Lesson Plans SET A for Grades 9-10-Lesson 2 Level 9-10 Algebra Basics

Lesson 2 Level 9-10 Algebra Basics - Homework

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This document provides a set of algebra-related problems designed for Levels 9-10, meant to aid in practicing skills covered in Math Kangaroo classes. Students are advised to consult their notes, slides, or recordings if they need a refresher before attempting the problems. Here is a brief summary of the problems and their solutions:<br /><br />1. Mary arranged numbers in a nine-cell circle where the sum of each diameter is 32 and the circumference is 100. The solution indicates the center number is 7.<br /><br />2. Given two numbers, their sum is 30, and the sum of their squares is 856. The result for three times one number added to three times the other is 25,020.<br /><br />3. For variables \(x\) and \(y\), you are to solve the system of equations \(3x - y = 9\) and \(2x + 5y = 8\). The solution yields \(x = \frac{69}{23}\) and \(y = \frac{10}{23}\).<br /><br />4. Another system of equations with variables \(x\), \(y\), and \(z\): \(2x + 3y - z = 11\), \(3x - 2y + z = 19\), and \(4x + z - 3y = 17\). The solutions are \(x = 3\), \(y = 7\), and \(z = 4\).<br /><br />5. The problem involves a number, \(n\), where \(n - 2(\frac{1}{n}) = 10\). The values found for this number are \(n = 5 + 3\sqrt{33}\) and \(n = 5 - 3\sqrt{33}\).<br /><br />6. Lena wrote a sequence on the board: 1, 4, 7, , 3n + 1, and deleted one number. The remaining numbers have a mean of 19.5. The largest number originally is 37, and the deleted number is 13. <br /><br />These exercises are meant to reinforce algebraic concepts and problem-solving skills.

Keywords

algebra problems

Math Kangaroo

Level 9-10

problem-solving

equations

systems of equations

number sequences

sum of squares

algebraic skills

practice exercises