JUST IN TIME MATERIAL GRADE 11 KZN DEPARTMENT OF EDUCATION CURRICULUM GRADES DIRECTORATE TERM

Transcription

1 JUST IN TIME MATERIAL GRADE 11 KZN DEPARTMENT OF EDUCATION CURRICULUM GRADES 10 1 DIRECTORATE TERM This document has been compiled by the FET Mathematics Subject Advisors together with Lead Teachers. It seeks to unpack the content and give more guidance to the teachers. 1

2 TABLE OF CONTENTS TOPIC PAGE EXPONENTS & SURDS 3-7 EQUATIONS,INEQUALITIES 8-16 & NATURE OF ROOTS NUMBER PATTERNS 17-1 ANALYTICAL GEOMETRY - 3 REFERENCES 3

3 EXPONENTS & SURDS DATES 11/1 13/1 (3 days) 16/1 0/1 (5 days) 3/1 5/1 (3 days) % COM- CURRICULUM STATEMENT PLETED 1. Simplify epressions using the laws of eponents for rational eponents where %. Solve equations using the laws of eponents for rational eponents where 3. Add, subtract, multiply and divide simple surds. 4. Solve simple equations involving surds. 8% 6% MARCH COMMON TEST WEIGHTING Eponents and surds 1±3 marks out of 75marks CAPS EXAM GUIDELINE WEIGHTING FOR FINAL EXAMINATION Algebra, Equations (and inequalities) 45 ± 3 marks out of 150marks TERMINOLOGY-use of correct terminology EXPONENT/INDEX POWER BASE NB: To be read as eponents 3 or inde 3 NOT to the power 3 DEFINITION Definition: indicates the number of times the base must multiply itself (check grade 9 CAPS document) use numbers ONLY (include negative integers) use variables ONLY use numbers and variables TOGETHER to eplain further 3

4 REVISION OF THE RULES AND LAWS OF EXPONENTS: Book work : Ensure that concept is understood completely by learners Use numbers only, variables only, numbers and variables together for all laws and rules as eamples. Also give eamples of powers with rational eponents and numerical surds. Emphasise and eplain and Eplain difference between but MISCONCEPTIONS OF LAWS EXERCISE 1 (NUMERICAL) 1. Evaluate, without using a calculator: EXERCISE (VARIABLES). Simplify the following:

5 EXERCISE 3 (NUMBERS AND VARIABLES) 3. Simplify the following: EXERCISE 4 (ADDITION AND SUBTRACTION) 4. Simplify the following: EXERCISE 5 (MULTIPLICATION AND DIVISION) 5. Simplify:

6 SURDS RULES Before we begin our lessons on surds, we look at some properties of roots. SURDS RULES Ø Ø Ø Ø Ø MISCONCEPTIONS Ø Ø EXERCISE 6 6. Simplify: Show that : can be written as 6

7 EQUATIONS OF EXPONENTS AND SURDS If bases and eponents are not the same, we can NOT add or subtract (i.e. ) but. EXERCISE 7 7. Solve for the unknown:

8 EQUATIONS & INEQUALITIES ATP REFERENCE 6/1 03/ (7 days) 06/ 10/ (5 days) 13/ 17/ (5 days) 1. Quadratic equations (by factorisation ).. Complete the square. 3. Quadratic equations (by using the quadratic formula). 4. k - method 5. Quadratic inequalities in one unknown. (Interpret solutions graphically.) 6. Equations in two unknowns, one of which is linear and the other quadratic. 7. Nature of roots. 13% 17% 0% MARCH COMMON TEST WEIGHTING Equations and inequalities 3±3 marks out of 75marks CAPS EXAM GUIDELINE WEIGHTING FOR FINAL EXAMINATION Algebra Equations (and inequalities) 45 ± 3 marks out of 150marks HINTS TO LEARNERS: SOLVING QUADRATIC EQUATIONS. (a) Simplify until one side is zero. (b) Factorise the quadratic equations and get two solutions. You may check your answers. (c) When the question instruct you to correct to certain decimal places, then you may use the quadratic formula or by completing the square. (d) For the inequality, refer to (a). (e) Interpret solutions graphically or in a number line. (f) Don t cross multiply against an inequality sign. When doing that you will loose solution Solve for by factorisation = 0 () ( 1) = 1 (3) = 4 (4) 8

