SUBJECT: ADDITIONAL MATHEMATICS CURRICULUM OUTLINE LEVEL: 3 TOPIC OBJECTIVES ASSIGNMENTS / ASSESSMENT WEB-BASED RESOURCES. Online worksheet.
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1 TERM 1 Simultaneous Online worksheet. Week 1 Equations in two Solve two simultaneous equations where unknowns at least one is a linear equation, by substitution. Understand what it means when the pair h/nonlinear-simultaneousequations of equations has no solution. Understand what it means when the pair of equations have infinite solutions. Apply solving of simultaneous equations to word problems. ACADEMIC YEAR: 014 Page 1
2 TERM 1 Quadratic 3 Equations and Inequalities Sketch quadratic curve. Finding range of values of quadratic inequality using sketch. Find the maximum or the minimum value of a quadratic expression by completing Worksheet Worksheet 3 Worksheet 4 om/quadratic/discriminant-inquadratic-equation.php the square. Identify the nature of roots of a quadratic equation by considering the value of b 4ac. Understand the conditions for a quadratic equation to have: Post-independent learning test : Simultaneous Equations ( 0% of TA1 ) (i) two real roots (ii) two equal roots (iii) no real roots Apply the properties of the discriminant of a quadratic equation to solve problems. Apply the relation between discriminant and nature of a root to solve problems involving intersection of a line and a curve. i.e. to understand the related conditions for a given line to: (i) intersect a given curve (ii) be a tangent to a given curve (iii) not intersect a given curve ACADEMIC YEAR: 014 Page
3 TERM 1 3 Quadratic equations and Inequalities Identify the conditions for ax + bx + c to be always positive (or always negative) State the sum and product of the roots of a quadratic equation, and use them to evaluate expressions involving these om/quadratic/discriminant-inquadratic-equation.php roots. Form Quadratic Equations whose roots are related to the roots of another quadratic equation. ACADEMIC YEAR: 014 Page 3
4 TERM 1 The Modulus Week 4 Function Understand the function y f ( x) f ( x) is linear or quadratic = where Sketch the graph of absolute valued functions aths-revision/coremaths/algebra-andfunctions/functions/modulus/intr oduction.php Solve problems involving absolute valued functions ACADEMIC YEAR: 014 Page 4
5 TERM 1 Polynomials 5 7 Know the general form of a polynomial and the use of terms such as degree, coefficients and constant term. Find the values of unknown constants for identities Worksheet Worksheet 3 ions-of-higher Degree/_Factor-Remainder- Theorems.php Perform multiplication and division of polynomials long division and synthetic division. Express a polynomial in terms of a divisor, quotient and remainder. i.e. P ( x) = ( x a) Q( x) = R Find the remainder when an expression is divided by a linear factor. Use the following facts to translate problems into mathematical equations and solve them : When the polynomial f(x) is divided by ( x ± a), the remainder R is given by R = f ( a) When the polynomial f(x) is divided by ( ax ± b) where a 0, the remainder is given by R = f ( a) ; ACADEMIC YEAR: 014 Page 5
6 TERM 1 Coordinate 8-10 Geometry The Straight Line GEOMETRY Use the formula ( x x ) + ( y ) d = to evaluate 1 y1 the distance between two given points. Find area of plane figures given its vertices Worksheet Worksheet 3 g.com/coordinategeometry.html Find the midpoint of two given points. Find the gradient of two given points. Know the relationship between the gradients of two parallel lines and two perpendicular lines Find the equation of a straight line given the x- and y-intercepts its gradient and the y-intercept its gradient and a point two points Find the equation of perpendicular bisector. ACADEMIC YEAR: 014 Page 6
7 TERM Indices and Online worksheets. Week 1 Surds Use the rules a b = ab and a a b = to b Post-independent learning test. ( 0% of TA3 ) simplify surds _Surds Transform surds to indices and vice versa Rationalize the denominator, including examples such as: p a, q c b a ±, d c ± b a, d b ± c d p ± q Solve unknowns in surds identities Spend time discussing the fundamental theorem of algebra. Solve problems involving rationalizing of surds Solve simple exponential equations and simultaneous exponential equations Solve exponential equations using appropriate substitution Solve exponential equations in e x. ACADEMIC YEAR: 014 Page 7
8 TERM Logarithms 3 Apply Rules of Indices to simplify expressions and to solve exponential equations. Convert an equation in index form into Worksheet Worksheet 3 Worksheet 4 bra/logs/log1/log1.html logarithmic form and vice versa, in particular, x e y = x = ln y Apply Laws of Logarithms to solve logarithmic equations. Apply the change of base of logarithms. Solve logarithmic equations in any given base(s) Sketch and plot the graphs of where a > 1, 0 < a < 1 and a =1 Sketch and plot the graphs of Sketch and plot the graphs of and x y = a x y = e. y = loga y = ln x where a > 0 ( usually a > 1 ) Interpret related graph forms such as x y 3x = e and x y = 3e. ACADEMIC YEAR: 014 Page 8
