10 minutes quiz
•Download as DOCX, PDF•
0 likes•355 views
The document contains a 10 minute quiz on quadratic equations with 3 questions. The first question asks to find the value of k given that x=4 is a root of the equation 2x^2 - kx - 12 = 0. The second asks to find the range of values for p given that the equation x^2 - 5x + p = 0 has two different roots. The third asks to find the range of values for q given that the equation 3x^2 - 6x + 4q = 0 has no roots.
Report
Share
Report
Share
Recommended
Day 8 examples u7w14
This document contains 5 problems involving finding terms in expansions of polynomials. The problems involve finding specific terms that contain a given power of x in expansions of polynomials such as (3x^4 - 1)^9, (-x^3 + 2)^6, (x + 1)^3x, (x + 1)^x, and determining the value of m if one term in the expansion of (2x - m)^7 is -262500x^2y^5.
Adding and subtracting polynomials
This document provides an overview of adding and subtracting polynomials. It defines monomials, binomials, and trinomials as polynomials with 1, 2, or 3 terms respectively. Polynomials can have any number of terms. Terms must have like variables to be combined using addition or subtraction. Examples are provided for determining the type of polynomial, simplifying polynomials by combining like terms, and adding and subtracting polynomials. Practice problems are assigned from the workbook.
Adding Polynomials
This document defines polynomials and describes how to perform operations on them such as addition and subtraction. It provides examples of adding and subtracting monomials and polynomials. Monomials are terms with variables and coefficients, and polynomials are the sum of monomials. Like terms refer to monomials with the same variables and exponents that can be combined. To add polynomials, like terms are lined up and their coefficients are summed. To subtract polynomials, the operation is changed to addition by using the keep-change-change method and then like terms are combined.
C8 8.6
This document contains 6 math word problems asking the reader to divide various polynomial expressions. Each problem is followed by the word "Solution" indicating the answer or worked out steps are to follow. The problems involve dividing expressions such as x^2 - 5x + 6 by x - 3, ax^2 - ay^2 by ax + ay, and (a^2 + 2ab + b^2) - (a^2 + 2ac + c^2) by 2a + b + c.
Add polynomials
The student will be able to:
1. Add and subtract polynomials.
The document provides examples of adding and subtracting polynomials by combining like terms. It includes adding and subtracting polynomials using column form. There are also practice problems for students to find the sum or difference of polynomials.
Add/Subtract polynomials
1. The document provides examples of adding and subtracting polynomials by grouping like terms and using column form.
2. Students are asked to perform operations like adding (9y - 7x + 15a) + (-3y + 8x - 8a) and subtracting (4x^2 - 2xy + 3y^2) - (-3x^2 - xy + 2y^2).
3. The objectives are for students to learn how to add and subtract polynomials.
Addition of polynomials
1. The document demonstrates how to add polynomials by combining like terms.
2. Examples shown include adding polynomials with variables x, y, z, a, b, c, m, n.
3. The correct sums are found by combining coefficients of identical terms and writing the result as a single polynomial.
Addition and subtraction in polynomials
Like terms are terms whose variables and exponents are the same. To add polynomials, group like terms together and add their coefficients. To multiply polynomials, use the FOIL method: First terms, Outer terms, Inner terms, Last terms.
Recommended
Day 8 examples u7w14
This document contains 5 problems involving finding terms in expansions of polynomials. The problems involve finding specific terms that contain a given power of x in expansions of polynomials such as (3x^4 - 1)^9, (-x^3 + 2)^6, (x + 1)^3x, (x + 1)^x, and determining the value of m if one term in the expansion of (2x - m)^7 is -262500x^2y^5.
Adding and subtracting polynomials
This document provides an overview of adding and subtracting polynomials. It defines monomials, binomials, and trinomials as polynomials with 1, 2, or 3 terms respectively. Polynomials can have any number of terms. Terms must have like variables to be combined using addition or subtraction. Examples are provided for determining the type of polynomial, simplifying polynomials by combining like terms, and adding and subtracting polynomials. Practice problems are assigned from the workbook.
Adding Polynomials
This document defines polynomials and describes how to perform operations on them such as addition and subtraction. It provides examples of adding and subtracting monomials and polynomials. Monomials are terms with variables and coefficients, and polynomials are the sum of monomials. Like terms refer to monomials with the same variables and exponents that can be combined. To add polynomials, like terms are lined up and their coefficients are summed. To subtract polynomials, the operation is changed to addition by using the keep-change-change method and then like terms are combined.
C8 8.6
This document contains 6 math word problems asking the reader to divide various polynomial expressions. Each problem is followed by the word "Solution" indicating the answer or worked out steps are to follow. The problems involve dividing expressions such as x^2 - 5x + 6 by x - 3, ax^2 - ay^2 by ax + ay, and (a^2 + 2ab + b^2) - (a^2 + 2ac + c^2) by 2a + b + c.
Add polynomials
The student will be able to:
1. Add and subtract polynomials.
The document provides examples of adding and subtracting polynomials by combining like terms. It includes adding and subtracting polynomials using column form. There are also practice problems for students to find the sum or difference of polynomials.
Add/Subtract polynomials
1. The document provides examples of adding and subtracting polynomials by grouping like terms and using column form.
2. Students are asked to perform operations like adding (9y - 7x + 15a) + (-3y + 8x - 8a) and subtracting (4x^2 - 2xy + 3y^2) - (-3x^2 - xy + 2y^2).
