Mathematics Grade 11 Eastern Cape Prelim 2024 Paper & Memo

Downloaded from Stanmorephysics.com Province of the Sept Ssiean CAPE EDUG ATION OR TAMBO INLAND DISTRICT NATIONAL SENIOR CERTIFICATE AUGUST TEST GRADE 1i ~ MATHEMATICS MARKS: 50 TIME: 1 Hour This question paper consists of pages, including FORMULA SHEET

Downloaded from Stanmeraphysigs: cam ORTI /2024 Grade 11 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of THREE questions. 2. Answer ALL the questions. 3. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determine your answers. 4. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 5. Answers only will NOT necessarily be awarded full marks. 6. If necessary, round off answers to TWO decimal places, unless stated otherwise. 7. Diagrams are NOT necessarily drawn to scale. 8. Number the answers correctly according to the numbering system used in this question paper. 9. Write neatly and legibly.

Downloaded from Stanmerapkysigs: cam ORTI/2024 Grade 11 QUESTION 1 Consider the function defined by: f(x) = = -3 x+ 1.1 . Write down the equations of asymptotes of f- (2) 1.2 ‘Write down the equations of the axis of symmetry of f- (4) 1.3. The coordinates of the y — intercept of f- (2) 1.4 The coordinates of the x — intercept of f- (3) 1.5 Write g(x) a function resulting from the reflection of f about the x — axis. (3) 1.6 Sketch the graph of f in the DIAGRAM SHEET provided at the end of the question (4) paper. Label all your intercepts, asymptotes and axis of symmetry of the graph. [18] QUESTION 2 The sketches below represent the graphs of functions defined by: f(x) =a sin (bx) and g (x) =— 2 cos (x + 60°) —~ ¥ ‘Ss i> oS > 2 Determine: 2.1 the value of g(69,3°) (2) 2.2 the coordinates of A, the y — intercept of g. (2) 2.3. the value of a in the graph of /- ()

Downloaded from Stanmeraphysigs: cam ORTI /2024 Grade 11 2.4 the period of g. (1) 2.5 the coordinates of D, the turning point of g. (2) 2.6 Determine the values of x, in the given domain, for which g (x) <0 (4) 2.7, Determine the value of Amplitude of g (x) —- Amplitude of f(x) (3) 2.8 Anew function A(x) results for g(x) reflecting about the x axis and shifting 60° to the right. Write down the function h. 3) [18]

Downloaded from Stanmerapkysigs: cam ORTI/2024 Grade 11 QUESTION 3 A large fishing ship got stuck along PSJ coast. For a week 2 small boats A and B have a = been pulling the sheep to no success. The angle of elevation from A and B are 30° and 50°, respectively. The following is a model showing the 25 meter high fishing ship: Boat A 3.1 Write down the size of BCD. qd) 3.2. Calculate the length of BC. (3) 3.3. Determine the length of AB if AABC is isosceles and ACB = 25°. (5) 3.4 Determine the area of ABD. (5) [14] TOTAL: 50

Sownloaded from Stanmeraphysigs: cam ORTI /2024 Grade 11 NAME: GRADE: DIAGRAM SHEET

Downloaded from Stanmeraphysigs: cam ORTI /2024 Grade 11 INFORMATION SHEET pa bE VBE = 4Aac 2a A= P(i+in) A= P(l-in) A= P(1-i)' A=P(1+i)" T, =a+(n=1d S =F Ra+(n-1M] jog =(14E)" -1 T, =ar"™! 5, =a I) el s,=—* » -l<r<l i => pails’ = paal-(+i)" I L “e) = tim ft )- Sf) J'(x)= lim i 2 +X, +2 d= (x, ie) +(y,-y;) m2 em) 2 2 y=met+e yy, =m(x-x,) m=22— 41. m=tan0 Xy-® (x-a) +(y-bY =r? InAABC: —4 Z £ sin A ~ sin B ~ sinC a =b’ +c? —2be.cos A Area AABC = 5a sinC sin(a + B) = sina.cos B + cosa.sinB cos(a + B) = cosa.cos 8 — sina.sin B cos*a — sin?a 1—2sin?a —1 cos2a@ = 2cos? gant y= n sin(a — B) = sina.cosB — cosa.sinB cos(a — B) = cosa.cosB + sina.sinB sin 2a = 2 sina.cosa n o= isl n P(A or B) = P(A) + P(B) — P(A and B) — Le-xXy-5) b= Yi(x-xY

Bovevlarsedofrom Stannrexephysiasscom ORTI AUGUST 2024 ae EASTERN CAPE Department of Education OR TAMBO INLAND MARKS: 50 TIME: 1 HOUR THIS QUESTION PAPER CONSISTS OF FOUR PAPES.

@oveiondedofrom Stannenephysiasescom ORTI AUGUST 2024 Question 1 x=1 v ay ya-3 ¥ (2) 12 |y=(e+1)-3 Method ~ | = x-2 y=x-2Vv lyE -@+N-3 Method ¥ sax 4 y=—x-4Vv (4) 1.3 2 Substitution ¥ iO =4a @s-1) Coordinates V (2) 14) 9 2 3 Substitution x+1 x—value V AG wD) =2 Coordinates ¥ ah a: x=-5 (-7:0) (3) 15 2 vv (2) 9@) = xeit a 1.6 Horizontal Asymptote ¥ Vertical asymptote (4) [18] 2|Page

@oveiondedofrom Stannenephysiasescom ORTI AUGUST 2024 QUESTION 2 2.1. |. g(69.3) = —2 cos(69.3° + 60°) Substitution ¥ =1.27 Answer ¥ (2) 2.2 |A(O;2) or A(O;-1) or A(0;1.9) One mark for any of the three answers ¥ ql) 23 |a=1 Answer ¥ (1) 2.4 | 360° Answer ¥ (1) 2.5 | D(120°; -1) or Any of thetwo ¥ D(120°; 1) . (1) 2.6 | 30°<x < 210° VVVV Accept O0<x<30° or 120°<x< 5 vv or x vv (4) 2.7 | Amp of g =2 Amp of g v Amp of f = 1 ; ial Amp of g — Amp of f =2-1 Answer ¥ (3) =1 2.8 | h(x) = 2cosx or h(x) = —2cosx Three marks for any of the accept two vvv (3) [18] Question 3 3.1 | BCD = 40° ¥ (1) 3.2 eHepia 25 Substitution Vv BC Answer ¥ (3) BC = 32.64m 3.3 | AC = BC = 32.64m AC = BC = 32.64m V¥ ACB = 25° AB? = 32.64? + 32.64? — 2 x 32.64%cos25° Calculations using cosine AB = 14.13m rule VV Answer ¥ (5) 3| Page

Bovavieadernofrom Stansexspkysiasscom ORTI AUGUST 2024 ; 25 a tan50° = — BD BD = 20.98m ¥ BD = 20.98m 25 jo = v tan30° = 7 AD = 25V3m Subst to cosine rule ¥ BDA = 80° v = 447.33m? Answer v (5) [14] TOTAL MARKS 50 4|Page