Mathematics Grade 12 Paper 1 KZN Mock 2023 Paper & Memo

Downloaded from Stanmorephysics.com MARKS: 150 TIME: 3 hours KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE N.B. This question pap a COHSBES METZ pag s and an information sheet. ight Reserved Please Turn Over

Mathes Thloaded from Stanmore f sics.com September 2023 Preparatory Examinations INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question/paper consists of 13 questions. 2. Answer ALL questions. 3. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answers. 4. Answers only will not necessarily be awarded full marks. 5. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise. 6. Tf necessary, answers should be rounded off to TWO decimal places, unless stated otherwise. Ts Diagrams are NOT necessarily drawn to scale. 8. Number the answers correctly according to the numbering system used in this question paper. Write neatly and legibly. Copyright Reserved Please Turn Over

Mathes Thloaded from Stanmore E sics.com September 2023 Preparatory Examinations QUESTION 1 1.1 Solve for x: | (2) 1120 te3y=7 (write your answer to two decimal places). (4) L130 x—5r44>0 3) 114 3*-10.3'+21=0 ©) 1.2 Solve simultaneously for xand y : (6) xt+y=2; w4+y+6x=4y-4 1.3 +95 _72 The roots of a quadratic equation are x= =a : For which values of n will the roots be equal? (3) [23] QUESTION 2 2.1 Consider the arithmetic sequence: See 5 see 99. 2.1.1 | Determine the twentieth term of the sequence. (2) 2.1.2 How many terms are in this sequence? (2) 2.2 The first term of an arithmetic sequence is a and the thirteenth term @3=24. 2.2.1 Determine the common difference of the sequence. (2) 2.2.2 Hence determine the sum of the first 200 terms in terms of a. (2) [8] Copyright Reserved Please Turn Over

Mathes Thloaded from Stanmore f sics.com September 2023 Preparatory Examinations QUESTION 3 The values below are the consecutive terms of a quadratic sequence. The fourth term is 49. —3 7-5-5 495/77 lll; USL 3.1 Determinethellhird term of the quadratic sequence. (1) 3.2 Determine the general term, T,, of the quadratic sequence. (4) tn 3.3 Between which two consecutive terms of the quadratic sequence is the first difference 418? (3) [3] QUESTION 4 4.1 The first two terms of a geometric sequence are x and x+1. 4.1.1 | Write down the common ratio. (1) 4.1.2. Write down the third term. (2) 4.1.3 If x=2, will the sequence converge? Motivate your answer. (2) 4.2 The given sequence below has four terms only, such that the first three terms, T, ; T, and T, form an arithmetic sequence and the last three terms 7, ; T, and 7, form a geometric sequence: 6; a; b; 16. Calculate the values of a and b. (5) [10] QUESTION 5 . -3 Given: g(x) =——-1 3-x 5.1 Write down the equations of the asymptotes of g. (2) 5.2 Calculate the x and y intercepts of g. (3) 5.3 Draw the graph of g showing all asymptotes and intercepts with the axes (3) 5.4 Determine the equation of the axis of symmetry of g with a negative gradient. (2) [10] Copyright Reserved Please Turn Over

Mathes Thloaded from Stanmore } sics.com September 2023 Preparatory Examinations QUESTION 6 The graphs of a parabola f and a straight line g intersect at P and S as shown below. Points R (-5 0| fee —12) are on the parabola, and Q(0;2) is a point on g. V is the turning rear the parabola. The straight line makes an angle of 45° with the x- axis. ae om S TQ ;-12) ot Vv 6.1 Show that the equation of g is g(x)=—x+2. (2) 6.2. Write down the coordinates of S. (2) 6.3 Show that the equation of f is f(x) =8x° -12x-8. (4) 6.4 Determine the coordinates of V the turning point of f. (3) 6.5 Use the graph to determine the values of k, if f(x) =k has two distng equal roots. (1) 6.6 For which values of x is f’(x).g'(x) <0? ka (1) 6.7 Anew graph A is obtained by first reflecting the graph of f about the y - axis and then shifting it in the upward direction so that the x- axis is the tangent of the new graph A. Write down the coordinates of point T’ (the image of T) which lies on the graph of h. (2) [15] Copyright Reserved Please Turn Over