3. The objectives are for students to learn how to add and subtract polynomials.
Addition of polynomials
1. The document demonstrates how to add polynomials by combining like terms.
2. Examples shown include adding polynomials with variables x, y, z, a, b, c, m, n.
3. The correct sums are found by combining coefficients of identical terms and writing the result as a single polynomial.
Addition and subtraction in polynomials
Like terms are terms whose variables and exponents are the same. To add polynomials, group like terms together and add their coefficients. To multiply polynomials, use the FOIL method: First terms, Outer terms, Inner terms, Last terms.
Lesson 6 subtraction of polynomials
The document summarizes how to subtract polynomials. It explains that to subtract polynomials, one changes the sign of all terms in the subtrahend, changes the operation to addition, and then proceeds to add the polynomials by aligning like terms and combining coefficients. It provides examples of subtracting various polynomials, as well as exercises for students to practice subtracting polynomials.
Digital signature
This document discusses generating prime numbers for use in digital signature algorithms. It provides an overview of groups and subgroups, defines finite cyclic groups, and explains that groups of prime order are cyclic. It then describes how the Digital Signature Algorithm works, including choosing safe primes p and q, calculating public parameters, generating signatures, and verifying signatures. It also discusses attacks on the algorithm such as index calculus and Pollard's rho algorithm, and why certain parameters are chosen to strengthen security against these attacks.
Sifat Limit Fungsi Aljabar dan Contoh Soal
The document discusses properties of limits of functions in algebra. It presents 9 properties of limits, including: (1) the limit of a constant k is equal to k; (2) the limit of x as x approaches a is equal to a; (3) the limit of kf(x) is equal to k times the limit of f(x); (4) the limit of the sum of two functions is equal to the sum of their individual limits. It also provides examples of calculating limits using these properties, such as finding the limit of 7x - 4 as x approaches 2.
Module 9 Topic 1 - Adding & Subtracting polynomials
The document provides notes on polynomials, including defining polynomials, describing their terms and degrees, adding and subtracting polynomials, and working through examples of finding degrees, adding, subtracting, and combining like terms of polynomials. The notes include 5 pages on adding and subtracting polynomials and working through examples step-by-step to show the process.
Chinese remainder theorem
A Chinese Remainder Theorem (CRT) is explained intuitively, which helps reader to understand its connection with Abstract Algebra concepts like Groups and Rings.
Here, Author has tried to simplify the concept by explaining sub topic of Groups and Rings which is required by understanding CRT in Abstract Algebra.
Factoring Polynomials ch 5
The document provides steps for factoring trinomial expressions:
1. Look for a common monomial to factor out of both terms.
2. Identify if there are squares present and factor accordingly using the difference of squares formula.
3. To factor trinomials with a leading coefficient of 1, find two numbers whose product is the last term and sum is the coefficient of the middle term.
Day 3 examples
1) The document discusses logarithmic properties and how to solve logarithmic equations and expressions. It provides examples of evaluating logarithmic expressions using log properties and rewriting expressions as single logarithms.
2) Logarithmic properties and theorems covered include the log property that log(MN) = logM + logN, and rewriting expressions with more than one logarithm as a single logarithm.
3) Examples show how to use these properties to evaluate expressions such as log6 8 + log6 9 - log6 2 and rewrite expressions like (x - 2) - 3logx as a single logarithm.
0405 ch 4 day 5
The document discusses logarithmic functions and graphs logarithmic equations, exploring their asymptotes, intercepts, domains, and ranges. It also covers properties of natural logarithms, including that ln(1)=0, ln(e)=1, and that logarithmic and exponential functions are inverses of each other.
10 1 Adding Subtracting Polynomials
This document discusses two methods for adding and subtracting polynomials: horizontal and vertical. For addition, terms with the same variables are combined by adding the coefficients. For subtraction, the signs of the terms in the second polynomial are changed to addition signs before combining like terms. Both horizontal and vertical methods can be used, with horizontal grouping like terms and vertical lining them up before combining coefficients.
Writing quadratic equation
The document discusses quadratic equations and their roots. It provides examples of writing the quadratic equation given the roots. Specifically:
1) It shows how to write the quadratic equation x^2 - 8x + 12 = 0 given the roots are 2 and 6.
2) It shows how to write the quadratic equation 2x^2 - 9x + 4 = 0 given the roots are 4 and 1/2.
3) The key steps are finding the sum and product of the roots, and using those values to write the quadratic equation in the form x^2 - (sum of roots)x + (product of roots) = 0.
Math1000 section1.2
This document discusses exponents and radicals in Math 1000 taught by Stuart Jones. It provides examples of evaluating expressions with exponents such as -24 and (-2)4. It also covers the rules for exponents such as adding when multiplying bases and subtracting when dividing bases. Radicals are also introduced along with examples of simplifying expressions with radicals. Rational exponents are defined as the nth root of x written as x1/n. Throughout, examples are worked through step-by-step to simplify expressions with exponents and radicals.
Solving polynomial equations in factored form
The document provides instructions for solving polynomial equations in factored form. It begins by explaining that to solve an equation like (x – 5)(x + 4) = 0, one should not use the FOIL method but rather split the equation into two separate problems that each equal zero: x – 5 = 0 and x + 4 = 0. It then works through several examples of solving factored polynomial equations by finding the values of x that make each factor equal to zero. The document also covers factoring out the greatest common factor from expressions.
