CASIO FX 991ES PLUS: Calculator skills - factorising quadratics

HEGARTYMATHS
16 Sept 201305:54
EducationalLearning
32 Likes 10 Comments

TLDRIn this Hegarty Maths video, Mr. Haggerty demonstrates how to use a calculator to verify the factorization of quadratic expressions, a valuable skill for checking work in exams. He walks through the process using different examples, explaining how to set the calculator to 'quadratic' mode and input coefficients to find solutions. This method ensures accuracy, especially for more complex expressions, and encourages students to double-check their factorization for potential mistakes.

Takeaways
  • 🔢 The video teaches calculator skills for GCSE and A-level maths.
  • 🧮 The focus is on checking the factorization of quadratic expressions using a calculator.
  • ✅ Factorizing involves finding two numbers that multiply to a given product and add up to a given sum.
  • 📐 The example given is factorizing x^2 + 7x + 12 into (x + 3)(x + 4).
  • 🔍 Use the calculator in equation mode to verify the factorization.
  • 🔢 For 2x^2 - 7x + 3, the factorization is verified as (2x - 1)(x - 3).
  • 📝 The video also covers factorizing more complex expressions, like 13x^2 - 6x - 99.
  • 🔧 The calculator helps confirm that 13x^2 - 6x - 99 factorizes to (x - 3)(13x + 33).
  • 📊 Checking factorization with a calculator involves solving for x and using these solutions to form factors.
  • 🔗 The process emphasizes that while calculators help check work, understanding manual factorization is crucial.
Q & A

  • What is the main purpose of the video?

    -The main purpose of the video is to demonstrate how to use a calculator to check the factorization of quadratic expressions, particularly for students preparing for GCSE and A-level maths exams.

  • What is a quadratic expression?

    -A quadratic expression is a polynomial of degree 2, which can be generally written in the form ax² + bx + c, where a, b, and c are constants.

  • Why is it important to check factorization in an exam?

    -Checking factorization in an exam is important to ensure accuracy and avoid mistakes, as incorrect factorization could lead to wrong solutions or deductions in marks.

  • What are the two numbers that multiply to 12 and add up to 7?

    -The two numbers that multiply to 12 and add up to 7 are 3 and 4.

  • How can you factorize the expression x² + 7x + 12?

    -The expression x² + 7x + 12 can be factorized as (x + 3)(x + 4), as these are the numbers that multiply to 12 and add up to 7.

  • What mode should you set on the calculator to solve quadratic equations?

    -You should set the calculator to 'equation' mode, specifically 'quadratic' which is usually number 3 on the calculator.

  • What are the values of a, b, and c for the quadratic expression 2x² + 7x + 3?

    -For the quadratic expression 2x² + 7x + 3, a is equal to 2, b is equal to 7, and c is equal to 3.

  • How does the calculator provide solutions for a quadratic equation?

    -The calculator provides solutions for a quadratic equation by giving the values of x that satisfy the equation, which are the roots of the equation.

  • What are the solutions for the quadratic equation 2x² - 7x + 3?

    -The solutions for the quadratic equation 2x² - 7x + 3 are x = 3 and x = 1/2, as provided by the calculator.

  • How can you verify the factorization of a quadratic expression using the calculator?

    -You can verify the factorization by inputting the coefficients a, b, and c into the calculator's quadratic mode, and then checking if the solutions provided match the factors you have.

  • What is an example of a more complicated factorization problem presented in the video?

    -An example of a more complicated factorization problem is factorizing the expression 13x² - 6x - 99, which factors to (x - 3)(13x + 33).

  • What is the final example given in the video for the viewers to try on their own?

    -The final example given in the video is to factorize the expression 2x² - x - 3, which factors to (x - 1)(2x + 3).

Outlines
00:00
📚 Learning to Check Quadratic Factorization with a Calculator

In this educational video, Mr. Haggerty from Hegarty Maths introduces viewers to the process of using a calculator to verify the factorization of quadratic expressions, particularly for GCSE and A-level maths. The video demonstrates how to input a quadratic equation into the calculator's equation mode and how to interpret the solutions provided by the calculator to confirm the correct factorization. The example given involves factorizing an expression where the numbers multiply to 12 and add up to 7, resulting in the factorization of \( x + 3 \) and \( x + 4 \). The video also covers a more complex example, guiding viewers through the calculator's steps to verify the factorization of a quadratic expression with the correct solutions.

05:05
🔍 Advanced Quadratic Factorization Verification

Continuing the tutorial, Mr. Haggerty presents a more advanced example of quadratic factorization, encouraging viewers to think about the numbers that can be used to factorize the expression. The video then shows how to use the calculator to check the factorization by entering the coefficients of the quadratic equation and verifying the solutions. The example provided involves a quadratic equation with coefficients that lead to solutions of \( x = 3 \) and \( x = -\frac{33}{13} \). The video explains how to subtract these values from the original equation to derive the correct factors, demonstrating the practical application of the calculator in verifying factorization in an exam setting.