Mathes Thloaded from Stanmore j sics. com September 2023 Preparatory Examinations QUESTION 7 The diagram showsjthe,graphs of f(x)=log,x and f-. Point A(—1;4) lies on the graph of the inverse of 7 rf AGC 14 f x Oo B 7.1. Write down the coordinates of A’, the image of A after reflection in the y = x. dd) 7.2. Show that the value of a is : : (2) 7.3. Determine the equation of f' in the form y =...... () 7.4 Calculate the length of AB. (3) 7.5. Write down the value(s) of x for which f(x) <-—-l. (1) [8] Copyright Reserved Please Turn Over

Mathes Thloaded from Stanmore l sics.com September 2023 Preparatory Examinations QUESTION 8 8.1 Minenhile bought a laptop for R15 800. The laptop depreciates at 12% p.a. ona reducing balance. After how many years will the value of this laptop be R10 767,26? (3) 8.2 Calculate the/éffective yearly interest rate if an investment offers a nominal interest rate of 7,64%p.a compounded half yearly. (2) 8.3. Mandla is planning to buy a car in 2 years’ time. He invests R500 in a savings account at the end of each month for 2 years, starting in one month’s time so that he can use the money as a deposit for his car. Interest is calculated at 5,8% p.a. compounded monthly. 8.3.1 | How much money will be in his savings account at the end of 2 years? (3) 8.3.2 The cost of the car is R368 400. Mandla uses all the money from his savings account as the deposit for his new car. He takes out a loan to pay off the balance after paying the deposit. Interest is calculated at 10,4% p.a. compounded monthly. Calculate Mandla’s monthly instalments if the car must be paid for in 6 years. (4) 8.3.3. Calculate the outstanding balance immediately after paying the 56" instalment. (3) [15] Copyright Reserved Please Turn Over

Mathes Thloaded from Stanmore } sics.com September 2023 Preparatory Examinations QUESTION 9 9.1 From first principles, determine the derivative of f(x) = 2x" +9. (5) 9.2 Determine llowing: 9.2.1 : x if y=x(2x+l). (2) 9.2.2 dy. _ zit yrx=xt3 @) 92300 g |: +3x = : bi (3) 9.3 The derivative ofa function f at point P is given below: 2+h) +1|-[2°41 ag PN ol Bel AO h 9.3.1 | Write down the equation of f. (2) 9.3.2. A tangent is drawn at P. Determine the equation of the tangent to f at point P. (3) [18] Copyright Reserved Please Turn Over

Mathes Thloaded from Stanmore p sics.com September 2023 Preparatory Examinations QUESTION 10 The diagram below shows the graph of f(x)=ax’ +bx*. The x- coordinates of L and M, are 1 and 2 respectivelys-Phe average gradient of f between L and M is 5,5. The equation of the tangent to the cui f at x=6 is y=-18x+e. N L e oO 10.1 Show that a--1 and b=3 2 (5) 10.2 . 1; dee . . The equation {(x)= “3% +3x° is given. Determine the coordinates of N, the turning point of f. (4) 10.3. The graph of f is concave up for x<k. Calculate the value of k. (3) [12] Copyright Reserved Please Turn Over

Mathes Thloaded from Stanmore K sics.com September 2023 Preparatory Examinations QUESTION 11 A match box consists of an outer cover, open at both ends, into which slides a rectangular box without a top. e The length of x is one and a half times its breadth. e The thickness e material is negligible. e The volume box is 25cm?. If the breadth of the box 1s x cm: 11.1 Write down the height of the box in terms of x. (2) 11.2 Show that the amount of the material used for the box is given by: (2) A= 100 +4,5x7 + 20 x 1,5x 11.3 Hence determine the breadth of the box such that the material used is a minimum. (3) [7] Copyright Reserved Please Turn Over