9 1.. Solve for by completing the square = 0 (4) 11 4= 0 (5) 3 = 4+ 8 (5) 1.3. Solve for by squaring both side or introducing a square root on both sides = + 4 (5) = (5) ( 3) = 4 (5) ( ) = 3 (CORRECT TO TWO DECIMAL PLACES) (4) 1.4. Solve for by using a quadratic equation = 0 (4) 3 = ( + ) (4) = 5 (5) 1.5. Solve for in an inequality problem < 0 (3) ( )(4 + ) 0 (4) (4) ( ) < 0 (3) 1.6. Solve for by k method = 0 (4) 4 4 (5) = (7) 3 Show that there are ONLY TWO real solutions. (6) 9

10 HINTS TO LEARNERS: SIMULTANEOUS EQUATIONS Make or y the subject of the formula in the linear equation. Avoid solving for and y if it has a co-efficient other than one. Ensure after substitution you have an equation in 1 variable or y not both. Then solve the quadratic equation. Substitute these values (from 40 in either equation to get the corresponding values. It is advisable to substitute into the equation obtained in 1 (Changing the subject of the formula) Solve for and y simultaneous y and 3 y ( y) ( ) = + = (7) = 0 (4) y = and y y + = 1 (6) 3y+ 5= 0 and 3 y = 7 (6) EXAM TYPE QUESTIONS QUESTION Solve for in each of the following: = 0 (3) = 1 (5) Given: 7 = (4) 8< 0 (3) f ( ) = Solve for if f( ) = 0 (correct to TWO decimal places.) (4) 1.. Hence, or otherwise, calculate the value of the d for which d = 0 has equal roots (3) 1.3 Solve for and y simultaneously: y = 3 and y = 0 (6) 10

11 QUESTION.1 Solve for in each of the following:.1.1 (3 5) = 0 ().1. 3 = 7 (Give answer correct to TWO decimal places) (4) = 3 (6).1.4 (3 + 1) < 0 (3). Calculate, without using a calculator (3).3 Solve for and y simultaneously: y = 3 and + 5y + y = 15 (6) QUESTION Solve for (to decimals if necessary) () 3.1. (4) (4) (3) 3. Solve for and y simultaneously: 3.3 Calculate, without using a calculator, the value of a and b if a and b are integers and: (7) (4) 11

12 QUESTION Solve for : = 0 (3) = (4) < 0 (3) = 0 (4) 4. Solve for and y if y = + and + y = 0. (6) 4.3 Solve for if 7 4 y + y = 0. (correct to decimal places). (4) y QUESTION Solve for () 5.1. (correct to TWO decimal places) (4) (4) 5. Solve for and simultaneously if: and (5) 5.3 The solution of a quadratic equation is given by: Determine the largest integral value of -values will be rational. for which these (3) 5.4 Determine the value(s) of a for which the graphs of and will not intersect each other. (5) 1

13 WHAT TO BE NOTED WHEN TEACHING THE NATURE OF ROOTS: o The eplanation of the term roots, has to be linked with the -intercepts of a quadratic function (parabola). o Methods that are used to calculate the roots of a quadratic equation are: (i) FACTORISATION (ii) COMPLETING A SQUARE (iii) QUADRATIC FORMULA Ø Epected types of solutions when calculating the roots of quadratic equations are as follows: (i) REAL OR NON-REAL (ii) RATIONAL OR IRRATIONAL (iii) EQUAL OR UNEQUAL The above can be illustrated as follows: COMPLEX NUMBERS REAL NUMBERS RATIONAL NUMBERS NNNUNUMBERS IRRATIONAL NUMBERS NON-REAL NUMBERS 4; 100; 5 7 ; 3; 5; 5 8; ; 8-4; -8; -100 THE DISCRIMINANT Ø The discriminant is represented by the symbol which is called delta Ø which is found within the square root sign of the quadratic formula Ø It is used to determine the nature of roots of any quadratic equation Ø When determining the nature of the roots of a quadratic equation,, it should be noted that a, b, and c should be elements of rational numbers. 13

14 Ø If Roots are real 0 = perfect square perfect square (p and q 0) (p and q Q) = 1;4;9;16p² = 10; ; 3p² + = 5p²q² = 0 = p², (p 0) = 4(p-q)², p q = (p-q)², (p q) Roots: Rational and Roots: Rational and Roots: Irrational and unequal equal unequal Ø If b² - 4ac < 0 Roots are non-real or imaginary Eamples = -1 ; - ; -9 ; -100 OR = -p² ; -4q², where (p and q) 0 OR = 4(p q)², where (p q) Ø Note the following: ROOTS DISCRIMINANT Real 0 Equal = 0 Real and Unequal > 0 Rational = perfect square OR = 0 Irrational > 0 and not a perfect square Non-real/Imaginary < 0 SUMMARY When answering questions based on the nature of roots the following should be done: v Write the equation in a standard form which is a² + b + c = 0 v Calculate the value of the discriminant v Three types of questions may be asked: (i) Determine the nature of roots of the given quadratic equation (ii) Determine the value of the unknown while the nature of roots is given (iii) Prove or show the nature of roots of the given quadratic equation where sometimes completing of a square will help 14

