NATIONAL SENIOR CERTIFICATE EXAMINATION MATHEMATICS JUNE EXAMINATION 05 GRADE 0 PAPER MARKS : 00 TIME: HOURS This paper consists of 7 pages.
Mathematics MDoE/June Eam 05 INSTRUCTIONS: Read the following instructions carefully before answering the questions.. This question paper consists of 8 questions. Answer ALL the questions.. Clearly show ALL calculations, diagrams, graphs, etcetera that you have used in determining the answers. 3. Answers only will not necessarily be awarded full marks. 4. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise. 5. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise. 6. Diagrams are NOT necessarily drawn to scale. 7. Number the answers correctly according to the numbering system used in this question paper. 8. It is in your own interest to write legibly and to present the work neatly. Copyright reserved
Mathematics 3 MDoE/June Eam 05 QUESTION. Show that 3.5 6 is a rational number (3). Determine between which two integers 5 7 lies. (3).3 Find the product of ( 3y)( 3y + 7y ) and simplify your answer (3).4 Simplify:.4. (4) 3.4. 4 (3) n n.4.4.3 n 6. (3).5 Show that 3 can be simplified to 3 4 QUESTION. Solve for :. (3) [].. ( + 5) 3( +) = 9 (4).. 3.5 - = 5 (). Solve for and represent your answer on a number line: 5 3 < 9 (4).3 The formula for the total surface area of a cylinder is given by: SA = rh + r Make H the subject of the formula: ().4 Three rulers and five pencils cost R6. One ruler and two pencils cost R0. Let the cost of a ruler be rand and the cost of a pencil be y rand..4. Write down a system of equations, in terms of and y that reflect the above mentioned situation. ().4. Solve the system of equations in QUESTION.4. simultaneously and state the cost of a ruler and the cost of a pencil. (4) [8] Copyright reserved
Mathematics 4 MDoE/June Eam 05 QUESTION 3 3. As a start Linda earns R400 per month as a sales assistant. Each month thereafter she receives a R40 increase. 3.. Write down what Linda will earn each month for the first three month (3) 3.. Write down a formula for the amount she earns after n months. () 3..3 How much will Linda earn after one year? () 3. A pattern of rectangular and triangular shapes is constructed as follows: Figure Figure Figure3 3.. Calculate the total number of arrows in the first four figures () 3.. Determine the number of arrows in the th n figure in the form... T n () 3..3 Which figure will have eactly 43 arrows? (3) [4] QUESTION 4 4. In the triangle given below, find the value of cos and the size of angle. () 9 5 4. 5 If sin =, 3 ( 0 < < 90 o ), determine each of the following without the use of a calculator: 4.. tan (3) 4.. sin + cos () 4.3 Without using a calculator, find the value of: cos 45 sin 30 (3) 4.4 If = 37 0 and y = 4 0, use your calculator to determine the value of the following correct to one decimal place the value of sin ( + y) () [] Copyright reserved
Mathematics 5 MDoE/June Eam 05 QUESTION 5 5. In the diagram below, AD BC and AB AC. A B D C Write down TWO ratios for each of the following: 5.. sin B () 5.. cos B () [4] QUESTION 6 6. Calculate with reasons the value of in the diagram. The diagram consists of straight lines. Line AB // CD E H A T + 30 B C K D G F (3) Copyright reserved