Mathes Thloaded from Stanmore : sics.com September 2023 Preparatory Examinations QUESTION 12 A group of 40 people was asked which bus company they liked to travel by: Elto, Greybound or Translucky bus company. © 3 people likedravelling by all 3 bus companies. e 7 people liked-toKravel by Translucky and Elto. e 3 people did fotitke using any of the bus companies. e The probability of a randomly selected person liking to travel by Greybound and Elto is 5 e The probability of a randomly selected person liking to travel by Greybound and Translucky is z 1 e The probability of a randomly selected person liking to travel by Translucky only is io’ e The probability of a randomly selected person liking to travel by Elto is > The partially completed Venn diagram drawn below represents the given information. ELTO GREYBOUND & 7 TRANSLUCKY 12.1 Use the given information to determine the values of a, b, c, d and ep, U (5) 12.2. How many people liked to travel by Greybound bus company? (1) 12.3. Calculate the probability of a randomly selected person liking to travel by only one bus company. (2) [8] Copyright Reserved Please Turn Over

Mathes Thloaded from Stanmore i sics.com September 2023 Preparatory Examinations QUESTION 13 Nonhle who is a Grade 12 learner has 8 textbooks from eight different subjects: Mathematics, English, Accounting;History, Tourism, Afrikaans, Geography and Drama which she wants to arrange in a lin¢/oma shelf. 13.1 In how rhanyways can the textbooks be arranged? (1) 13.2 In how many ways can the textbooks be arranged if the Mathematics textbook and the Accounting textbook must be on each end of the shelf? (3) 13.3 If the Mathematics textbook and the Accounting textbook must be on each end of the shelf, what is the probability that the History textbook and the Tourism textbook are not next to each other? (4) [8] TOTAL MARKS: 150 Copyright Reserved

Mathes Thloaded from Stanmore ki sics.com September 2023 Preparatory Examinations INFORMATION SHEET: MATHEMATICS INLIGTING BLADSY _—b+Vb7 4ae 2a A= Pl +ni) 24 = P(l—ni) A= P(I-i)" A=P(+i)" T, =a+(n—Nd 8, = 5 (2a +(n-1)d) T, =ar"" s _ alr" =I 3 r#l 8, =“; -1er<1 " r-l I-r peslisi"-1 pawlcd+)") 1 7 i . Ff (x+h)— f(x) (x) = lim PC) h—>0 h xX) +X. +y, d=\(X)—%)? +0 -94)" wo a2 21 Ye x) y=mxt+e y-y, =m(x-x,) m= m=tand (=a) (pa =r In AABC: 4 = b = £ a* =b* +07 —2be.cos A area AABC = ab.sin C sn A sn B snC 2 sin(a + B) = sin a.cos 8+ cosa@.sin 3 sin(a —f) = sin @.cos 3 —cosa@.sin B cos(a +B)= cos a.cos #—sin a.sin & cos(a— #)= cos @.cos 8 +sin a.sin B cos’ a—sin* a cos 2a =41-2sin* a sin 2a@ =2sin a@.cosa 2cos* a1 > n 2 Sfx dens) n n P(A) = m8) P(A or B) = P(A) + P(B)LB(A and B) A 4 (x-x)\y-y) Copyright Reserved

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Mathe: "BSwnloaded from Stanmorephyaias,.com September 2023 Preparatory Examinations QUESTION 1 1.1.1 x=0 or x=4 AAY ¥ answer (2) 1.1.2 2x? +3x-7=0 A” standard form CAY substitution 2 x= 3) = 42-7) into formula 2(2) x=1,27or x =—2,77 CAY 1,27 va (4) Penalise 1 mark for CAY 2,77 incorrect rounding off. 1.1.3 (x-1)(x-4)>0 AY factors i | 1 T x<lorx>4 CAY x<1 CAY x>4 OR OR (x-1)(x-4)>0 AY factors . - 1 x<lorx>4 CAY x CAY x: G3) Copyright Reserved Please Turn Over