15 Ø The quadratics function and the nature of roots(eamples) ü Equal Roots Y Y 0 X 0 X ü Unequal Roots Y Y 0 X 0 X ü Non-real Roots Y Y 0 X 0 X 15

16 EXERCISES 1. Complete the table indicating the value of and the nature of roots in each case The roots Real/ Imaginary Rational/ Irrational Equal/ Unequal. Determine the nature of the roots of the following equations without solving:.1 (3). (3) 3. Determine for which value of, will have two equal roots? 1 4. For which values of will y be real if: y =? () Given ( ) = f. Calculate the value of d for which d = 0 has equal roots. (3) 6. Given: P = For what value(s) of will P be a real number? () 6. Show that P is rational if = 3. () 7 The solutions of a quadratic equation are given by For which value(s) of p will this equation have: 7.1 Two equal solutions () 7. No real solutions (1) 8. Given that, solve for if: a) () b) () c) () d) is non real () 16

17 NUMBER PATTERNS 0/ 0/3 (9 days) 1. Revise linear number patterns.. Investigate number patterns leading to those where there is a constant second difference between consecutive terms, and the general term is therefore quadratic. 6% MARCH COMMON TEST WEIGHTING Number Patterns 15±3 marks out of 75 marks CAPS EXAM GUIDELINE WEIGHTING FOR FINAL EXAMINATION Number Patterns 15±3 marks out of 150marks HINTS & STRATEGIES Ø Discuss terminology e.g = first term OR = general term and is often epressed as the term of a sequence, is always the natural number Ø Emphasize the relationship between linear function (general term) and linear sequence. Ø Do not use the formula for arithmetic sequences (. Ø Emphasize the relationship between the number quadratic functions (general term and quadratic sequence) Ø Key activity in mathematical description of pattern: finding the relationship between the number of the term and the value of the term. Arithmetic (Linear) Sequence (DONE IN GRADE 10) Ø Has general term: where is the constant difference Quadratic sequence Ø Has general term: Half the second difference a constant the position of the term in the sequence (ie: Term 1, Term, ) Ø If the sequence is quadratic, the term is of the form 17

18 Steps to writing an epression for the n th term of a quadratic sequence: 1. Calculate the first and second difference. If the first difference is constant the sequence is linear.. Calculate 3. Solve for b and c simultaneously by substituting two terms into the general equation. An alternative method of finding the general term of a quadratic sequence is by using the following formula: first term 1 st term of first difference second difference EXERCISES The sequence 3 ; 9 ; 17 ; 7 ; is quadratic. 1.1 Determine an epression for the n-th term of the sequence. (4) 1. What is the value of the first term of the sequence that is greater than 69? (4) In the sequence are the first four terms. Determine the values of and if the sequence is linear. (3) 3 Given the sequence 3; 6; 13; 4;. 3.1 Derive the general term of this sequence. (4) 3. Which term of this sequence is the first to be greater than 500. (5) 4 Given the linear pattern: 5 ; ; 9 ;... ; Write down the constant first difference. (1) 4. Write down T 4. (1) 4.3 Calculate the number of terms in the pattern. (3) 18

19 5 A linear pattern has a difference of 3 between consecutive terms and its 0 th term is equal to 64 ( T 0 = 64) Determine the value of T. (1) 5.. Which term in the pattern will be equal to 3T 5? (4) 6 Consider the quadratic pattern: 5 ; 1 ; 9 ; 56 ; Write down the net two terms of the pattern. () 6. Prove that the first differences of this pattern will always be odd. (3) 7 Consider the quadratic pattern: 3 ; 5 ; 8 ; 1 ;... Determine the value of T 6. (6) 8 A certain quadratic pattern has the following characteristics: T 1 = p T = 18 T 4 = 4T 1 T 3 T = 10 (6) Determine the value of p. 9 You are given the following sequence: P = -8 ; -4 ; difference where P has a linear pattern with a constant first Write down the net term of P and hence determine the n th term. (3) 9.1. Which term of P is the number 38? (3) 10 A sequence has a common second difference of 4 between terms. The first two terms are 3 and Write down the 3 rd and 4 th terms. () 10. Determine the n th term. (6) 10.3 Hence, determine the 50 th term. () 19

