Core 1 Linear Graphs and Equations For any straight line‚ the gradient (M) is: dy/dx or difference in y/difference in x which is (y2-y1)/(x2-x1) Equation of a line: y=mx+c which is used when the gradient and intercept is known or y-y1=m(x-x1) when the gradient and the co-ordinates (x1‚y1) of a single point that the line passes through is known. You’ll need to learn this equation. [The equation of the line can be kept in this form unless stated in the exam. (reduces error chance) Also
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1 Quadratic Equations in One Unknown (I) Review Exercise 1 (p. 1.4) 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. Let’s Discuss Let’s Discuss (p. 1.23) Angel’s method: Using the quadratic formula‚ Ken’s method: Using the quadratic formula‚ Let’s Discuss (p. 1.30) The solution obtained by using the factor method is the exact value of the root. However‚ the solution obtained
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PHILIPPINE e-LEARNING SOCIETY NATIONAL e-LEARNING CONGRESS 2014 e-PROCEEDINGS ISSN: 2094-5485 VOLUME 2014 COMPENDIUM PeLS NELC 2014 Conference Proceedings 1 ISSN: 2094-5485 VOLUME 2014 COMPENDIUM Greetings of peace! The annual National eLearning Congress is a tradition of the Philippine eLearning Society (PeLS). It is a venue for academics‚ researchers‚ eLearning practitioners‚ industry training and development specialists‚ ICT education service providers
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(c)- No Mode (d)- 54.0006‚ (e)- 18.0248‚ (f)- 324.8950‚ (g)- 66.8248 b) Apply the least-square regression and fit a first-order line to the given points. Determine the standard error of estimate and the coefficient of determination. Compare the fitting accuracy of this linear model with the model in part (a) that only uses the arithmetic mean of the variable . Answer: < 0.8964 ‚ c) Apply the least-square regression and fit a second-order curve to the given points. Determine the standard error of
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Tutors Name: _____________________________________________________________ Tutorial Day: ________________________ Tutorial Time: _________________________ Mathematics 103‚ Semester 1 - 2013 MID-SEMESTER TEST 2 Question 1 Determine the equation of the line that passes through the points 2‚ 12 and 5‚ 6 . (3 marks) Question 2 Find the limit‚ lim → 2 3 2 (3 marks) Question 3 is on the next page… Mathematics 103‚ Semester 1 - 2013 MID-SEMESTER TEST 3 Question 3 If
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Student Name/Number:___________________ Teacher Name:__________________________ 2011 MID COURSE EXAMINATION Preliminary - YEAR 11 Mathematics Time allowed – Two hours (Plus 5 minutes reading time) DIRECTIONS TO CANDIDATES Attempt ALL questions. ALL questions are of equal value. All necessary working should be shown in every question. Marks may be deducted for careless or badly arranged work. Board-approved calculators may be
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1.10 1.11 Chapter Overview 1 Real Numbers 2 Exponents and Radicals 12 Algebraic Expressions 24 ● DISCOVERY PROJECT Visualizing a Formula 34 Rational Expressions 35 Equations 44 Modeling with Equations 58 ● DISCOVERY PROJECT Equations through the Ages 75 Inequalities 76 Coordinate Geometry 87 Graphing Calculators; Solving Equations and Inequalities Graphically 101 Lines 111 Modeling Variation 123 Chapter 1 Review 130 Chapter 1 Test 135 ■ FOCUS ON PROBLEM SOLVING General Principles 138 2 Functions
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rational expressions‚ equations (linear‚ quadratic‚ radical‚ rational)‚ systems of equations‚ inequalities‚ functions‚ graphs of quadratic and linear equations and inequalities in two variables‚ complex numbers and applications. 2. Learning Outcomes Upon successful completion of this course‚ students will be able to: 1. perform operations involving polynomials and factoring polynomials 2. solve and graph equations and inequalities such as linear‚ absolute value‚ quadratic‚ rational‚ and radicals
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signs a(-b ) = - (ab) Exponents ��n = a.a.a…….a ‚ (-a)b = - (ab) ‚ ( -a ) ( -b ) = ab ‚ - ( -a ) = a ‚ ��0 = 1 if a ≠ 0 ‚ ��−n = 1 �� n = =- ‚ = n factors ‚ ‚ if a ≠ 0 1 Laws of exponents ��n ��m = ��m+n ‚ (��m )n = ��mn Square roots √��2 =|��| (����)n = ��n �� n ‚ �� �� �� �� = ����−�� = �� ��−�� ���� �� ≠ 0 ‚ ( )�� = �� �� �� �� ���� ‚ ���� �� ≠ 0 Geometry Review �� 2 = ��2 + �� 2 Pythagorean Theorem Geometry Formulas 1 Area
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roots of a quadratic equation and perform the following on it: Boundary Value Analysis (BVA). #include #include void main() { int a‚b‚c; int d=0; clrscr(); printf("The Quadratic Equation is of type ax2+bx+c=0"); printf("Enter value of a‚b‚c:"); scanf("%d \n %d \n %d"‚&a‚&b‚&c); d=((b*b)-(4*a*c)); if(a100) { printf("Invalid input"); } if(d==0) { printf("Real and Equal Roots"); } else if(d>0) { printf("Real roots"); } else { printf("Not a quadratic equation"); } getch();
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