Mathe: "BSwnloaded from Stanmorephyaias,.com September 2023 Preparatory Examinations 1.1.4 (3"-3)(3°-7)=0 3°=3 or x =7 ih log, 7 =x 1 1,77=x * I OR Let 3° =m 2. 3° =m? m -10m+21=0 (m-3)(m-7) =0 m=3 or m=7 3*=3 or 3° =7 log, 7=x x=1 or 1,77=x AY factors CAY 3* =3 or 3 =7 CAY using logs CAY x=1 CAY x=1,77 OR AY m=3 or m=7 CAY 3° =3 or 3°=7 CAY using logs (5) CAY x=1 CAY x=1,77 1.2 X= 2= Yorn) (2-y) +? +6(2=9)-4y+4=0 4-4) 4y? ty’ +12—6y—4y+4=0 2y°-14y 1 20=0 y’ -Ty+10=0 (y-2)(v-5)=0 y=2 or y=5 x=2-2=0 x=2-5=-3 Copyright Reserved AY equation (3) CAY substitution CAY standard form CAY x values (6) Please Turn Over

September 2023 Preparatory Examinations “atheB8wnloaded from Stanmorephysics..com 1.3 For equal roots A=0 25-n’ =0 AV 25-n’ =0 (5-n) =n)=0 AY factors n=t5 CAY answer OR OR For equal roots A=0 25-n’ =0 AY 25-n’ =0 =n Av 089 =+ y ns answer only = full marks CAY answer @) [23] Copyright Reserved Please Turn Over

“ate Swnloaded from Stanmorephyaics.com QUESTION 2 September 2023 Preparatory Examinations 2.1.1 3; 73 11 ;------ ------ 399. a=3 d=4 n=20 T, =a+¥("-1)d Ty =3+(20-1)4 AY substitute into * correct T, formula Ly =79 OR CAY answer 3; 7; WW ;------ ------ 399 OR 4,454; 0, T, =4n-1 T,, =4n-1 T,, =4(20)-1 AY substitute into correct T, Ty =79 formula (2) CAY answer 2.1.2 T, =399 T, =a+(n-l)d 399 =3+(n—-1)4 AY substitute into correct T, formula 396 =(n-1)4 99-n-1 100=n CAY answer OR OR T, =399 T, =4n-1 399 =An-1 AY substitute into correct T, formula 400 =4n 100=n Copyright Reserved Please Turn Over

“ahe"B8wnloaded from Stanmorephysics,.com September 2023 Preparatory Examinations CAY answer (2) 2.2.1 T, =a T,; =a+24 T,, =a 443-1) a+24 at 12d AY a+24=a+12d 24 = 12d 2=d AVE, (2) 222 | sg =$[2a+(n-1)d] 200 CAY substitute into Soop =| 2(a)+(200-1)2 an) [ (2) ( ) ] the correct formula Sry = 100(2a +398) Sy = 200a +39 800 CAY answer OR OR T, =a+(n-ld Typ =a + (200—1)(2) = at+398 2 8, = 5a +1) ” Sooo — 20044 (a +398)] CAY substitute into 2 the correct formula Sy) = 100(2a +398) = 200a+39 800 CAY answer [8] Copyright Reserved Please Turn Over

MathenpSisswnloaded from Sta 9 j siGSicom September 2023 Preparatory Examinations QUESTION 3 3.1 1311; 27; 49; 77; 111; 151; ... 10; 16; 22; 28; 34; 40; wo. Ce a a a Loar The thés is 27 AY answer (1) 3.2 Secorpiifference is 6 2a=6 az=3 AY a=3 10=3a+b 10=3(3)+b 1=b CAY b=1 1=3+l+e 3=c CAY c=-3 T, =3n? +n-3 CAY answer OR OR -; 16; 22; 28; 34; 40; wu. 6;.6; 6; 63.002. 2a=6 a=3 AY a=3 ‘T =an’+bntc 49 =3(4) +(4) +e 77 =3(5) +.b(5) +0 49 =484 4D +6 veeeeeseee (1) TIA TSASDHC vocceceseee (2) ae QW=2THBD eee Q)-() danny a cay b= 49 =48+4(l) +c CAY c=-3 3=c CAY answer (4) Copyright Reserved Please Turn Over

