Everything Maths Grade 11

CHAPTER 8. SOLVINGQUADRATIC INEQUALITIES 8.2 Step 3 : Determine whether thefunction is negative or positive in each of the regio ...

8.2 CHAPTER 8. SOLVINGQUADRATIC INEQUALITIES Step 1 : Subtractx−^13 from both sides 2 x + 3 − 1 x− 3 ≤ 0 Step 2 : Simplify the f ...

CHAPTER 8. SOLVINGQUADRATIC INEQUALITIES 8.2 Solve for x if: 4 (x− 3)^2 < 1. Solve for x: 2 x− 2 x− 3 > 3 Solve for x ...

Solving Simultaneous Equations 9 11.1 Introduction EMBAO In Grade 10, you learnthow to solve sets of simultaneous equations wher ...

CHAPTER 9. SOLVINGSIMULTANEOUS EQUATIONS 9.2 2 4 6 − 2 − 4 − 6 − 8 − 10 − 12 − 14 6 4 − − 2 − 2 4 6 y= 2 x − 4 y = 4 − x 2 (−4;− ...

9.3 CHAPTER 9. SOLVINGSIMULTANEOUS EQUATIONS 10 20 30 40 8 6 − 4 − − 2 − 2 4 6 8 y= − 3 x+ 9 y = x 2 − 9 � � (−6;27) (3;0) Step ...

CHAPTER 9. SOLVINGSIMULTANEOUS EQUATIONS 9.3 For example the solutionof y− 2 x =− 4 (9.2) x^2 + y = 4 (9.3) is: In (9.2) y = 2x− ...

9.3 CHAPTER 9. SOLVINGSIMULTANEOUS EQUATIONS Substitute (9.7) into (9.5): (− 3 x + 9)− x^2 + 9 = 0 x^2 + 3x− 18 = 0 Factorise to ...

CHAPTER 9. SOLVINGSIMULTANEOUS EQUATIONS 9.3 18. a− 2 b + 1 = 0 ; a− 2 b^2 − 12 b + 4 = 0 19. 2 a + b− 2 = 0 ; 8 a + b^2 − 8 = 0 ...

Mathematical Models 10 10.1 Introduction EMBAS Up until now, you haveonly learnt how to solveequations and inequalities, but the ...

CHAPTER 10. MATHEMATICAL MODELS 10.3 10.3 Real-World Applications EMBAU Some examples of where mathematical modelsare used in th ...

10.3 CHAPTER 10. MATHEMATICAL MODELS Example 1: Mathematical Modelling of Falling Objects QUESTION When an object is dropped or ...

CHAPTER 10. MATHEMATICAL MODELS 10.3 Example 2: Another MathematicalModelling of Falling Objects QUESTION When an object is drop ...

10.3 CHAPTER 10. MATHEMATICAL MODELS 0 100 200 300 400 0 10 20 30 40 Time (s) Distance (m) How far does the cartravel in 20 s? ...

CHAPTER 10. MATHEMATICAL MODELS 10.3 Step 4 : Conclusion No, the number of treeswill not increase indefinitely. The number of tr ...

10.3 CHAPTER 10. MATHEMATICAL MODELS Extension: Simulations A simulation is an attempt to model a real-life situation on a compu ...

CHAPTER 10. MATHEMATICAL MODELS 10.3 (d) From your graph, read off how much poweris supplied to the circuit when the current is ...

10.3 CHAPTER 10. MATHEMATICAL MODELS (travelling time). Now deduce that the total cost, C, in Rands, for a 2 000 km trip is give ...

Quadratic Functions and Graphs 11 12.1 Introduction EMBAV In Grade 10, you studied graphs of many different forms. Here you will ...

11.2 CHAPTER 11. QUADRATIC FUNCTIONS ANDGRAPHS (d) d(x) = (x + 1)^2 (e) e(x) = (x + 2)^2 Use your results to deduce the effect o ...