BEST MATH TUITION SINGAPORE

Mathematics can seem like a complex and highly abstract subject, but mathematical formulas provide a practical framework that helps students understand questions and arrive at the correct answer. To help your child memorise these formulas, you can support their learning with several encouraging techniques. Going Beyond Rote Memorisation Although memorisation can be helpful, maths memory relies more on your child’s ability to understand the concepts behind formulas and apply them effectively to solve specific problems. Simply memorising a formula will not work, as there is no real comprehension behind the formula’s underlying concepts in relation to solving specific questions. Under exam time pressure, rote memorisation may hinder problem-solving because your child cannot correctly apply the maths formula to find the answer. Panic in such a situation can prevent them from thinking clearly and undermine their confidence in maths. With sufficient practice, your child can gradually store these maths formulas in their long-term memory. This reduces cognitive load on their short-term working memory while they focus on a question, enhancing their ability to quickly solve it by applying the formula’s concepts accurately. Techniques to Memorise Maths Formulas The right approach can make a substantial difference by helping your child memorise maths formulas and apply them in the right situations. Use Visualisation Visual aids and mental imagery, such as graphs, charts, and flashcards, can be quite helpful for memorising maths formulas, as they provide clear details and examples of how a formula works. You can even assign visual cues to a formula’s components to make it easier for your child to remember them. The more unique they are, the more likely they are to recall the entire formula. Real-Life Examples Another aspect of visualisation involves using real-world examples that relate to a maths problem. Using these examples is a great way to help them understand more abstract maths concepts that are difficult to express with visual aids. This way, you can make the formula more approachable and memorable for your child, making it easier to recall and know when to use it. Mnemonics Mnemonics are verbal memory aids that provide a shortcut to remembering maths formulas. Much as visualisation uses imagery to aid memorisation, mnemonics rely on catchy or funny phrases and abbreviations to quickly recall a maths formula. One classic example is recalling PEMDAS, the order of operations (parentheses, exponents, multiplication and division, addition, subtraction). Your child could use the common mnemonic “Please Excuse My Dear Aunt Sally” to make it easier to recall this concept. Break Down into Chunks Complex maths questions can be challenging to understand all at once, so your child should learn to break them down into manageable chunks. This process involves breaking down a math question or complex equation into multiple components (or chunks) that are easier to understand. Chunking reduces your child’s cognitive load and improves their confidence when answering complex questions. Memory Palaces A memory palace uses recognisable locations to form a mental map that your child can use to memorise maths formulas. Your child would associate certain formulas with specific places in this memory palace, where each formula may be visualised as a prominent part of a room within the palace. They only need to visualise themselves exploring the memory palace’s rooms to recall the specific mathematical formulas they memorised. This vivid mental image they create facilitates faster recall, helping them solve maths questions with little difficulty. Repetition and Consistency Practice makes perfect, and your child needs plenty of it to allow them to memorise each maths formula that they are learning or have learned. Regular exercise with worksheets, past-year papers, and quizzes can help cement their understanding of how to use the relevant formulas for the correct questions. You can mix things up with fun, engaging activities that test their knowledge without making it feel like another classroom lesson. A balance of fun and focus can keep your child learning at all times. Study Groups Part of that consistency can come from study groups with your child’s peers, including classmates, each of whom brings different degrees of mathematical understanding to the table. As such, this allows students to learn from one another, deepening their understanding of maths formulas. This collaborative effort, in turn, can greatly boost your child’s self-esteem and counter maths anxiety. How Parents Can Support Their Child’s Maths Memory As parents, there are various ways you can support your child’s maths memory through positive reinforcement and other methods that maintain their curiosity and drive to learn new maths concepts. Avoid Cramming Repetition and consistency only work if they are set on a regular schedule, not back-to-back without breaks. This means that all work and no play makes it harder for your child to stay focused, and they may end up memorising what they learned without understanding the finer points behind each maths formula. Let them have some time to rest and relax before they get back to their lessons. Offer Encouragement Positive encouragement is another way to help your child, as it makes them feel that their learning efforts are paying off. Even if they make mistakes, offer them a shoulder they can lean on and tell them it is okay to fail occasionally. The important thing is to take the time to learn where they went wrong and pick themselves up to improve. Do what you can to help them up and keep their learning journey going. Minimise Distractions Setting boundaries and creating a conducive study space can help your child’s concentration and retention of maths formulas. It is advisable to keep gadgets and toys out of sight to avoid distracting them while they are studying. Matrix Math provides personalised maths tuition to help students strengthen their mathematical fundamentals across various topics, including memorising and understanding key concepts. Contact us today to learn more about our teaching approach! Read Also: Mastering Problem-Solving with Heuristic Maths in Singapore How Maths Tuition Helps Weak Students Improve Faster How to Help Your Child Develop Early Math Skills Effective Tips To Prepare

