6$ .

Week 7: Trigonometry Ratios

In this week, students will be introduced to trigonometric ratios and their applications in right-angled triangles.

Key Points:

Trigonometric Ratios: Sine ( $sin⁡\sin$ ), Cosine ( $cos⁡\cos$ ), and Tangent ( $tan⁡\tan$ ).
Right-Angled Triangle: Trigonometric ratios are used to find the lengths of sides or angles in a right-angled triangle.
Mnemonic for Trigonometric Ratios: SOH-CAH-TOA.

Example Questions:

Find $sin⁡θ\sin \theta$ if the opposite side is 3 and the hypotenuse is 5.
Calculate $cos⁡θ\cos \theta$ in a right-angled triangle where the adjacent side is 4 and the hypotenuse is 5.
What is the value of $tan⁡θ\tan \theta$ if the opposite side is 6 and the adjacent side is 8?
Solve for the angle $θ\theta$ if $sin⁡θ=0.6\sin \theta = 0.6$ .
Find the length of the hypotenuse if $cos⁡θ=0.8\cos \theta = 0.8$ and the adjacent side is 6.
Calculate $tan⁡θ\tan \theta$ if the opposite side is 7 and the adjacent side is 24.
What is the relationship between sine, cosine, and tangent?
How do you use trigonometry to solve for unknown sides of a triangle?
Find $sin⁡θ\sin \theta$ if the adjacent side is 5 and the hypotenuse is 13.
Solve for the missing side using trigonometric ratios.

Week 8: Revision

This week focuses on revising all the topics covered in the term. It is important to review all concepts, especially the challenging ones.

Example Questions:

What is the difference between a sequence and a series?
Solve the inequality $4 x + 1 < 9$ .
Calculate the sum of the first 5 terms of an arithmetic series.
Graph the inequality $x + 2 > 3$ .
Find the value of $tan⁡θ\tan \theta$ in a right-angled triangle.

Week 9: Examination

This week marks the final revision and examination. Students will be tested on their understanding of all topics covered in the second term.

Example Questions:

Solve for x: $5 x - 2 = 18$ .
Calculate the sum of the first 10 terms of the sequence 1, 4, 7, 10, …
Find the value of $sin⁡θ\sin \theta$ in a right-angled triangle where the opposite side is 4 and the hypotenuse is 5.
Solve the compound inequality $2 x - 3 > 5$ and $x + 2 < 6$ .
Find the sum of the first 6 terms in the geometric series 2, 6, 18, 54, …