20 10.4 Calculate how many terms have a value less than 8. (5) 11. Given the first four terms of a quadratic sequence: Calculate. Show ALL working. (9) 1. Given the sequence: Assuming that this pattern remains consistent, write an epression for the nth term of the sequence () 13 The first three figures of a pattern comprising dots and sticks are shown 13.1 Write down the number of dots and the number of sticks in the fourth figure. 13. Determine epressions in terms of for each the number of dots and the number of sticks in the figure. (4) dots are available to make a figure in the sequence. Calculate how many sticks will be needed for this figure (4) 13.4 An athlete runs 0 km on a certain Monday. Thereafter, he increases by 10% everyday. Calculate the number of kilometres he ran on the following Saturday. () 14. The second term of a quadratic sequence is equal to 1. The third term is equal to and the fifth term is equal to 14.1 Determine the second difference of the quadratic sequence. (5) 14. Hence, determine the first term of the quadratic sequence. () 0

21 15. Cells are continually dividing and thus increasing in number. A cell divides and becomes two new cells. The process repeats itself forming a particular sequence. The following sketch represents cell division. Stage 1 Stage Stage 3 v Stage How many cells will there be altogether after twenty stages? 15. How many cells will there be altogether after stages? 15.3 What type of relationship eists between the two variables (the stage and the number of cells)? 16. The following sequence of numbers forms a quadratic sequence: - 3 ; - ; - 3 ; - 6 ; - 11 ; The first differences of the above sequence also form a sequence. Determine an epression for the general term of the first differences. (3) 16. Calculate the first difference between the 35 th and 36 th terms of the quadratic sequence. () 16.3 Determine an epression for the n th term of the quadratic sequence. (4) 16.4 Eplain why the sequence of numbers will never contain a positive term. () 1

22 ANALYTICAL GEOMETRY 03/3 08/3 (4 days) 09/3 15/3 (5 days) 1. The equation of a line through two given points.. The equation of a line through one point and parallel or perpendicular to a given line. 3. Collinear lines 4. The inclination (θ) of a given line. 5. Applications. 9% 3% MARCH COMMON TEST WEIGHTING Analytical Geometry 5±3 marks out of 75 marks CAPS EXAM GUIDELINE WEIGHTING FOR FINAL EXAMINATION Analytical Geometry 30±3 marks out of 150 marks Formulae distance formula ( 1 ) + ( y1 y) midpoint formula 1+ 1 ; + y gradient of a straight line y1 y 1 i.e. the average of ( 1; y1) and ( ; y ) equation of a straight line - y = m + c - a + by + c = 0 - y y1 = m( 1) NB: Learners must know the equations of the vertical and horizontal lines e.g =a for a vertical line and y=b for a horizontal line. Learners must know that a vertical line and a horizontal line intersect at an angle of 90. A vertical line is a perpendicular to the -ais and a horizontal line is perpendicular to the y-ais. Learners must also be able to find the gradient given the equation of a line but making sure they make y subject of the formula first. parallel lines have equal gradients i.e. m1 = m perpendicular lines have negative inverse gradients i.e. m1 m = 1

23 angle of inclination m= tan θ 1. angle of inclination when the gradient of the line is positive (m 0). angle of inclination when the gradient of the line is negative (m 0) 3. using angle of inclination to determine the angle between two lines. collinear points (lying on a straight line) ( ) m = m = m AB BC AC - A, B, C are collinear if NB: Learners should know the formulae by heart. GRADE 10 REVISION EXERCISE Eercise 1 1) Determine the lengths of the line segments joining the following points: a) A(;-5) and B(-1;-8) b) P(5;5) and Q(-;3) c) S(10;-6) and R(-3;) d) M(-1;-5) and N(1;-10) ) Determine the midpoints of the line segments joining the following points: a) A(;-5) and B(-1;-8) b) P(5;5) and Q(-;3) c) S(10;-6) and R(-3;) d) M(-1;-5) and N(1;-10) 3) Determine the gradients of the line segments joining the following points: a) A(;-5) and B(-1;-8) b) P(5;5) and Q(-;3) 4) In triangle ABC, with A(4;6), B( ; y) and C(-4;-6), P(5;1) is the midpoint of AB. Determine : a) The coordinates of point B. b) The perimeter of the triangle. c) If the triangle is right-angled. 5) Determine two possible values of if AB is units and A is the point (4;6) and B is the point (;-5). 6) Determine if AB and CD are parallel, perpendicular or neither given the points: a) A(-8;-4) and B(;4) and C(-4;0) and D(-0;0) b) A(5;6) and b(4;) and C(8;4) and D(4;8) 7) Determine whether or not the points A(-5;-7) and B(4;11) and C(8;59) are collinear. 3