Day 4worked
The document discusses solving various types of log and exponential equations. It includes examples of solving log equations with log 4 log(3 4)x x= − log 2 log( 24 4 )x x= − + and solving natural log equations like ln (3x+5)2 = 4 • ln x = 0.1. It also provides an example of solving an exponential equation like 205.27 2 =+x e 301 =+x e. For homework, it assigns problems from page 331, problems 1-18, 25-28, and 35-38.
11.3
This document provides examples and explanations for multiplying, dividing, and otherwise working with rational expressions. It defines rational expressions as involving polynomials in both the numerator and denominator, with the denominator not equal to 0. Examples are provided for multiplying and dividing rational expressions involving monomials and polynomials. A multi-step word problem is also worked through to find a model for and approximate a baseball player's career batting average as a rational expression involving years played.
Number theoryตัวจริง
1) This document discusses number theory concepts such as divisibility, prime numbers, greatest common divisor, and relatively prime numbers. It provides definitions, theorems, and examples to illustrate these concepts.
2) Key concepts covered include the division algorithm, expressing integers in distributed bases, finding the greatest common divisor using factorization or the Euclidean algorithm, and determining when two numbers are relatively prime.
3) Theorems and proofs are provided to demonstrate properties such as squares of odd numbers being odd, and the remainder when dividing a specific expression by 3. Examples show working through calculations and proofs step-by-step.
4th quarter long test review
This document contains a 10 question review for a 4th quarter long test covering circle equations, polynomial division, factoring, and finding zeros of polynomials. The questions cover finding equations of circles given properties like center and radius, performing polynomial division and finding quotients and remainders, factoring polynomials, and solving polynomials for real zeros.
Number theoryตัวจริง
1) The document discusses number theory concepts such as divisibility, prime numbers, greatest common divisor, and relatively prime numbers.
2) It provides definitions, theorems, proofs, and examples to illustrate these concepts. For instance, it defines the greatest common divisor (GCD) as the largest integer that divides two numbers and proves properties of GCD.
3) The document presents three methods - using common divisors, prime factorizations, and the division algorithm - to calculate the GCD of two numbers.
Yr.12 Transition Workshop 2012- 2013
The question defines two quartic functions, f(x) and g(x), and states they both cross the x-axis at -2. It is asked to determine the values of a and b in the functions. By setting each function equal to 0 and solving the simultaneous equations, the values are found to be a = -3 and b = -28.
Yr.12 Transition Workshop 2012-2013
The question defines two quartic functions, f(x) and g(x), and states they both cross the x-axis at -2. It is asked to determine the values of a and b in the functions. By setting each function equal to 0 and solving the simultaneous equations, the values are found to be a = -3 and b = -28.
F4 02 Quadratic Expressions And
The document contains examples and exercises on quadratic expressions and equations. It includes expanding expressions, factorizing expressions, solving quadratic equations, and word problems involving quadratic equations. The exercises cover a range of skills related to quadratic expressions and equations.
F4 c2 quadequations_new__1_
1. The document provides 10 problems involving quadratic equations. It gives the solutions to finding the range of values for parameters in quadratic equations so that the equations have certain properties like real roots or intersecting lines.
2. The solutions involve setting quadratic equations equal to zero and using the quadratic formula or factoring to solve for roots and parameters. Inequalities are used to determine ranges of parameter values.
3. The key steps shown are setting up and solving quadratic equations, using the quadratic formula or factoring, and determining parameter ranges through inequalities derived from having real or intersecting roots.
More Related Content
What's hot
Lesson 6 subtraction of polynomials
The document summarizes how to subtract polynomials. It explains that to subtract polynomials, one changes the sign of all terms in the subtrahend, changes the operation to addition, and then proceeds to add the polynomials by aligning like terms and combining coefficients. It provides examples of subtracting various polynomials, as well as exercises for students to practice subtracting polynomials.
Digital signature
This document discusses generating prime numbers for use in digital signature algorithms. It provides an overview of groups and subgroups, defines finite cyclic groups, and explains that groups of prime order are cyclic. It then describes how the Digital Signature Algorithm works, including choosing safe primes p and q, calculating public parameters, generating signatures, and verifying signatures. It also discusses attacks on the algorithm such as index calculus and Pollard's rho algorithm, and why certain parameters are chosen to strengthen security against these attacks.
Sifat Limit Fungsi Aljabar dan Contoh Soal
The document discusses properties of limits of functions in algebra. It presents 9 properties of limits, including: (1) the limit of a constant k is equal to k; (2) the limit of x as x approaches a is equal to a; (3) the limit of kf(x) is equal to k times the limit of f(x); (4) the limit of the sum of two functions is equal to the sum of their individual limits. It also provides examples of calculating limits using these properties, such as finding the limit of 7x - 4 as x approaches 2.
Module 9 Topic 1 - Adding & Subtracting polynomials
The document provides notes on polynomials, including defining polynomials, describing their terms and degrees, adding and subtracting polynomials, and working through examples of finding degrees, adding, subtracting, and combining like terms of polynomials. The notes include 5 pages on adding and subtracting polynomials and working through examples step-by-step to show the process.
