Solving Linear Inequalities
Mr-Mathematics.com
by mrmath_admin
1w ago
In this GCSE mathematics revision lesson on solving linear inequalities, students develop a variety of skills. The first focuses on “Fluency” by having students practice solving straightforward inequalities to find ranges for a variable. The Mastery questions challenge students to solve compound inequalities and express solutions in set notation. The Problem Solving question, applies inequalities to real-world problems, requiring students to translate a word problem into mathematical inequalities and use them to find a range of possible areas for a geometric figure. Scheme of Work Link Equa ..read more
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Circle Theorems GCSE Mathematics
Mr-Mathematics.com
by mrmath_admin
2w ago
Students learning circle theorems for GCSE Mathematics often encounter these misconceptions: Misapplying theorems without recognising specific conditions required for each. Confusing the alternate segment theorem, applying it incorrectly due to misunderstanding conditions. Incorrectly assuming angle properties in circles without the necessary chords or tangents. Mixing up relationships between tangents and secants, leading to errors in angle size and segment length assumptions. Overlooking the importance of cyclic quadrilaterals and misinterpreting their angle relationships. Clarifying these ..read more
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Planes of Symmetry in 3D Shapes
Mr-Mathematics.com
by mrmath_admin
2w ago
This lesson for Key Stage 3 or foundation GCSE students delves into the symmetry of 3D shapes. Using isometric paper, it starts with simple shapes and progresses to more complex ones, helping students grasp symmetry concepts. The lesson includes a worksheet for further practice. Success Criteria: Visualize and identify symmetry planes in 3D shapes. Accurately sketch symmetry planes using isometric paper. Discuss shared properties of solids based on reflective symmetry. Key Questions: “How many symmetry planes are in this shape?” “What does the number of symmetry planes say abou ..read more
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Further Pure 1: Summation of Series
Mr-Mathematics.com
by mrmath_admin
2w ago
Tackling sums of series in Year 12 Further Maths can be tough. In this blog I take you through four worked examples ranging from deriving the linear summation formula to applying it to solve complex summations. Introducing the Sum of Natural Numbers View on YouTube Skills: Recognising and applying the formula for the sum of the first n natural numbers. Understanding sigma notation. Advice: Make sure to illustrate the derivation of the formula for the sum of the first n natural numbers to deepen understanding. Visual aids, such as a number line or pairing numbers in a sequence, can b ..read more
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GCSE Trigonometry Skills & SOH CAH TOA Techniques
Mr-Mathematics.com
by mrmath_admin
2w ago
GCSE trigonometry skills are essential for students to solve the three types of right-angled triangle problems presented, common in GCSE Mathematics and crucial for those aiming for grades 4 or 5. Here’s a summary of the key skills required for each problem, along with tailored advice for students and teachers, and probing questions to assess comprehension. GCSE Trigonometry Skills & SOH CAH TOA Techniques View on YouTube Skill: Understanding and applying the trigonometric ratios (Sine, Cosine, and Tangent) to find angles. Advice: Remember that for any right-angled triangle, SOH-CAH-TO ..read more
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Regions in the Complex Plane
Mr-Mathematics.com
by mrmath_admin
3w ago
When finding regions in the complex plane common misconceptions include confusing a number’s modulus with its components and misinterpreting loci inequalities, which can result in inaccurate shading. Recognizing geometric implications, like modulus inequalities forming circles, is key. The tutorials below are designed to help students in identify complex regions within an Argand diagram, complete with summaries and teacher-crafted questions to solidify understanding. Regions in the Complex Plane View on YouTube Content Criteria: Understanding of the geometric representation of complex n ..read more
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Grade 5 Revision Lesson 1
Mr-Mathematics.com
by mrmath_admin
3w ago
Students are challenged to solve a range of Grade 5 non-calculator problems involving: Standard form Solving quadratic equations graphically Probability trees Simultaneous equations Composite area involving circles Expanding quadratics expressions Angles in polygons Column vectors The post Grade 5 Revision Lesson 1 appeared first on Mr-Mathematics.com ..read more
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GCSE Maths Equation Solving Strategies
Mr-Mathematics.com
by mrmath_admin
3w ago
For students aiming for grades 4 or 5, the ability to translate real-world problems into mathematical equations is essential. Teachers should emphasise the process of understanding the problem, clearly defining variables, and then constructing and solving equations. Practice with a variety of contexts can build confidence and versatility. Additionally, teachers can use probing questions to ensure students are not only able to find the solution but also understand the underlying mathematical concepts. GCSE Maths Equation Solving Strategies These four examples show how to setup and solve linear ..read more
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Problem-Solving with Loci in the Complex Plane
Mr-Mathematics.com
by mrmath_admin
3w ago
In my experience, Year 12 Further Mathematicians can struggle with loci problems in the complex plane, challenged by the array of concepts they need to apply. I advocate a three-part breakdown: identify the locus, sketch it accurately, and then leverage geometric properties. Below, are four exemplar problems that encapsulate the key skills typically examined. Worked solution to Maximum Argument Value Question on Maximum Argument Value Key Skills Understanding how to interpret and solve equations involving the modulus of complex numbers. Knowledge of how to find the argument of a complex nu ..read more
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Complex Numbers: Modulus – Argument Form
Mr-Mathematics.com
by mrmath_admin
1M ago
In these videos I show you how to derive the modulus – argument of complex numbers from an Argand Diagram. We progress from plotting complex numbers on an Argand Diagram to converting between the x + iy and modulus – argument. Future lessons go on to performing calculations with complex numbers in modulus-argument form and proving De’ Moivres theorem. Part 1 – Deriving the Modulus-Argument form of complex numbers. Deriving the Modulus-Argument form of complex numbers. Part 2 – Writing complex numbers in Modulus – Argument form. Writing complex numbers in Modulus – Argument form Part 3 – Conv ..read more
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