Mathe: September 2023 Preparatory Examinations "Béwnloaded from Stanmorenhysigs.com T, =3n +n-3 3.3 First difference 10; 16; 22; 28; 34; 40... T =6n AY T.=6n+4 0 = OF IG 418= 414 69=n CAY value of n W=n+l CAY between T,, between T;, and T, and Try ~. between 7,, an 69 70 OR OR v = - 418=T,., -T, AY 418=T,,, -T, 418 =3(n+1) +(2+1)—3-Gn? +n—3) 418 =3(n? +2n+l)+n+1-3-3n —n4+3 418 =3n? +6n+3+n—-2-3n’ -—n+3 418 =6n+4 414=6n 69=n CAY value of n 70=n+1 CAY between Ty (3) “. between 7;, and 7, and T,, [8] Copyright Reserved Please Turn Over

September 2023 Preparatory Examinations “ate Swnloaded from Stanmorephyaias.com QUESTION 4 4.1.1 _xtl AY answer qd) x 4.1.2 T,=T,xr xtl K=(x+t2 CAY (x41)x—— (x+ 1) CAY answer (2) T, = x 4.1.3 (2+1) 3 CAY value of r r= == 2 2 “no, sinee r> CAY answer with (2) OR motivation No, for the series to converge: — 1 <r<1 4.2 For AP: 7-1, =T,-T, a-—6=b-a 20 = 6 = Deessssseesseesssseees (0) AY equationiGh) For GP: rt 7, 7, b_16 a b Copyright Reserved Please Turn Over

September 2023 Preparatory Examinations “aheBSwnloaded from Stanmoreplivaics,.com 16d =D veeeecrrseee (2) AY equation (2) CAY standard form CAY values of a CAY values of b b=2(9)-6=12 b=2()-6=-4 (5) [10] Copyright Reserved Please Turn Over

Mathemayiss wn i loa d le d fr om St ‘a Ye } S, i G Sa ¢ ‘om September 2023 Preparatory Examinations QUESTION 5 5.1 x=3 AY answer ye-l AY answer (2) => 5.2 x — int : 0-5 i AY sub y=0 j= -x 3-x=-3 x=6 CAY x=6 y intercept = ——-1=-2 AY y=-2 OR OR _ 3 _ *=@=3) 3 =—-] y x-3 — intercept: 3 AY sub y=0 0=—--1 x-3 1-3 x-3 x-3=3 CAV x=6 x=6 —intercept = 3 ja v y P 0-3 AY y=-2 QB) Copyright Reserved Please Turn Over

Mathempayiss nl loa d le d fr om St ‘a Ye i S, i G Sa ¢ ‘om September 2023 Preparatory Examinations 53 ; L AY shape \ CAY intercepts = 3 en? CAV asymptotes (3) \ 5.4 yr-xt+e -[=-34e CAY sub (3;-1) 2=c yeoxt2 CAY answer OR OR 3 a —3-x - yey 1 wernt yeord2 CAY answer OR OR yer] ye—(x—3)-1 AY -(x-3)-1 ys-xt+3-1 yeerd2 CAY answer (2) [10] Copyright Reserved Please Turn Over

“aheBSwnloaded from Stanmorepliyaics,.com September 2023 Preparatory Examinations QUESTION 6 6.1 m= tan135° AY m=tan135° m=-l AY m=-1 (2) “y=-xt2 6.2 0=-*+2 AY equating to zero x=2 “S (2;0) AY answer (2) Answer only = full marks 6.3 y=a(x—x )(x—x) ymafx+h)(0-2) -12=a( 143 (1-2) y =8x? -12x-8 Accept method of simultaneous equations AY sub x= and 2 x=2 AY sub (1;-12) » 3 y=a(? 3-1] (4) 6.4 -b x=— 2a _-(-12) ~ 2(8) x Alw AY x value CAY substitution CAY y value Copyright Reserved Please Turn Over

September 2023 Preparatory Examinations g(x) =16x—-12 0=16x-12 12=16x OR x-intercepts S(2;0) and x{-40] midpoint x = OR “ahe"B8wnloaded from Stanmorepliysics,.com OR AY 0=16x-12 CAY x value CAY y value OR AY subst into correct midpoint formula CAY x value CAY y value OR AY completing the square Copyright Reserved Please Turn Over