Chinese remainder theorem
A Chinese Remainder Theorem (CRT) is explained intuitively, which helps reader to understand its connection with Abstract Algebra concepts like Groups and Rings.
Here, Author has tried to simplify the concept by explaining sub topic of Groups and Rings which is required by understanding CRT in Abstract Algebra.
Factoring Polynomials ch 5
The document provides steps for factoring trinomial expressions:
1. Look for a common monomial to factor out of both terms.
2. Identify if there are squares present and factor accordingly using the difference of squares formula.
3. To factor trinomials with a leading coefficient of 1, find two numbers whose product is the last term and sum is the coefficient of the middle term.
Day 3 examples
1) The document discusses logarithmic properties and how to solve logarithmic equations and expressions. It provides examples of evaluating logarithmic expressions using log properties and rewriting expressions as single logarithms.
2) Logarithmic properties and theorems covered include the log property that log(MN) = logM + logN, and rewriting expressions with more than one logarithm as a single logarithm.
3) Examples show how to use these properties to evaluate expressions such as log6 8 + log6 9 - log6 2 and rewrite expressions like (x - 2) - 3logx as a single logarithm.
0405 ch 4 day 5
The document discusses logarithmic functions and graphs logarithmic equations, exploring their asymptotes, intercepts, domains, and ranges. It also covers properties of natural logarithms, including that ln(1)=0, ln(e)=1, and that logarithmic and exponential functions are inverses of each other.
10 1 Adding Subtracting Polynomials
This document discusses two methods for adding and subtracting polynomials: horizontal and vertical. For addition, terms with the same variables are combined by adding the coefficients. For subtraction, the signs of the terms in the second polynomial are changed to addition signs before combining like terms. Both horizontal and vertical methods can be used, with horizontal grouping like terms and vertical lining them up before combining coefficients.
Writing quadratic equation
The document discusses quadratic equations and their roots. It provides examples of writing the quadratic equation given the roots. Specifically:
1) It shows how to write the quadratic equation x^2 - 8x + 12 = 0 given the roots are 2 and 6.
2) It shows how to write the quadratic equation 2x^2 - 9x + 4 = 0 given the roots are 4 and 1/2.
3) The key steps are finding the sum and product of the roots, and using those values to write the quadratic equation in the form x^2 - (sum of roots)x + (product of roots) = 0.
Math1000 section1.2
This document discusses exponents and radicals in Math 1000 taught by Stuart Jones. It provides examples of evaluating expressions with exponents such as -24 and (-2)4. It also covers the rules for exponents such as adding when multiplying bases and subtracting when dividing bases. Radicals are also introduced along with examples of simplifying expressions with radicals. Rational exponents are defined as the nth root of x written as x1/n. Throughout, examples are worked through step-by-step to simplify expressions with exponents and radicals.
Solving polynomial equations in factored form
The document provides instructions for solving polynomial equations in factored form. It begins by explaining that to solve an equation like (x – 5)(x + 4) = 0, one should not use the FOIL method but rather split the equation into two separate problems that each equal zero: x – 5 = 0 and x + 4 = 0. It then works through several examples of solving factored polynomial equations by finding the values of x that make each factor equal to zero. The document also covers factoring out the greatest common factor from expressions.
Day 4worked
The document discusses solving various types of log and exponential equations. It includes examples of solving log equations with log 4 log(3 4)x x= − log 2 log( 24 4 )x x= − + and solving natural log equations like ln (3x+5)2 = 4 • ln x = 0.1. It also provides an example of solving an exponential equation like 205.27 2 =+x e 301 =+x e. For homework, it assigns problems from page 331, problems 1-18, 25-28, and 35-38.
11.3
This document provides examples and explanations for multiplying, dividing, and otherwise working with rational expressions. It defines rational expressions as involving polynomials in both the numerator and denominator, with the denominator not equal to 0. Examples are provided for multiplying and dividing rational expressions involving monomials and polynomials. A multi-step word problem is also worked through to find a model for and approximate a baseball player's career batting average as a rational expression involving years played.
Number theoryตัวจริง
1) This document discusses number theory concepts such as divisibility, prime numbers, greatest common divisor, and relatively prime numbers. It provides definitions, theorems, and examples to illustrate these concepts.
2) Key concepts covered include the division algorithm, expressing integers in distributed bases, finding the greatest common divisor using factorization or the Euclidean algorithm, and determining when two numbers are relatively prime.
3) Theorems and proofs are provided to demonstrate properties such as squares of odd numbers being odd, and the remainder when dividing a specific expression by 3. Examples show working through calculations and proofs step-by-step.
4th quarter long test review
This document contains a 10 question review for a 4th quarter long test covering circle equations, polynomial division, factoring, and finding zeros of polynomials. The questions cover finding equations of circles given properties like center and radius, performing polynomial division and finding quotients and remainders, factoring polynomials, and solving polynomials for real zeros.
Number theoryตัวจริง
1) The document discusses number theory concepts such as divisibility, prime numbers, greatest common divisor, and relatively prime numbers.
2) It provides definitions, theorems, proofs, and examples to illustrate these concepts. For instance, it defines the greatest common divisor (GCD) as the largest integer that divides two numbers and proves properties of GCD.
3) The document presents three methods - using common divisors, prime factorizations, and the division algorithm - to calculate the GCD of two numbers.
