BEST MATH TUITION SINGAPORE

Number patterns are an integral part of our lives. As students strengthen their mathematical foundations, their pattern recognition abilities will help them understand how number sequences can form. From simple linear number series to the complex Fibonacci sequence, number patterns play a key role in solidifying a student’s mathematical foundations, especially when tackling more advanced concepts, such as geometry and probability. What are Number Patterns? Consider the following number sequence: 1    5    9    13    17    21 Each number in this sequence is a term, with the first term (T1) being the number 1, and the fifth term (T5) being the number 17. This sequence follows a pattern in which students add 4 to the current term to obtain the next one. For example, the second term (T2) 5 is derived by adding 4 to the first term (T1). The general term of this linear number sequence is represented as Tn. To find a specific term in this sequence, as well as other similar sequences, students may use this formula: Tn = a + (n – 1)d In this formula, “n” represents the ordinal numerical value of a term in the sequence, while “a” corresponds to the first term of the sequence, and “d” is the common difference between two terms. Students can use this formula to find any term in a sequence without tediously listing all previous terms. Using the earlier example, if we want to find the 100th term in the sequence: 1    5    9    13    17    21… n = 100, a = 1, d = 5 – 1= 4 T100 = 1 + (100 – 1)(4) = 1 +(99)(4) = 397 How to Find Number Pattern Rules Number pattern formulae may have different rules depending on the type of sequence. Pay close attention to how the sequence progresses and the difference between consecutive terms to help determine the appropriate rule to use. Square Numbers Simply put, a square number sequence is made up of a series of numbers that are each multiplied by themselves. The following sequence is a series of square numbers: 1, 4, 9, 16, 25… 12, 22, 32, 42, 52… The formula for square numbers is straightforward: Tn = n2  Determining a Number Pattern Formula Pattern recognition is a key concept that helps students identify the formula for the number pattern they encounter. Obtaining the right formula starts with these steps: Identify the Pattern First, carefully study the number sequence provided and determine the underlying pattern as students move from one term to the next. Consider this example sequence: 2, 7, 12, 17, 22… In this case, each term increases by a constant amount of five. Confirm the Sequence Various types of sequences follow different patterns that determine their terms. Students should always double-check that the sequence matches the identified number pattern. In our previous example, it is an arithmetic sequence because it increases by a constant of 5. 2 (+5) 7 (+5) 12 (+5) 17 (+5) 22 (+5) … Apply the Formula Students will need to use a combination of arithmetic operations, powers of numbers, and algebra to correctly apply the formula. They can then generalise the number pattern and apply it to every term in the sequence, including terms not provided. Using the above example, the first term (T1) is two. We then progressively add the constant 5 to each term to find the subsequent terms. If we wish to determine the nth term (Tn), we will use two in the formula and add (n – 1) multiplied by the common difference between any two consecutive terms. Tn = 2 + (n – 1)5 Tn = 5n – 3 Verify the Answer Now that the formula is set, verify your answer by checking whether it correctly predicts the terms in the sequence. For example, by using the second term (T2): T2= 2 + (2 – 1)5 = 2 + 5 = 7 It is always good practice to triple-check the formula to ensure students get the correct answer. Number Pattern Examples Example 1 Consider the following figures of circles and squares. It helps to illustrate the sequence using a table. Figure No. of circles No. of squares 1 4 1 2 6 2 3 8 3 Note that the number of circles increases by 2 for each subsequent figure, while the number of squares increases by 1. Section A If you need to determine which figure has 38 circles, you can start by subtracting 4 from 38, as the first figure begins with 4 circles: 38 – 4 = 34 As the number of circles increases by 2 for each subsequent figure, you will then divide 34 by 2 to determine the number of intervals to reach the figure with 38 circles: 34 ÷ 2 = 17 To find the figure, add 1 to the above sum to account for starting from the first figure. 17 + 1 = Figure 18 Section B If you are asked to find the number of circles in Figure 100, you can start by determining how many squares there are in Figure 100. Doing so is relatively straightforward, as the table shows that the number of squares corresponds to the figure number. As such, Figure 1 has 1 square, Figure 2 has 2 squares, and so forth. Figure 200 = 200 squares Number of intervals to Fig. 200 = 200 – 1 = 199 From there, you can work your way backwards from Section A’s methodology. 199 × 2 = 398 398 + 4 = 402 Thus, there are 402 circles in Figure 200. Example 2 Consider the following rows of circles: Note the number sequence highlighted by the red circles. It progresses to 1, then 4, and subsequently 9 and 16. This sequence would form a square number pattern. 1, 4, 9, 16 12, 22, 32, 42 You will notice that the largest number for each row coincides with the base value of the square.