“athe"BSwnloaded from Stanmoreplivaias,.com September 2023 Preparatory Examinations ( 3) 25 y=8| x-—| -— 4 2 CAY V x value and y value 23) @) 4 2 _ v 6.5 k> -25) CAY answer (1) 6.6 CAY answer x>H OR OR (-1)(16x—12)<0 -l6x <-12 - 3 AV answer (1) 4 6.7 { 1 } AY x-—coordinate T| -L= 2 AY y-—coordinate (2) [15] Copyright Reserved Please Turn Over

“ate Swnloaded from Stanmoreplivaias,.com September 2023 Preparatory Examinations QUESTION 7 71 (4:-1) AV answer qd) 7.2 y=log,x -l=1 AY sub(4;-1) a’ AY a'=4 1 a=— 4 (2) 73 ly an 4 AY answer qd) 7A A(-L4) and B(1;0) AY B(1;0) 2 2 CAY sub points A AB= ,(-1-1) +(4-0 (-I-l) +(4-0) and B AB= V4+16 = 20 CAY answer AB = 25 =4,47 @) 75 x>4 AY answer qd) 8] Copyright Reserved Please Turn Over

Mathe: September 2023 Preparatory Examinations "Béwnloaded from Stanworenliysigs,.com QUESTION 8 81 | 4=P(1-i)’ 12)’ AY sub into correct 10767, 26 ff oof 1-15 | formula 10767, 26 =(0.88)" 15800 CAY correct use of logs 10767, 26 log cose) 75800 = 2,999998...=n CAY answer n=3years G) 8.2 _\m 100 m r 7,.64Y AY subst into correct (1 )=(14 et) formula 2 ro 0 ie) | 200 (2) v r=7,79% CAY answer 8.3.1 To : z 4 i R500 R500 R500 R500 7 oon x|(1+i)"-1 100 pte) Copyright Reserved Please Turn Over

“athe"BSwnloaded from Stanmoreplivaias,.com September 2023 Preparatory Examinations 5.8 \4 AY values of i & 7 500 [ 2 | -1 . Ke 1200 CAY subst into ~ 5,8 correct 1200 ia afl CAY answer GB) 8.3.2 | R368 100 - R12 691,25 = R355 708,75 CAY R355 708,75 x|1—(1+i)" P= [ ( ) ] AY n=72 i 10,4)” CAY sub into x] 1—| 1+ correct 355708,75--- ~ "J formula aoa 10,4 1200 R6661,78 =x CAY answer (4) 833 xf(iesy'-1] Bal Outstanding = P(1 +i)’ -+——~_+ alance Outstanding = P(1 +i) ; CAY 10.4. 355708, 751 +14)" 6661,78 [1 2 } 1 1200 355708, 75} 1 10.4 " 1200 = + _ , ( ve | 10,4 CAY 6 1200 6661,78 (+104) -1 ° 1200 10,4 1200 Balance outstanding = R99 128,46 CAV R99 128,46 oR in Remaining instalments = 72—56=16 donot conn 10,4" AvLn=16 6661,78 1-{1+ } . Bal _ 1200 CAV’ subst into correct alance © 10,4 formula 1200 Copyright Reserved Please Turn Over

Mathenis5 wnloaded from Sta Ye is sigs,.com September 2023 Preparatory Examinations = R99128,52 CAY R99128, 52 (3) [15] Copyright Reserved Please Turn Over

MathenpSisswnloaded from Sta nenlivsias.com September 2023 Preparatory Examinations QUESTION 9 Penalise ONCE for incorrect notation, either in 9.1 or 9.2. 9.1 f(x) =2x° +9 +h) +9 +4xh+2h? +9 AY calculating f(x + h) (x+h)- f(x) h 2x? +4xh+2h? +9-2x° -9 f (x)= lim h CAY sub into formula 2 f(x) =lim 4xh+2h oh CAY simplifying - h(4x+2h) =lim So”? £O) io CAY factors f(x= lim 4x +2h : CAY answer f (x) =4x (5) 9.2.1] y=2x? +x AY product dh ) Y _ aya] CAY answer (2) dx 9.2.2 Vytx =xt3 rey 2 AY squaring both ( y+x) =(x+3) sides pox ax? 46x49 AY correct product y= x 45x49 — nl * =2x45 CAY ans 3) 9.2.3 l -l a 4x7 + 3x ? AY 4x1 43x 2 dx = 4x2 3 3 CA CAYY each term (3) = Ae x Copyright Reserved Please Turn Over