What's hot (18)
Module 9 Topic 1 - Adding & Subtracting polynomials
Module 9 Topic 1 - Adding & Subtracting polynomials
Similar to 10 minutes quiz
Yr.12 Transition Workshop 2012- 2013
The question defines two quartic functions, f(x) and g(x), and states they both cross the x-axis at -2. It is asked to determine the values of a and b in the functions. By setting each function equal to 0 and solving the simultaneous equations, the values are found to be a = -3 and b = -28.
Yr.12 Transition Workshop 2012-2013
The question defines two quartic functions, f(x) and g(x), and states they both cross the x-axis at -2. It is asked to determine the values of a and b in the functions. By setting each function equal to 0 and solving the simultaneous equations, the values are found to be a = -3 and b = -28.
F4 02 Quadratic Expressions And
The document contains examples and exercises on quadratic expressions and equations. It includes expanding expressions, factorizing expressions, solving quadratic equations, and word problems involving quadratic equations. The exercises cover a range of skills related to quadratic expressions and equations.
F4 c2 quadequations_new__1_
1. The document provides 10 problems involving quadratic equations. It gives the solutions to finding the range of values for parameters in quadratic equations so that the equations have certain properties like real roots or intersecting lines.
2. The solutions involve setting quadratic equations equal to zero and using the quadratic formula or factoring to solve for roots and parameters. Inequalities are used to determine ranges of parameter values.
3. The key steps shown are setting up and solving quadratic equations, using the quadratic formula or factoring, and determining parameter ranges through inequalities derived from having real or intersecting roots.
Add Maths Module
The composite function is gf(x) = 2x - 2. We are given f(x) = 2 - x. To find g, let f(x) = u in gf(x). Then u = 2 - x. Substitute u = 2 - x in gf(x) = 2u - 2. This gives g(x) = 2 - 2x. Therefore, fg(x) = f(2 - 2x) = (2 - (2 - 2x)) = 2x - 2.
35182797 additional-mathematics-form-4-and-5-notes
1) The function f(x) = 2x^2 + 8x + 6 can be written as f(x) = 2(x+2)^2 - 2. The maximum point is (-2, -2) and the equation of the tangent at this point is y = -2.
2) The function f(x) = -(x-4)^2 + h has a maximum point at (k, 9) so k = 4 and h = 9.
3) The function y = (x+m)^2 + n has an axis of symmetry at x = -m. Given the axis is x = 1, m = -1 and the minimum point is (1
Ceramah Add Mth
This document provides guidance on solving additional mathematics problems and preparing for the additional mathematics paper 1 and paper 2 exams. It discusses exam formats, common mistakes students make, key strategies for achieving high marks, and examples of solved exam questions. The document emphasizes understanding the problem, planning a strategy, checking answers, and showing working clearly. It also provides tips on time management and the types of questions that may appear.
modul 2 add maths
This document contains sample problems related to quadratic equations and quadratic functions for Form 4 Additional Mathematics. It is divided into three sections - the first two sections contain sample problems testing concepts related to solving quadratic equations and inequalities. The third section contains sample problems related to identifying properties of quadratic functions such as finding the minimum or maximum value, range of a quadratic function, expressing a quadratic in standard form and sketching its graph.
1.3 Solving Linear Equations
1) The document provides examples of solving linear equations involving fractions.
2) Several multi-step linear equations are solved through addition, subtraction, multiplication and division.
3) The solutions are provided after showing the step-by-step work.
Form 4 Add Maths Note
This document provides notes on functions and quadratic equations from Additional Mathematics Form 4. It includes:
1) Definitions of functions, including function notation f(x) and the relationship between objects and images.
2) Methods for solving quadratic equations, including factorisation, completing the square, and the quadratic formula.
3) Properties of quadratic functions like finding the maximum/minimum value and sketching the graph.
4) Solving simultaneous equations involving one linear and one non-linear equation through substitution.
5) Conversions between index and logarithmic forms and basic logarithm laws.
Form 4-add-maths-note
This document provides notes on key concepts in additional mathematics including:
1) Functions such as f(x) = x + 3 and finding the object and image of a function.
2) Solving quadratic equations using factorisation and the quadratic formula. Types of roots are discussed.
3) Sketching quadratic functions by finding the y-intercept, maximum/minimum values, and a third point. Quadratic inequalities are also covered.
4) Methods for solving simultaneous equations including substitution when one equation is nonlinear.
5) Properties of exponents and logarithms, and how to solve exponential and logarithmic equations.
Modul bimbingan add maths
The document is a mathematics textbook for Additional Mathematics Form 4. It covers topics on functions, simultaneous equations, quadratic equations, and quadratic functions. It contains examples and practice questions for students to work through with answers. The questions range from simple calculations to solving equations and inequalities involving quadratic expressions.
Ecuaciones noveno
The document is a plan for improving math skills in solving equations for a 9th grade class. It provides 14 equations for students to solve:
a) 6x – (4x – 7) = 5x – (4 – 9x) + (-4x + 35)
b) 9x + (-2x + = 3x + (5 – 6x) – (-5x – 18)
c) 4x – (3x – 10) = 2x – (8 – 5x) + (3x – 18)
The equations increase in complexity, involving grouping terms with parentheses and brackets, combining like terms, and solving for x. The assignment is to be
Assign1 21314-sol
This document contains solutions to 5 calculus assignment problems:
1) Finding values of x such that an inequality is satisfied, with the solution being 3 < x < 4.
