Quadratic Equations and Expressions: Part B

University:
Yale University
Course:
MATH 530 | Mathematical Economics
Academic year:

2024
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0

Pages:

8
Author:

customer-8072267

SUBJECT GRADE EXAMINER NAME Mathematics PAPER DATE MARKS MODERATOR 11 Ms Brown TEACHER Quadratic Equations and Expressions: Part B 15 February 2024 40 Mr Hayward and Mrs Tee DURATION 45 minutes QUESTION NO DESCRIPTION MAXIMUM MARK 1 Quadratic Expressions, Inequalities and Formula 17 2 Quadratic Equations 7 3 Simultaneous equations 9 4 Problem Solving 7 TOTAL ACTUAL MARK 40 INSTRUCTIONS: 1. This paper consists of 8 pages and 4 questions. Two extra pages for additional working has been provided, if this page is used, label the question accurately. Please check that your question paper is complete. 2. Read the questions carefully. 3. Answer all questions on the question paper and hand it in at the end of the test. 4. It is in your interest to write legibly and present your work neatly. 5. Clearly show ALL calculations, diagrams, graphs, etc. that you have used in determining your answers. Answers only will NOT necessarily be awarded full marks. 6. You may use an approved non-programmable and non-graphical calculator, unless otherwise stated. 7. Round off your answers to ONE decimal place unless otherwise stated. A Formula you may need: 𝑥= −𝑏±√𝑏2 −4𝑎𝑐 2𝑎 QUESTION 1 a) Given: 17 MARKS √𝑥 𝑥+2 For which values of 𝑥 will the above expression be: b) 1) undefined? 2) non-real? Write 𝑥 2 + 4𝑥 + 5 Grade 11 (2) in the form (𝑥 + 𝑝)2 + 𝑞 by completing the square. 2 of 8 (3) Quadratic Equations and Expressions: Part B c) Consider the inequality: 4𝑥 2 < 9 Determine the solution to this inequality if: d) 1) 𝑥 ∈ ℝ (Real Numbers) (3) 2) 𝑥 ∈ ℤ (Integers) (1) The roots of a quadratic equation are given by 𝑥= −4±√16+8𝑘 6 where 𝑘 ∈ {−3 ; −2 ; −1 ; 0 ; 2 ; 4 ; 6}. 1) Write down TWO values of 𝑘 for which the roots will be rational. (2) 2) Write down ONE value of 𝑘 for which the roots will be non-real. (1) 3) Write down ONE value of 𝑘 for which the roots will be equal. (1) Grade 11 3 of 8 Quadratic Equations and Expressions: Part B e) The one root of 𝑚𝑥 2 − 4𝑥 + 1 = 0 is equal to 1. 1) Calculate the value of 𝑚 . (2) 2) Hence, determine the value of the other root. (2) QUESTION 2 a) Given: 7 MARKS 2 𝑚 = 4𝑚 − 7 Show that 𝑚 = − b) 1 4 or 𝑚 = 2. Hence, or otherwise, solve for 𝑥 : Grade 11 4 of 8 (2) 2 𝑥2 − 𝑥 = 4(𝑥 2 − 𝑥) − 7 (5) Quadratic Equations and Expressions: Part B QUESTION 3 9 MARKS 𝑝+𝑞 =3 Given: 𝑝2 − 𝑝𝑞 + 𝑞 2 = 3 and a) Solve for 𝑝 and 𝑞. (6) b) Hence, or otherwise, solve for 𝑥 and 𝑦: (3) 1 𝑥 Grade 11 + 1 𝑦 =3 and 1 1 𝑥 𝑥𝑦 2 − + 5 of 8 1 𝑦2 =3 Quadratic Equations and Expressions: Part B QUESTION 4 7 MARKS Rhett and Joshua play a game where they each need to arrange discs in rectangular blocks. Row Column Rhett placed his 240 discs in 𝑥 rows, each row containing the same number. Joshua arranged his 270 discs in (𝑥 + 3) rows, each with the same number of discs. However, Rhett had 2 discs per column more than Joshua. By arranging the information in a table, and setting up an equation, determine how many discs Rhett placed in each row. Grade 11 (7) 6 of 8 Quadratic Equations and Expressions: Part B EXTRA WORKING: Grade 11 7 of 8 Quadratic Equations and Expressions: Part B Grade 11 8 of 8 Quadratic Equations and Expressions: Part B

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