24 8) If A is the point A(;3) and B is the point B(-;y), determine the values of : a) if AD is perpendicular to the line y=-3+6 and D is the point D(4;) b) and y if the midpoint of AB is (1;6) 9. In the diagram below, a kite, ABCD is drawn 9.1.1) Calculate the length of BC and leave your answer in simplest surd form. 9.1.) Prove that DB AC 9.1.3) Hence, determine the coordinates of E, the midpoint of DB ) Determine the equation of AC 10 Calculate the value of in each of the following cases if K, I, N and G are the points K (-; 3), I (1; 4), N (-4; 1) and G(; 4). 10.1) KI NG 10.) KI NG 10.3) I, N and G are collinear. 4

25 Grade 11 Classroom Eercises 1. ΔABC has vertices A( 3; 5), B( 1;7) and C(4; 3). Determine: 1.1 the coordinates of the midpoint, M, of AB. 1. the equation of CM, the median from C. 1.3 the gradient of BC. 1.4 the equation of the altitude, AP, from A. 1.5 the equation of the perpendicular bisector, KL, of BC.. BP is a median of ΔABC..1 Find the coordinates of P.. Determine the equation of BP..3 Show that BP does not pass through the origin..4 If CD//PB, find the coordinates of D. Grade 11 Further Eercises 1. A(-4;1), B(;5) and C(6;-3) are the coordinates of ΔABC. M and N are the midpoints of AB and BC respectively. 1.1 Calculate: the gradient of AB 1.1. the angle of inclination of AB, correct to 1 dec. pl the gradient of AC the angle of inclination of AC, correct to 1 decimal place. A(-4;1) M y B(;5) N the acute angle between AB and AC the coordinates of M and N. C(6;-3) 1. Show that AC is twice the length of MN. 5

26 . Find the equation of the line:.1 parallel to the line y= 1, through (4;15).. perpendicular to y= 1, through ( 6;1)..3 through ( 4;7), parallel to the y ais. 3. P(;5), Q(-3;1) and R(5;-3) are the coordinates of ΔPQR. 3.1 Calculate the coordinates of S, the midpoint of QR. 3. Find the equation of the median from P. 3.3 What is the gradient of QR? y P(;5) 3.4 Give the gradient of a perpendicular to QR. 3.5 Find the equation of the perpendicular bisector of QR. Q(-3;1) S R(5;-3) 3.6 Find the equation of the altitude from P. 4. A triangle has vertices A( 4;3), B(0;1) and C( 3; ). Calculate: 4.1 the equation of the altitude CG, in the form y = m+ c. 4. the coordinates of point G if G is on AB. 4.3 the size of ˆ ACB, correct to 1 decimal place. 4.4 the coordinates of D, the fourth verte of parallelogram ABCD 1.4. ABDC ADBC A(-4;3) C(-3;-) y B(0;1) 6

27 5. A( 4; 1 ), R( ;3 ), M( 6; 3) are the vertices of a triangle in the Cartesian plane. 5.1 Calculate the coordinates of S, the midpoint of AM. 5. Calculate the length of RA, leaving your answer in simplified surd form. 5.3 Show that Δ ARM is right-angled. 5.4 Show that RAM ˆ = 45, giving reasons. 6. A1;8, ( ) B1;6, ( ) C6; ( 4 ) and D( 5; ) are the vertices of quadrilateral ABCD. 6.1 Show that ABCD is a parallelogram. 6. Determine whether ABCD is a rhombus. M y A(1;8) B(1;6) 6.3 Find the co-ordinates of M, the midpoint of AD. D(-5;-) 6.4 Determine the equation of the median CM, of ΔACD, giving the equation in the form y = m+ c. C(6;-4) 7. K(-8;-1), L(0;5) and M(9;-7) are the vertices of ΔKLM. θ is the angle of inclination of KL. 7.1 Calculate θ, correct to one decimal place. 7. Prove that ΔKLM is right-angled. y L(0;5) 7.3 Find the area of ΔKLM. 7.4 Find the equation of altitude LP. 7.5 Calculate the size of ˆ LKM, correct to 1 decimal place. K(-8;-1) P M(9;-7) 7