2) Proving that the square of any odd integer is odd.
3) Proving there is no rational number whose square is 2.
4) Determining the value of x where a quadratic equation has a minimum, which is x = 1.
5) Proving an equation involving sums and powers using mathematical induction, for all natural numbers n and where r ≠ 1.
First Quarter - Chapter 2 - Quadratic Equation
Okay, let's think through this with the new information:
* The equation modeling the height is: h = -16t^2 + vt + c
* The initial height (c) is still 2 feet
* The initial velocity (v) is now 20 feet/second
* The target height (h) is still 20 feet
So the equation is:
20 = -16t^2 + 20t + 2
0 = -16t^2 + 20t + 18 (subtract 20 from both sides)
Evaluating the discriminant:
(20)^2 - 4(-16)(-18) = 400 - 288 = 112
Since the discriminant is positive
Algebra Electronic Presentation Expert Voices F I N A L
This document provides an overview of various algebra topics including absolute values, solving quadratic equations by completing the square, using the quadratic formula, generating equations given roots, determining the nature of roots using the discriminant, solving rational equations, and solving radical equations. Examples and practice problems are provided for each topic along with worked out solutions. Relevant websites with additional resources on these algebra topics are also listed.
Unit2.polynomials.algebraicfractions
This document discusses algebraic fractions and polynomials. It covers dividing polynomials by monomials and other polynomials. The key steps of polynomial long division and Ruffini's rule for polynomial division are explained. Finding the quotient, remainder, and whether a polynomial is divisible are discussed. Finding the roots of polynomials and using the remainder theorem are also covered. Various techniques for factorizing polynomials are presented, including taking out common factors, using identities, the fundamental theorem of algebra, and Ruffini's rule.
Core 1 revision notes a
This document provides a summary of core mathematics concepts including:
1) Linear graphs and equations such as y=mx+c and finding the equation of a line.
2) Quadratic equations and graphs including using the quadratic formula, completing the square, and finding the vertex and axis of symmetry.
3) Simultaneous equations and interpreting their solutions geometrically as the intersection of graphs.
4) Other topics covered include surds, polynomials, differentiation, integration, and areas under graphs.
Algebra Presentation on Topic Modulus Function and Polynomials
Algebra Presentation on Topic Modulus Function and Polynomials
Created by Shakira and Frilla HS12B Performance Task BINUS School Bekasi
Qu
This document provides examples and explanations for solving quadratic equations by graphing. It begins by defining key vocabulary terms related to quadratic equations, such as standard form and roots. It then shows two examples of solving quadratic equations by first using the quadratic formula to find the x-intercepts, then graphing the equation and determining where the graph crosses the x-axis. The examples illustrate how to set up and graph quadratic equations in standard form in order to estimate or determine the exact solutions to the equations.
Similar to 10 minutes quiz (20)
35182797 additional-mathematics-form-4-and-5-notes
35182797 additional-mathematics-form-4-and-5-notes
Algebra Electronic Presentation Expert Voices F I N A L
Algebra Electronic Presentation Expert Voices F I N A L
Algebra Presentation on Topic Modulus Function and Polynomials
Algebra Presentation on Topic Modulus Function and Polynomials
More from nurliyanazakaria
Quadraticsportfoliopowerpoint 100325142401-phpapp02
The document discusses different forms of quadratic equations and how to graph them. It covers the standard form ax^2 + bx + c, vertex form a(x-h)^2 + k, and intercept form a(x-p)(x-q). It explains how to identify the vertex and axis of symmetry in standard form, and how to graph quadratics in all three forms by plotting points and drawing the parabola.
Scheme of Work
The document outlines the scheme of work for AddMaths and Maths courses for Form 5 students at Mara Junior Science College Serting in 2012. It details the topics covered in each subject over the semester from January to June, including dates and duration. Some notable topics covered include differentiation, integration, trigonometry, probability, motion, and earth geometry. The schedule also notes re-orientation weeks, tests, breaks and the final examination period.
More from nurliyanazakaria (6)
Quadraticsportfoliopowerpoint 100325142401-phpapp02
Quadraticsportfoliopowerpoint 100325142401-phpapp02
Recently uploaded
“I’m still / I’m still / Chaining from the Block”
“An Outlook of the Ongoing and Future Relationship between Blockchain Technologies and Process-aware Information Systems.” Invited talk at the joint workshop on Blockchain for Information Systems (BC4IS) and Blockchain for Trusted Data Sharing (B4TDS), co-located with with the 36th International Conference on Advanced Information Systems Engineering (CAiSE), 3 June 2024, Limassol, Cyprus.
20240609 QFM020 Irresponsible AI Reading List May 2024
Everything I found interesting about the irresponsible use of machine intelligence in May 2024
Mind map of terminologies used in context of Generative AI
Mind map of common terms used in context of Generative AI.
Removing Uninteresting Bytes in Software Fuzzing
Imagine a world where software fuzzing, the process of mutating bytes in test seeds to uncover hidden and erroneous program behaviors, becomes faster and more effective. A lot depends on the initial seeds, which can significantly dictate the trajectory of a fuzzing campaign, particularly in terms of how long it takes to uncover interesting behaviour in your code. We introduce DIAR, a technique designed to speedup fuzzing campaigns by pinpointing and eliminating those uninteresting bytes in the seeds. Picture this: instead of wasting valuable resources on meaningless mutations in large, bloated seeds, DIAR removes the unnecessary bytes, streamlining the entire process.