A widespread topic of discussion surrounding O Level Mathematics is whether a bell curve determines the final grade. But is this actually true, or is there more to the grading system than what the majority think? What is the Bell Curve? Bell curve grading assigns grades relative to the performance of an entire cohort, based on a normal distribution with a predetermined average. It is named after the bell-shaped distribution of grades. The grading system aims to adjust for inconsistencies and accommodate different grading styles among teachers, ensuring the exam reflects student grades based on their relative achievement. While it helps to promote healthy competition among students, it may be considered unfair when students’ grades are lowered to match predetermined bell curve calculations. Various approaches aim to ensure a fairer grading scheme that still accounts for the multitude of learning capabilities among students, and the Singapore Examinations and Assessment Board (SEAB) continually refines examination standards each year. Why Does the Bell Curve Persist? The bell curve is a frequent point of discussion during every examination cycle. In 2023, SEAB clarified that all national examinations, including the O Levels, are not graded using a bell curve. Instead, they follow a “standards-referenced” approach in assessing a “candidate’s level of mastery in a subject”. However, it is common for test scores to follow a bell curve distribution, as it reflects the varied levels of understanding among students. SEAB’s clarification indicates that the national grading format does not “force fit” students to a preset bell curve, as each examination is carefully designed to “syllabus objectives and learning outcomes” that cater to “students of different abilities”. The bell curve is an incidental occurrence that merely reflects the natural variation of understanding across subjects. Bell Curves and Grade Moderation Many educational institutions use the bell curve as a moderation tool to maintain fairness in grading. Grades are assigned based on a student’s level of mastery in a subject, ranging from A1 (highest) to F9 (lowest). If more candidates demonstrate higher-quality work and a stronger understanding each year, a higher percentage of them will receive better grades. Grade moderation helps to protect students from grade deflation or inflation. Rather than comparing a student’s performance to their peers, grades are aligned with the yearly syllabus to reflect how well each student meets the set standards. This ensures fairness and consistency when grading student performance. In the context of O Level Mathematics, it reflects the student’s mathematical foundations and how well they can apply them to solve various questions. What Students Can Do About the Bell Curve An important thing to note is that the bell curve should not be seen as a barrier to scoring well. While it does increase competitiveness among students, it can also easily drain a student’s motivation to do their best in any examination, including the mathematics paper. This can be detrimental to a student’s overall performance and even self-esteem, especially when they need more revision and personalised guidance to overcome their worries and doubts. As such, an effective way for students to overcome their fear is by collaborating with their peers. While healthy competition is good, too much of it can be discouraging, making it more important to find ways to work and learn from one another. Seeking guidance through tuition classes can also be beneficial in supporting their understanding. Study Groups Study groups are an excellent and engaging way for students to learn from one another, with opportunities to share insights on various mathematics concepts, questions, and formulas.  Peers may understand certain mathematical concepts and questions more clearly, providing guidance that is concise and easily understood. This also fosters a spirit of collaboration that can greatly motivate each member of the study group, giving everyone a boost of confidence by celebrating their successes, no matter how small. Tuition Classes Tuition sessions are led by tutors who take a more personalised approach to teaching mathematical concepts and providing helpful revision. Tutors can take the time to adjust their teaching style based on each student’s individual needs, allowing them to grasp concepts more easily. Whether through one-on-one sessions or carefully curated teaching plans, tuition classes can strengthen a student’s mathematical foundation, ensuring a clearer understanding of the subject. For students preparing for the O Level Mathematics papers, Matrix Math offers personalised classes that give students a helpful advantage to organise and solidify their foundations. Contact us today to learn more about how we can empower your child to do their very best! Read Also: Is O-Level Math Tuition Important and Necessary in Singapore? Mastering O Level Maths in Singapore: A Guide to Success with Matrix Math Tuition Center What Are The Laws of Indices In Maths? Prepare Yourself For O Level Maths What Does O-Level Grading Mean To Students? Understanding And Managing Homework Battles