Mathematics 6 MDoE/June Eam 05 6. ABCD is a parallelogram with diagonals AC and BD intersecting at O. A B O D C Prove that: 6.. AOB DOC (4) 6.. The diagonals bisect each other () QUESTION 7 Given functions g ( ) 9 and f ( ) 6 7. Draw f and g on the same system of aes. (4) 7. Calculate the values of for which f() g(). (4) 7.3 Hence or otherwise, use your graphs to write down the values of for which 7.3. g( ) f ( ) () 7.3. g ( ) 0 () 7.4 Give the equation of the reflection of g in the ais. () [3] [9] Copyright reserved
Mathematics 7 MDoE/June Eam 05 QUESTION 8 8. The graph of f () = and k g( ) are represented below. The graphs intersect at A. y f A(; ) g 0 Answer the following questions by using the graphs. 8.. What is the domain of f? () 8.. Give the equation of the asymptote of the graph of y =. () 8..3 What is the value of k? () 8. Sketched below are the graphs of g ( ) cos and f ( ) sin for [ 0 ; 360] y g 90 80 70 360 - f - Write down the amplitude of the following: 8.. g () 8... f () 8.3 For which value(s) of is f decreasing for [ 0 ; 360]? () TOTAL: 00 marks [8] Copyright reserved
NATIONAL SENIOR CERTIFICATE MATHEMATICS/WISKUNDE JUNE EXAMINATION JUNIE EKSAMEN 05 GRADE/ GRAAD 0 MEMORANDUM MARKS/ PUNTE : 00 TIME/ TYD : H
Mathematics/ Wiskunde MDoE/June/Junie Eamination/Eksamen 05 QUESTION/VRAAG. Let / stel 3,565656556...( ) 00 00 356,5656...... :99 353 99 353 353 99. 5 7 75 75 answer/ antw. 75 (3) 69 75 3 75 4 96 method/ metode answer/ antw. 5 7 lies between/ lê tussen 3 and/en 4.3 ( 3y)( 3y 7y ).4. ( 3y 7y ) 3y( 3y 7y ) ( 3y + 7y ) 3y( 3y + 7y ) 3 3 4 6 y 4y 6y 9y y 3 3 4 y 3y y 3 ( )( ) ( ) ( ) (3) 4 3 and/en y 3 6 y 4y 6y 9y answer/ antw. ( )( ) simplification/ vereenvoudiging (3) answer/antw. (4)
Mathematics/ Wiskunde 3 MDoE/June/Junie Eamination/Eksamen 05 ( ) ( ).4..4.3 = 4 = = 4 ( ( ). 4 n n n 6. n 4n )( ) n.. n n 4n ( ) factors/faktore answer/antw. (3) (n+) and/en 4n method/ metode answer/antw. (3).5 ( ) ( 3) ( -) ( 3) [( ) ( 3)][( ) ( 3)] ( 3)( 3) ( )(3 4) QUESTION/ VRAAG.. ( 5) 3( ) 9 0 3 6 9 0 7 5 0 ( 3)( 5) 0 3 0 or 5 0 [ ( ) ( 3)] [( ) ( 3)] simplification/ vereenvoudiging (3) simplification/ vereenvoudiging [] standard form/ stdvorm factors/ faktore answer (both -values)/ Antw. (beide -waardes)
Mathematics/ Wiskunde 4 MDoE/June/Junie Eamination/Eksamen 05 3 or / of 5 (4).. 3.5 5 5 5. 5 3 9 5 5 answer/ antw. () 5 3 9 3 method/ metode 6 6 3 3 change of inequality sign when divided by -/ verander die ongelykheids teken sodra deling deur - plaasvind.3 SA = rh + r SA r = rh SAr H r -3 - value of / waarde van correct representation on number line/ korrekte voorstelling op getallelyn (4) SA r = rh answer/ antw. ().4. 3 5y 6 3 5y 6 y 0 y 0 ().4. 3 5y 6...(i) y 0...(ii) equation (iii)/