Mathenis5 wnloaded from Sta repliysiGs..com September 2023 Preparatory Examinations 9.3.1) Swat] AY A Y answer (2) 9.3.2 | AtPx=2..y=241=9 P(2;9) CAY y-—coordinate m=12 CAY m=12 y=l2x 9=12(2)+e -l5=c y=12x-15 CAY answer (3) [18] Copyright Reserved Please Turn Over

“atheBSwnloaded from Stanmoreplivaics,.com September 2023 Preparatory Examinations QUESTION 10 10.1 | f(x) =ax* + bx? f() = all +0(IY =atb Ay aust _5 _ 2 FOR)= a2 (2) =8a+4b AY correct subst into goon 2-7 average gradient Ave entra ( A ) formula Ave grad = — 5,5 —TA43D cceveveeseseseevees (1) S'(x) =3ax? +2bx S'(6) =3a(6)° +26(6) Av equation (1) 18 = 1080 412D.veesrsescsseeee (2) AY equation (2) (x42 22528041 2B occccersecseeeenre (3) AY solving 40 = 80 Ao csosesestssseseen 3)-Q) simultaneously -1 ea 2 -l 5,5= {F) 3b 2 5,5=-3,5+3b 9=3b (5) 3=b 10.2 3x? AY f' f (x)= 4 6x Le 2 0= 23x" 46x Cv legiating ; Sid 0 =-3x? +12x Jonny ry 0=x° -4x 0=x(x-4) Copyright Reserved Please Turn Over

September 2023 Preparatory Examinations “atheBSwnloaded from Stanmoreplivaics,.com x=0 or x=4 xsd CAY x=4 (4) AtN x=4.. y= F(a) +3(4) =16 N(4;16) CAV y=16 10.3 f(x) =-3x+6 CAY f(x) -3x+6>0 CAY -3x+6>0 -3x>-6 x<2 k=2 CAY answer (3) OR f(x) =-3x+6 0 =-3x+6 x=2 wk=2 OR Midpt x = —— =2 x=2 =2 [12] Copyright Reserved Please Turn Over

“atheBSwnloaded from Stanmorepliysics,.com September 2023 Preparatory Examinations QUESTION 11 11.1 Volume = Ibh 25=(I,5x)(x)h AY substitution AY answer (2) 11.2 Area = 4€55x)h + 3(1,5x)x + 2xh AY substitution in to SA formula 0 =-300+27x* —100 0 =27x° - 400 400 = 27x° [400 x= 3/— 27 x=2,46 woe 2 Area = 4(1, 5x) x + HL, 5x?) + 2% Av substituting h 2) 1,5x° 1,5x Area = 100 4 542 + 50 x 15x 11.3 1 A= 10027! 44,522 + 20% 1,5 F-10087 +910 av 9 dx = 9-0 x x CAY simplification CAY value of x (3) [7] Copyright Reserved Please Turn Over

September 2023 Preparatory Examinations “ahe"BSwnloaded from Stanmoreplivaics,.com QUESTION 12 121 | a=4 AY b=13 AY c=5 AY d=4 CAY e=6 CAY (5) 12.2 | Greybound bus = 23 people CAY answer qd) Y addi 23 P(only one bus) = Orae?2 12 3 CAY adding (2) 40 4010 CAY answer [8] Copyright Reserved Please Turn Over

Mathe: "Béwnloaded from Stanmoreniiysics,.com September 2023 Preparatory Examinations QUESTION 13 13.1 | 8!ways =40 320 ways AY 8! OR 40 320 dd) 13.2 1x6k1+ 1=1440 ways AY 6! OR AY 1x61 2x61 Oways Av 1440 (3) 13.3 1-[ SS OE) | 2 AY subtracting from1 1440 1440 3 CAY denominator OR Av 215! 1440 —(2!5!42!5!) CAY answer 1440 4 2 “ 3 [8] TOTAL MARKS: 150 Copyright Reserved