In this work, we equipped AFL, a popular fuzzer, with DIAR and examined two critical Linux libraries -- Libxml's xmllint, a tool for parsing xml documents, and Binutil's readelf, an essential debugging and security analysis command-line tool used to display detailed information about ELF (Executable and Linkable Format). Our preliminary results show that AFL+DIAR does not only discover new paths more quickly but also achieves higher coverage overall. This work thus showcases how starting with lean and optimized seeds can lead to faster, more comprehensive fuzzing campaigns -- and DIAR helps you find such seeds.
- These are slides of the talk given at IEEE International Conference on Software Testing Verification and Validation Workshop, ICSTW 2022.
Presentation of the OECD Artificial Intelligence Review of Germany
Consult the full report at https://www.oecd.org/digital/oecd-artificial-intelligence-review-of-germany-609808d6-en.htm
UiPath Test Automation using UiPath Test Suite series, part 6
Welcome to UiPath Test Automation using UiPath Test Suite series part 6. In this session, we will cover Test Automation with generative AI and Open AI.
UiPath Test Automation with generative AI and Open AI webinar offers an in-depth exploration of leveraging cutting-edge technologies for test automation within the UiPath platform. Attendees will delve into the integration of generative AI, a test automation solution, with Open AI advanced natural language processing capabilities.
Throughout the session, participants will discover how this synergy empowers testers to automate repetitive tasks, enhance testing accuracy, and expedite the software testing life cycle. Topics covered include the seamless integration process, practical use cases, and the benefits of harnessing AI-driven automation for UiPath testing initiatives. By attending this webinar, testers, and automation professionals can gain valuable insights into harnessing the power of AI to optimize their test automation workflows within the UiPath ecosystem, ultimately driving efficiency and quality in software development processes.
What will you get from this session?
1. Insights into integrating generative AI.
2. Understanding how this integration enhances test automation within the UiPath platform
3. Practical demonstrations
4. Exploration of real-world use cases illustrating the benefits of AI-driven test automation for UiPath
Topics covered:
What is generative AI
Test Automation with generative AI and Open AI.
UiPath integration with generative AI
Speaker:
Deepak Rai, Automation Practice Lead, Boundaryless Group and UiPath MVP
GraphRAG for Life Science to increase LLM accuracy
GraphRAG for life science domain, where you retriever information from biomedical knowledge graphs using LLMs to increase the accuracy and performance of generated answers
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdf
Monitoring and observability aren’t traditionally found in software curriculums and many of us cobble this knowledge together from whatever vendor or ecosystem we were first introduced to and whatever is a part of your current company’s observability stack.
While the dev and ops silo continues to crumble….many organizations still relegate monitoring & observability as the purview of ops, infra and SRE teams. This is a mistake - achieving a highly observable system requires collaboration up and down the stack.
I, a former op, would like to extend an invitation to all application developers to join the observability party will share these foundational concepts to build on:
HCL Notes and Domino License Cost Reduction in the World of DLAU
Webinar Recording: https://www.panagenda.com/webinars/hcl-notes-and-domino-license-cost-reduction-in-the-world-of-dlau/
The introduction of DLAU and the CCB & CCX licensing model caused quite a stir in the HCL community. As a Notes and Domino customer, you may have faced challenges with unexpected user counts and license costs. You probably have questions on how this new licensing approach works and how to benefit from it. Most importantly, you likely have budget constraints and want to save money where possible. Don’t worry, we can help with all of this!
We’ll show you how to fix common misconfigurations that cause higher-than-expected user counts, and how to identify accounts which you can deactivate to save money. There are also frequent patterns that can cause unnecessary cost, like using a person document instead of a mail-in for shared mailboxes. We’ll provide examples and solutions for those as well. And naturally we’ll explain the new licensing model.
Join HCL Ambassador Marc Thomas in this webinar with a special guest appearance from Franz Walder. It will give you the tools and know-how to stay on top of what is going on with Domino licensing. You will be able lower your cost through an optimized configuration and keep it low going forward.
These topics will be covered
- Reducing license cost by finding and fixing misconfigurations and superfluous accounts
- How do CCB and CCX licenses really work?
- Understanding the DLAU tool and how to best utilize it
- Tips for common problem areas, like team mailboxes, functional/test users, etc
- Practical examples and best practices to implement right away
TrustArc Webinar - 2024 Global Privacy Survey
How does your privacy program stack up against your peers? What challenges are privacy teams tackling and prioritizing in 2024?
In the fifth annual Global Privacy Benchmarks Survey, we asked over 1,800 global privacy professionals and business executives to share their perspectives on the current state of privacy inside and outside of their organizations. This year’s report focused on emerging areas of importance for privacy and compliance professionals, including considerations and implications of Artificial Intelligence (AI) technologies, building brand trust, and different approaches for achieving higher privacy competence scores.
See how organizational priorities and strategic approaches to data security and privacy are evolving around the globe.