Mathematics/ Wiskunde 5 MDoE/June/Junie Eamination/Eksamen 05 From/ van (ii) 0 y...(iii) Substitute/ vervang (iii) into/ in (i) 3(0 y ) 5y 6 30 6y 5y 6 y 4 vergelyking(iii) substitution/ vervanging y 4y = 4 From/ uit (iii) 0 (4) A ruler cost R and a pencil cost R4 n Liniaal kos R en n potlood kos R4 y = 4 = QUESTION/ VRAAG 3 3.. 400; 440 ; 480 440 480 () 3.. T n = 40n + 360 40n 360 () 3..3 T n = 40n + 360 substitute/vervang n = T () = 40() + 360 answer/antw. () = R 840 3.. 8; ; 4;.... The number of arrows increases by 3/ Die aantal pyle vermeerder met 3 i.e the sequence is/ die ry is 8; ; 4; 7 forming the sequence/ vorming van ry (4) [8] Sum of arrows in st 4 figures/ som van pyle in die eerste 4 figure is: = 8 + + 4 + 7 = 50 adding the sequence/ optel van ry answer/ antw. (3) 3.. The common difference is 3. Die algemene verskil is 3. method/ metode answer/ antw. () [Give full marks for answer only i.e. T n 3n5] [ Gee volpunte indien slegs
Mathematics/ Wiskunde 6 MDoE/June/Junie Eamination/Eksamen 05 T 3 T 3 T 3 3 T n 3 58 5 54 3n 5 die antwoord neergeskryf het] 3..3 T n 3n5 3n5 43 3n 38 n 46 Figure 46 will have 43 arrows. formula/ formule 3n 5 43 answer/ antw. (3) Dus sal figuur 46, 43 pyle gebruik. [4] QUESTION/ VRAAG 4 4. cos 9 cos 9 = 68, 0 answer/antw. () 4.. 3 5 tan 5 sketch/ skets = answer/antw. (3) 4.. sin cos 5 3 3 5 44 69 69 substitution/ vervanging answer/ antw. () 4.3 cos 45 sin 30 =
Mathematics/ Wiskunde 7 MDoE/June/Junie Eamination/Eksamen 05 4.4 sin37 4 answer/antw. (3) sin 6 substitution/ vervanging,75 answer/ antw. () [] QUESTION/ VRAAG 5 5.. AD sin B AB sin B AC BC sin B AD AB AC sin B () BC 5.. BD cos B AB BD cos B AB cos B AB BC AB cos B () BC [4] QUESTION/ VRAAG 6 6. ATE = 3.(Alts, vert.opp. s AB// CD,) (Ooreenk e, AB //CD) ATE + ETH + HTB = 80 o (sum of s on a str. Line/ 3 + + ( + 30 o ) = 80 o 5 + 30 o = 80 o 5 = 50 o ( op rtlyn) ATE = 3 ( statement & reason)/ (stelling en rede) 3 + + ( + 30 o ) = 80 o (statement & reason)/ (stelling en rede) answer/ antw. (3) = 30 o
Mathematics/ Wiskunde 8 MDoE/June/Junie Eamination/Eksamen 05 6.. AOB and/ en DOC A = C.(Alts/ verw. s AB// DC) B = D.(Alts/ verw. s AB// DC) AB = DC (Opposite sides of a parallelogram/ teenoorst sye parm) AOB DOC (,, S) statement & reason /stelling en rede statement & reason Stelling en rede statement & reason/ Stelling en rede answer / antw. (4) AOB DOC (Proved/ bewys in 6..) In AOB AO = OC from congruency/ uit kongruensie statement & reason/ Stelling en rede answer/ antw. () DO = OB from congruency/ uit kongruensie the diagonals bisect each other/ hoeklyne halveer mekaar. [9] QUESTION/ VRAAG 7 7. 9 y 6 g and y-intercepts of g/ en y-as afsnit van g f and y-intercept of f/ X en y-as afsnit van f -3 0 3 shape of g/ vorm van g shape of f/ vorm van f (4)
Mathematics/ Wiskunde 9 MDoE/June/Junie Eamination/Eksamen 05 7. f ( ) g( ) 9 6 3 0 3 0 ( 3)( ) 0 9 6-3 0 factors/ faktore 3 or both -values Beide -waardes (4) 7.3. 3 critical values - & 3 Kritiesepunte - en 3 correct inequalities Korrekte ongelykhede () 7.3. 3 3 critical values -3 & 3 7.4 After reflection in the -ais g will become/ na refleksie in -as g ( ) ( 9) or g ( ) 9 Kritiesepunte -3 en 3 correct inequalities Korrekte ongelykhede () answer/antw. QUESTION 8 8.. R answer/antw. () 8.. y = - answer/antw () 8..3 k substitution/ vervanging () [3] k answer / antw. () 8.. Amplitude = answer/antw. () 8.. Amplitude = answer / antw. () 8.3 90 70 critical values/ kritiese punte correct inequalities Korrekte ongelykheids
Mathematics/ Wiskunde 0 MDoE/June/Junie Eamination/Eksamen 05 tekens () [8] TOTAL/ TOTAAL: 00 Marks/ Punte