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TOPIC 1 (QA016) : NUMBER SYSTEM AND EQUATIONS

1.2 Indices, Surds and Logarithms. 1.1 Real Numbers. TOPIC 1 (QA016) : NUMBER SYSTEM AND EQUATIONS. 1. 2. 3. 4. 5. Intervals (a) open interval (b) close interval (c) half-open interval 6. Real number line (a) Empty circle : Open bracket : ( OR )

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TOPIC 1 (QA016) : NUMBER SYSTEM AND EQUATIONS

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  1. 1.2 Indices, Surds and Logarithms 1.1 Real Numbers TOPIC 1 (QA016) : NUMBER SYSTEM AND EQUATIONS 1. 2. 3. 4. 5. Intervals (a) open interval (b) close interval (c) half-open interval 6. Real number line (a) Empty circle : Open bracket : ( OR ) (b) Dense circle : Close bracket : [ OR ] 7. (a) Interval notation / form (b) Solution set ** INDICES P N W Z Q P = prime numbers N = natural numbers W = whole numbers Z = integers Q = rational numbers = irrational numbers CHECK ANSWERS : (Equation) 1. Surds 2. Logarithms ** SURDS ** LOGARITHMS

  2. TOPIC 2 (QA016) : INEQUALITIES AND ABSOLUTE VALUES 1) LINEAR INEQUALITIES 2) QUADRATIC INEQUALITIES STEP 1 : Write in the form of e.g : ** TIPS (i) coefficient of x2 is +ve (ii) your RHS is 0 STEP 2 :Factorize STEP 3 : Solve quadratic inequalities by using : (a) Algebraic method (Table of sign) OR (b) GRAPHICAL METHOD • ABSOLUTE VALUE (Equations) • ABSOLUTE VALUE (Inequalities) (NEXT PAGE) INEQUALITIES ABSOLUTE VALUES CHECK ANSWERS!! Answer : ________ Answer : ________ Answer : ________ Answer : ________ 1st Method: Answer : ________ 2nd Method : (Squaring both sides) If < ,  If > ,  Answer : ________ ** Write your final answer in the form of (i) interval notation OR (ii) solution set

  3. 2) ABSOLUTE VALUE (Inequalities) TIPS : Symbol “ > , ” Symbol “ < , ” rotate clockwise 90o solve solve number line Symbol “ ” Symbol “ ” Answer : _________________ ** if your RHS is a constant  NO extra condition TIPS : EXTRA CONDITION rotate clockwise 90o solve solve solve number line Answer : ___________ ** Write your final answer in the form of (i) interval notation OR(ii) solution set

  4. QA016 G.S A.S GEOMETRIC SEQUENCE ARITHMETIC SEQUENCE TOPIC 3 : SEQUENCES 1) 2) 3) 1) 2) 3) Arithmetic OR OR Geometric

  5. 4.3 - INVERSE OF MATRICES 3methods : ADJOINT MATRIX METHOD, 2 x 2 MATRIX 3 x 3 MATRIX Use the formula : ELEMENTARY ROW OPERATIONS (ERO) ERO AB = k I 4.1 - MATRICES 1) Types of matrices 2) Operations on matrices - ADDITION - SUBTRACTION - SCALAR MULTIPLICATION - MULTIPLICATION OF TWO MATRICES ** Order of matrix : m x nn x p mx p 3) Transpose of matrix , TOPIC 4 (QA016) : MATRICES & SYSTEMS OF LINEAR EQUATIONS 4.2 - DETERMINANT OF MATRICES 1) Minor , Mij 2) Cofactor, Cij 3) Determinant , 2 x 2 MATRIX 3 x 3 MATRIX Method : COFACTOR EXPANSION ** you can expand any rows or columns STEP 6 STEP 1 STEP 2 STEP 5 ** this step is depends on your lecture notes STEP 3 STEP 4 4.4 – SYSTEM OF LINEAR EQUATIONS WITH THREE VARIABLES 2methods : INVERSE MATRIX AX = B A-1AX = A-1B IX = A-1B X = A-1B GAUSS-JORDAN ELIMINATION METHOD

  6. 9.1 Tangent and Normal Equations 9.3 Applications of Differentiation in Economics and Business • Gradient of the tangent , • mT= • 2) Gradient of the normal , • 3) Equation of the tangent : • 4) Equation of the normal : (a) COST, C(x) QA016 TOPIC 9 : Applications of Differentiation 1) Cost Function , C(x) = fixed cost + variable cost 2) Average cost function , 3) Marginal cost function, (b) REVENUE, R(x) 1) Revenue Function , 2) Average revenue function , 3) Marginal revenue function, 9.2 Extremum Problems First derivative : or 1st method 2nd method : First derivative test 3rd method : Second derivative test (a) Determine the stationary points (c) PROFIT, (b) Determine the intervals where the function is increasing/decreasing 1) Profit Function , 2) Average profit function , 3) Marginal profit function, (c) Determine the maximum/minimum point • find minimum cost , maximum revenue and maximum profit by using second derivative test.

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