28 8. A(0;), B( 5; 3), C (; ) and D( ; y ) are the vertices of parallelogram ABCD. The -intercept of AB is H ( k ;0). CD cuts the -ais at J and makes an angle of θ, as indicated, with the -ais. y 8.1 Determine the gradient of CD. 8. Calculate the size of θ, correct to one decimal place. 8.3 Determine the value of k. B( 5; 3) A (0;) 8.4 Determine the numerical values of the coordinates of D. H ( k ;0) O θ J C(; ) D ( ; y) 8.5 Prove that ΔABC is isosceles. 8.6 What type of quadrilateral is ABCD? Give a reason for your answer. 8.7 Prove this by another method. 9. Lines AB and AC cut the -ais at D and E respectively. The equation of line AB is y = 6 and the equation of line AC is y = + 1. BC produced cuts the -ais at F. G ( ab ; ) is a point in the Cartesian plane. Calculate: 9.1 the coordinates of A. 9. the magnitude of ˆ AEF. y A G ( ab ; ) 9.3 the gradient of line BF, correct to two decimal places, if ECF ˆ = the coordinates of points D and E. O D B (; ) E C F 9.5 the values of a and b if AG is a horizontal line and BG AC 8

29 GRADE 11 Typical past eam question 1. ABCD is a quadrilateral with vertices A(;5), B( 3; 10); C( 4;3) and D(1; ). B( 3 ; 10) y M A( ; 5) C( 4 ; 3) < θ O β > D(1 ; ) 1.1 Calculate the length of AC. (Leave the answer in simplest surd form.) () 1. Determine the coordinates of M, the midpoint of AC. () 1.3 Show that BD and AC bisect each other perpendicularly. (5) 1.4 Calculate the area of ABC. (4) 1.5 Determine the equation of DC. (3) 1.6 Determine, the angle of inclination of DC. (3) 1.7 Calculate the size of A C. (4) 9

30 . In the diagram below, trapezium ABCD with AD// BC is drawn. The coordinates of the vertices are BC intersects the -ais at F..1 Calculate the gradient of AD (). Determine the equation of BC in the form of (3).3 Determine the coordinates of F ().4 Show that (4).5 Calculate the area of (6) Question 3 PQRS is a parallelogram with as shown below 3.1 Determine the gradient of PQ () 3. Determine the equation of SR (3) 3.3 Determine the co-ordinates of M, the midpoint of PR (3) 3.4 Hence or otherwise, determine the value of and (3) 3.5 Determine the coordinates of E if PE is perpendicular to QR with point E on QR (7) 3.6 Calculate the area of PQRS (5) 30

31 Question 4 Given. M is the midpoint of BA; 4.4 Find the gradient of AD. () 4.5 Write down the gradient of BC () 4.6 Determine the equation of BC (4) 4.7 Write down the coordinates of M () 4.8 Determine the equation of CM (5) 4.9 Determine the coordinates of C. (5) 4.10 Determine the size of (4) Question 5 In the accompanying figure,abco is a rectangle. The length of OA is 6 units and is the midpoint of the diagonal AC. 5.1 Determine the value of A. (1) 5. Write down the coordinates of each of A, B and C (7) 5.3 Determine the value of p in each of the following cases. The straight line with equation Passes through the point (;) () 5.3..Makes an intercept of -4 on the -ais () Is parallel to the -ais (3) 31

32 Question 6 A( 0 ; 5) and B(-8 ; 1) are two points on the circumference of the circle centre M, in a Catersian plane. M lies on AB. DA is a tangent to the circle at A. The coordinates of D are (3 ; -1) and the coordinates of C are (-1 ; -1). Points C and D are joined. K is the point (0 ; -7). CTD is a straight line Determine the equation of CD. (1) 6.. Determine the equation of the tangent AD. (must be done after teaching Euclidean Geometry (4) 6.3. Determine the length of AM. (4) 6.4 Quadrilateral ACKD is one of the following: parallelogram; kite, rhombus, rectangle. Which one is it? Justify your answer. (4) REFERENCES 1. Smith K, Maths handbook and study guide,berlut Books, 01. Eadie A & Lampe G., Mathematics The answers 3. Department of Basic Education NSC Eamination Question Papers & Provincial Trial Eamination Question Papers