SSS 1 Revision and Examination for Further Mathematics – Second Term

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:

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

1. What is the range of the function f(x) = 2x + 3 for x = 1, 2, and 3?
2. If f(x) = 5x – 2, find f(3).
3. What is the domain of the function f(x) = x^2 + 1?
4. Solve for x if f(x) = 4x + 6 and f(x) = 18.
5. Identify the slope and y-intercept of the linear function f(x) = 2x + 4.
6. Find the value of f(5) if f(x) = x^2 – 3x.
7. What does it mean for a relation to be a function?
8. Graph the function f(x) = x + 2.
9. What is the value of f(0) for f(x) = 3x – 1?
10. 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:

1. Write the first five terms of the arithmetic sequence where the first term is 3 and the common difference is 4.
2. Find the nth term of the geometric sequence 2, 6, 18, 54, …
3. What is the sum of the first 10 terms of the arithmetic sequence 5, 8, 11, …?
4. Write the general term for the geometric sequence 5, 10, 20, 40, …
5. Find the sum of the first 5 terms of the series 3 + 6 + 9 + …
6. What is the common difference of the arithmetic sequence 7, 10, 13, 16, …?
7. Calculate the 10th term of the geometric sequence 3, 9, 27, 81, …
8. What is the sum of the first 6 terms in the sequence 2, 4, 8, 16, …?
9. Find the general form for the nth term of the sequence 1, 4, 7, 10, …
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)Sn​=2n​(a1​+an​), where a1a_1a1​ is the first term, ana_nan​ 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}Sn​=1−ra1​(1−rn)​ for r≠1r \neq 1r=1, where a1a_1a1​ is the first term, $r$ is the common ratio, and $n$ is the number of terms.

Example Questions:

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

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

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

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 ($\sin$), Cosine ($\cos$), and Tangent ($\tan$).
• 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:

1. Find $\sin \theta$ if the opposite side is 3 and the hypotenuse is 5.
2. Calculate $\cos \theta$ in a right-angled triangle where the adjacent side is 4 and the hypotenuse is 5.
3. What is the value of $\tan \theta$ if the opposite side is 6 and the adjacent side is 8?
4. Solve for the angle $\theta$ if $\sin \theta =0.6$.
5. Find the length of the hypotenuse if $\cos \theta =0.8$ and the adjacent side is 6.
6. Calculate $\tan \theta$ if the opposite side is 7 and the adjacent side is 24.
7. What is the relationship between sine, cosine, and tangent?
8. How do you use trigonometry to solve for unknown sides of a triangle?
9. Find $\sin \theta$ if the adjacent side is 5 and the hypotenuse is 13.
10. 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:

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

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