Mindmap
Keywords
💡Calculator
A calculator is an electronic device used to perform arithmetic operations and more complex calculations. In the context of the video, the calculator is used as a tool to verify the factorization of quadratic expressions, ensuring accuracy in mathematical problem-solving, particularly for students preparing for exams like GCSE and A-level.
💡Factorizing
Factorizing, or factorization, is the process of breaking down a complex expression into a product of simpler, more manageable expressions. In the video, factorizing is the main focus, specifically for quadratic expressions, which are second-degree polynomials. The script provides examples of how to factorize expressions correctly.
💡Quadratic Expressions
Quadratic expressions are algebraic expressions of the second degree, typically in the form of ax^2 + bx + c, where a, b, and c are constants. The video script discusses how to factorize these expressions using a calculator to check for errors, which is crucial for students learning algebra.
💡GCSE
GCSE stands for General Certificate of Secondary Education, which is an important qualification in the UK for students in their final years of secondary school. The video is aimed at helping students prepare for their GCSE exams by demonstrating how to use a calculator to check the factorization of quadratic expressions.
💡A-level
A-levels, or Advanced Levels, are subject-based qualifications in the UK that are typically taken by students after completing their GCSEs. The video mentions A-level as one of the educational levels for which the calculator skills demonstrated are relevant.
💡Mode Equation
In the context of the video, 'mode equation' refers to a setting or function on a calculator that allows the user to solve equations. The script explains how to switch to this mode to input the coefficients of a quadratic equation for verification purposes.
💡Coefficients
Coefficients are numerical factors in algebraic expressions that multiply the variables. In the video, the coefficients a, b, and c are used to define a quadratic equation, and the script demonstrates how to input these into a calculator to check the factorization.
💡Solutions
In mathematics, solutions refer to the values of variables that make an equation true. The video script explains how to use a calculator to find the solutions for a quadratic equation, which are then used to verify the factorization.
💡Factor
A factor is a part of a multiplication operation that, when multiplied with other factors, gives the original number or expression. In the script, factors are the expressions obtained after factorizing a quadratic equation, such as 'x + 3' and 'x + 4'.
💡Verification
Verification in this context means checking the correctness of a solution or result. The video script emphasizes the importance of using a calculator to verify the factorization of quadratic expressions to ensure no mistakes are made, especially in an exam setting.
💡Exam
An exam is a formal test or assessment of a student's knowledge and skills. The video is instructional and aims to prepare students for exams by teaching them how to use a calculator to check their factorization work, which is a common task in math exams like GCSE and A-level.
Highlights

Introduction to a video from Hegarty Maths by Mr. Haggerty focusing on calculator skills for GCSE and A-level maths.

Teaching how to use a calculator to check the factorization of quadratic expressions.

Emphasis on checking factorization in exams rather than performing the factorization with the calculator.

Example given: Factorizing the expression that multiplies to 12 and adds up to 7, resulting in (X + 3)(X + 4).

Demonstration of using calculator mode 'equation' to verify the factorization of a quadratic equation.

Explanation of how the calculator shows the solutions for the quadratic equation and how they relate to the factors.

A more complicated case is presented to illustrate the checking process on the calculator.

The process of checking factorization using the calculator for a quadratic equation with coefficients 2, -7, and 3.

The calculator provides solutions X = 3 and X = 1/2, which are then used to verify the factorization.

An example of a common mistake in books is addressed, with a factorization check using the calculator.

The calculator is used to check a factorization with coefficients 13, -6, and -99, leading to the correct factors.

A step-by-step guide on how to use the calculator to check the factorization of a quadratic equation.

Final example provided for the viewer to practice checking factorization on their own.

The final example's correct factorization is revealed, demonstrating the use of the calculator for verification.

The importance of checking answers in exams using the calculator is stressed for accuracy.

Conclusion of the video with a summary of the method for checking quadratic factorization with a calculator.

Transcripts

Browse More Related Video

Factorizing Using Casio 570MS Calculator

CASIO FX 991ES PLUS - Calculator skills - differentiation

How to solve a quadratic equation with Casio fx-991MS edition 2 scientific calculator

Quadratic Formula (Q1.) w/ calculator Casio fx 115 es plus

How to solve differentiation using your calculator(Casio Cs- 991 ES plus)

How to use Calculator for Evaluate Multiple Integrals - Easy Techniques

Rate This

5.0 / 5 (0 votes)

Thanks for rating:

Related Tags
Math EducationQuadratic FactorizationCalculator SkillsGCSE MathA-Level MathMr. HaggertyHegarty MathsSolving EquationsExam TipsCheck AnswersMath Tutorial