9 TERM Linear Law Week 4 ( Part 1 ) GEOMETRY Convert straight line graph to equation of the curve Reduce laws of higher order into simple Worksheet book/html/expoapps_3.htm straight line laws and use graphical method to find the unknowns. without plotting with plotting ACADEMIC YEAR: 014 Page 9
10 TERM Week 7 REVISION Assess and measure the effectiveness of teaching and learning and use of data to improve student performance and instructional programmes To achieve targets set by the department. 01 & 013 Mid Year Papers TERM MID YEAR To assess and measure the effectiveness Mid Year Exam Topics: EXAM & of teaching and learning and use of data Simultaneous equations in two 8 9 REVIEW OF to improve student performance and unknowns MID YEAR PAPERS instructional programmes. To achieve targets set by the department. Quadratic equations and Inequalities The modulus function Polynomials- Exclude Partial Fractions Coordinate Geometry Surds, indices and logarithms Linear Law ACADEMIC YEAR: 014 Page 10
11 TERM Curves and Week 10 Circles GEOMETRY Sketch graphs of equations of the form: n y = ax where n is a simple rational number y = kx Worksheet. egents/math/algtrig/atc1/circ lelesson.htm y = x Find the equation of the circle in the form: ( ) ( ) x a + y b = r x + y + gx + fy + c = 0 Intersection of two circles ACADEMIC YEAR: 014 Page 11
12 TERM 3 Trigonometric 1 7 Function Simple Trigonometric Identities and Equations AND Know six trigonometric ratios for angles of any magnitude (in degrees or radians) Appreciate the difference between sin x and sin 1 x Know the principal values of 1 cos x and tan 1 x 1 sin x, Know the trigonometric ratios of special angles (30, 45, 60 ) or (π/6, π/4, π/3) Worksheet Worksheet 3 Worksheet 4 Worksheet 5 Worksheet 6 Worksheet 7 Worksheet 8 rig.html student/m1555 Further Trigonometric Identities Evaluate required trigonometric ratios given the value of a trigonometric ratio Solve simple trigonometrical equations for angles between 0 o and 360 o TRIGONOMETRY Know the amplitude, periodicity and symmetries related to the sine and cosine functions. ACADEMIC YEAR: 014 Page 1
13 TERM 3 Trigonometric Function Use of the following identities / formulae: 1 7 Simple Trigonometric The basic identities: sin A cos A = tan A, = cot A, cos A sin A rig.html Identities and Equations sin ϑ + cos ϑ = 1, tan ϑ + 1 = sec ϑ AND 1+ cot ϑ = cos ec ϑ Addition formulae: Further Trigonometric sin (A ± B), cos (A ± B) Identities tan (A ± B) Double angle formulae for sin A, cos A, TRIGONOMETRY tan A. (to derive it from addition formulae) Solve trigonometric equations involving use of identities and angles of the form ( ax + b). Solve trigonometric equations where angles are in degrees of radians. Prove simple trigonometric identities Solve equation in the form a cos θ + b sinθ by expressing them in the form Rcos(θ ± ) or Rsin (θ ± ). ACADEMIC YEAR: 014 Page 13
14 TERM REVISION To assess and measure the effectiveness of teaching and learning and use of data to improve student performance and instructional programmes To achieve targets set by the department. LEVEL 1 - September Holiday Assignment 013 End of Year Paper TERM 3 Binomial 10 Theorem ( Part 1 ) use the binomial theorem to expand expressions in the form (x + y) n where n is a positive integer. s-binomial- theorem/4_binomial- theorem.php ACADEMIC YEAR: 014 Page 14
15 TERM 4 Binomial Week 1 Theorem ( Part ) Use of the general term n a r n r r b, 0 < r n find the term independent of x find a required coefficient Worksheet s-binomialtheorem/4_binomialtheorem.php find the required order of the expression. write out and simplify the product of two binomial expressions TERM 4-3 REVISION To assess and measure the effectiveness of teaching and learning and use of data to improve student performance and instructional programmes To achieve targets set by the department. 01 & 013 End Of Year Papers ACADEMIC YEAR: 014 Page 15
16 TERM 4 END OF YEAR To assess and measure the effectiveness End of Year Exam EXAM of teaching and learning and use of data All Sec 3 topics 4-6 to improve student performance and instructional programmes To achieve targets set by the department. ACADEMIC YEAR: 014 Page 16
17 TERM 4 Partial fractions At the end of the chapter, students should be 7-8 able to decompose rational functions (including cases where degree of the numerator alevel/pages.php?page=94 exceeds that of the denominator) in partial fraction where the denominator is no more complicated than ( ax + b)( cx + d ) ( ax + b)( cx + d ) ( ax + b)( x + c ) ACADEMIC YEAR: 014 Page 17
18 TERM 1 Component Weighting Remarks Daily Assignment 0% Based on punctuality & completeness Independent Learning 0% Simultaneous Equations Test 60% 40 marks Total 100% MY Paper Duration Description Max Marks Weighting h There will be 9-11 questions of varying marks and lengths. Candidates are required to answer ALL questions % TERM 3 Component Weighting Remarks Daily Assignment 0% Based on punctuality & completeness Independent Learning 0% Surds Test 60% 40 marks Total 100% EOY Paper Duration Description Max Marks Weighting 1 h There will be questions of varying marks and lengths. Candidates are required to answer ALL questions % ACADEMIC YEAR: 014 Page 18
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