This webinar will review:
- The top 10 privacy insights from the fifth annual Global Privacy Benchmarks Survey
- The top challenges for privacy leaders, practitioners, and organizations in 2024
- Key themes to consider in developing and maintaining your privacy program
GraphSummit Singapore | Enhancing Changi Airport Group's Passenger Experience...
Dr. Sean Tan, Head of Data Science, Changi Airport Group
Discover how Changi Airport Group (CAG) leverages graph technologies and generative AI to revolutionize their search capabilities. This session delves into the unique search needs of CAG’s diverse passengers and customers, showcasing how graph data structures enhance the accuracy and relevance of AI-generated search results, mitigating the risk of “hallucinations” and improving the overall customer journey.
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024
Neha Bajwa, Vice President of Product Marketing, Neo4j
Join us as we explore breakthrough innovations enabled by interconnected data and AI. Discover firsthand how organizations use relationships in data to uncover contextual insights and solve our most pressing challenges – from optimizing supply chains, detecting fraud, and improving customer experiences to accelerating drug discoveries.
Goodbye Windows 11: Make Way for Nitrux Linux 3.5.0!
As the digital landscape continually evolves, operating systems play a critical role in shaping user experiences and productivity. The launch of Nitrux Linux 3.5.0 marks a significant milestone, offering a robust alternative to traditional systems such as Windows 11. This article delves into the essence of Nitrux Linux 3.5.0, exploring its unique features, advantages, and how it stands as a compelling choice for both casual users and tech enthusiasts.
Uni Systems Copilot event_05062024_C.Vlachos.pdf
Unlocking Productivity: Leveraging the Potential of Copilot in Microsoft 365, a presentation by Christoforos Vlachos, Senior Solutions Manager – Modern Workplace, Uni Systems
Climate Impact of Software Testing at Nordic Testing Days
My slides at Nordic Testing Days 6.6.2024
Climate impact / sustainability of software testing discussed on the talk. ICT and testing must carry their part of global responsibility to help with the climat warming. We can minimize the carbon footprint but we can also have a carbon handprint, a positive impact on the climate. Quality characteristics can be added with sustainability, and then measured continuously. Test environments can be used less, and in smaller scale and on demand. Test techniques can be used in optimizing or minimizing number of tests. Test automation can be used to speed up testing.
20240605 QFM017 Machine Intelligence Reading List May 2024
Everything I found interesting about machines behaving intelligently during May 2024
How to Get CNIC Information System with Paksim Ga.pptx
Pakdata Cf is a groundbreaking system designed to streamline and facilitate access to CNIC information. This innovative platform leverages advanced technology to provide users with efficient and secure access to their CNIC details.
National Security Agency - NSA mobile device best practices
Threats to mobile devices are more prevalent and increasing in scope and complexity. Users of mobile devices desire to take full advantage of the features
available on those devices, but many of the features provide convenience and capability but sacrifice security. This best practices guide outlines steps the users can take to better protect personal devices and information.
Recently uploaded (20)
20240609 QFM020 Irresponsible AI Reading List May 2024
20240609 QFM020 Irresponsible AI Reading List May 2024
Mind map of terminologies used in context of Generative AI
Mind map of terminologies used in context of Generative AI
Presentation of the OECD Artificial Intelligence Review of Germany
Presentation of the OECD Artificial Intelligence Review of Germany
UiPath Test Automation using UiPath Test Suite series, part 6
UiPath Test Automation using UiPath Test Suite series, part 6
GraphRAG for Life Science to increase LLM accuracy
GraphRAG for Life Science to increase LLM accuracy
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdf
Observability Concepts EVERY Developer Should Know -- DeveloperWeek Europe.pdf
HCL Notes and Domino License Cost Reduction in the World of DLAU
HCL Notes and Domino License Cost Reduction in the World of DLAU
GraphSummit Singapore | Enhancing Changi Airport Group's Passenger Experience...
GraphSummit Singapore | Enhancing Changi Airport Group's Passenger Experience...
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024
GraphSummit Singapore | The Art of the Possible with Graph - Q2 2024
Goodbye Windows 11: Make Way for Nitrux Linux 3.5.0!
Goodbye Windows 11: Make Way for Nitrux Linux 3.5.0!
Climate Impact of Software Testing at Nordic Testing Days
Climate Impact of Software Testing at Nordic Testing Days
20240605 QFM017 Machine Intelligence Reading List May 2024
20240605 QFM017 Machine Intelligence Reading List May 2024
How to Get CNIC Information System with Paksim Ga.pptx
How to Get CNIC Information System with Paksim Ga.pptx
National Security Agency - NSA mobile device best practices
National Security Agency - NSA mobile device best practices
10 minutes quiz
- 1. ADDITIONAL MATHEMATICS QUADRATIC EQUATIONS: 10 Minutes Quiz Form 4 QUADRATIC EQUATIONS 1) Given x 4 is the root of equation 2 x 2 kx 12 0 . Find the value of k. 2) Given that the quadratic equation x 2 5 x 4 p 0 has two different roots. Find the range values of p. 3) Given that the quadratic equation 3x 2 6 x 4 q 0 has no roots. Find the range values of q. Answer: 1) 2(4)2-k(4)-12 = 0 -4k = -20 k=5 2) x2 5x 4 p 0 2 (-5) -4(1)(4-p) > 0 9 p> 4 3) 3x 2 6x 4 q 0 2 (-6) - 4(3)(4-q) < 0 h<1