The circle is a core part of teaching students geometry, as understanding its many properties is essential for many real-life applications, including design and engineering. Basic Properties of a Circle A circle is a closed two-dimensional (2D) shape where each point of its boundary has the same fixed distance from the centre. The word comes from the Latin term “circulus”, which translates to “small ring”. The shape of a circle is created from a connected series of points set at a fixed distance from a fixed central point. Core Circle Terminologies The graphic below helpfully illustrates a circle’s radius and diameter, as well as other core components that make up a circle. The distance from the circle’s boundary to the centre is known as the radius (r). Meanwhile, the longest distance between any two points on the circle, passing through the centre, is known as the diameter (d). When two points in a circle are connected by a line, but do not cross the centre, it is known as a chord. Conversely, if two points along the circumference are connected, it is an arc. Combining these fundamental aspects allows us to identify other parts of a circle. For one, the area enclosed between two radii (the plural of radius) and an arc is known as a sector. Meanwhile, a segment is the area enclosed by a chord and an arc. Lastly, tangents are lines that touch a single point of a circle’s circumference, while secants are lines that cut through the circle at two points. Essential Circle Formulae Students will need to learn these formulae to calculate various aspects of a circle. Here is a guide to find the area of a circle and other related shapes. Full Circles Diameter = 2 × r Circumference (Perimeter) = π × d Alternatively: Circumference (Perimeter) = 2 × π × r Area = π × r2 Note that π (pi) equals 3.14, “r” is the circle’s radius, and “d” is the diameter. Semi-Circles Area = 1⁄2 × π × r2 Perimeter = 1⁄2 × π × d + d Quadrants Area = 1 ⁄4 × π × r2 Perimeter = 1 ⁄4 × π × d + r + r Area of a Sector To find the sector’s area: A = θ ⁄ 360 × π × r 2 θ represents the angle of the arc, measured in radians. Boomerang A boomerang is represented by the shaded part in the following graphic: Area = Square – Quadrant = (r × r) – ( 1⁄4 × π × r2 ) Perimeter = 1⁄4 × π × d + r + r Arc Length For the arc length: L = θ ⁄ 360 × 2 π r Half Petals Area = Quadrant – Triangle = ( 1⁄4 × π × r2 ) – ( 1⁄2 × r2 ) Perimeter = 1⁄4 × π × d + Side of square Full Petals Area = Half Petal × 2 Perimeter = 1⁄4 × π × d × 2 Key Circle Theorems and Properties A circle is a closed shape with a single curved face. It does not “open up” or break at any point, and is a continuous line that curves into this circular shape. There are other theorems and properties that students should also note, as these can be useful in solving maths questions related to circles. Congruent Circles Two circles are only considered congruent (identical in shape and size) if they have the same radius. In the graphic below, if r1 = r2, then both circles are congruent. Triangle Hypotenuse as Diameter If a triangle’s hypotenuse is drawn as the diameter of a circle, then the angle opposite to the diameter is always 90°. Equal Chords If two chords are of equal length, they will always be at the same distance (equidistant) from the circle’s centre. Thus, if AB = CD, then EX = FX. Bisecting Chords Additionally, using the figure above, if lines EX or FX are perpendicular (intersecting to form right angles) to AB or CD, respectively, then each line will bisect its respective chord into two equal parts. Tangent Symmetry If two tangents start from the same external point and connect from T to the circle’s centre, X, then both tangents are of equal length. Moreover, the angle between a tangent and a circle’s radius is always a right angle. Lastly, if a line joins an external point (T) from or to the circle’s centre (X), it bisects the angle between the tangents. Therefore, TX bisects ∠ATB and ∠a = ∠b. Speaking of tangents, if two tangents extend towards each end of the circle’s diameter, both tangents are parallel to one another. Alternate Segments Theorem Note that, in the figure above, TU is a tangent, and AB is a chord. The angle formed between the tangent and the chord in one segment (for example, ∠TAC) is equal to the measure of the angle opposite in the alternate segment (in this case, ∠ABC). Angle at the Centre Theorem The angle at the centre is twice the angle at the circumference when subtended by the same arc. In the above example, ∠BXC = ∠BAC x 2. Segments and Angles Angles of the same segment formed from one chord are equal. Meanwhile, angles in opposite segments add up to 180°. Using the example below: ∠w + ∠x = 180° ∠y + ∠z = 180° This method is also known as the cyclic quadrilateral theorem. Matrix Math provides personalised maths tuition to help secondary students strengthen their fundamentals across various topics, including circles and geometry. Contact us today to learn more about our teaching approach! Read Also: Mastering Problem-Solving with Heuristic Maths in Singapore Does O Level Mathematics Have a Bell Curve? What Are The Laws of Indices In Maths? Prepare Yourself For O Level Maths Mastering O Level Maths in Singapore: A Guide to Success with Matrix Math Tuition Center Is O-Level Math Tuition Important and Necessary in Singapore?