Mathematics Grade 12 EC March Test 2026 Paper & Memo

Downloaded from Stanmorephysics.com p. cos Province of the eT) EASTERN CAPE EDUCATION OR TAMBO COASTAL DISTRICT NATIONAL SENIOR CERTIFICATE GRADE 12 MATHEMATICS MARCH TEST 2026 MARKS: _ 100 TIME: 2 HOURS This question paper consists of 11 pages

Downleaded from Stanmorephysics.com ORTCD/March 2026 NSC INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1 This question paper consists of 8 questions three diagram sheets and formular sheet. 2 Answer ALL the questions. 3 Clearly show ALL calculations, diagrams, graphs, et cetera, that you have used in determining your answers. 4 An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise. 5 If necessary, ALL answers should be stated otherwise. O decimal places, unless 6 Number the answers correctly accord bering system used in this question paper. 7 Diagrams are NOT necessarily dra’ 8 Write neatly and legibly. Copyright reserved Please turn over

Dawnleaded from Stanmorephysics.com ORTCD/March 2026 NSC QUESTION 1 Given the quadratic pattern: 5;12;21; 32;... 1.1 Determine the general term 7, of the pattern. (4) 1.2 Calculate the value of the 25” term. (2) 1.3. Which term of the sequence has the value of 1152? (4) 1.4. Show that the difference between any two consecutive terms will always be an (3) odd number [13] QUESTION 2 vam ; The sum of the first 7 terms of an arith 2.1.1 Determine the first three terms of the sequence. (3) 2.1.2 Calculate the 20" term (7, ) using the S, formula. (3) : — 2.2 \ (3) For which value(s 2.3. Given a geometric series w ratio I (5) Let S,, be the sum of the f um of the first 2n terms. Prove that the sum of th nby S,.r” [14] Copyright reserved Please turn over

Dawnleaded from Stanmorephysics.com ORTCD/March 2026 NSC QUESTION 3 Given f(x) = 4 38 x1 3.1. Write down the equation: 3.1.1 Vertical asymptote qd) 3.1.2. Horizontal asymptote qd) 3.2 Calculate the x and y intercepts of f- (3) 3.3 Sketch the graph of /; showing al (4) 3.4 For which values of x is f(x) <0 ~~ (2) [11] Copyright reserved Please turn over

Dawnleaded from Stanmorephysics.com ORTCD/March 2026 NSC —— auesinon The 1s below show the graphs of g(x)= ax? and h(x) =log, x . The point P (2;8)lies on the graph of g. tafimorephysies.com 4.1 Determine the value of a (2) 4.2 Ifh passes through (8;3), find the value of b. (2) 4.3 Write down the equation of h™' (x) in the form y=... (2) 4.4 Determine the domain of h. (2) 4.5 Determine the value(s) of x for which 45.1 g(x).h(x)<0 (2) 45.2 xh(x)20 (2) [12] Copyright reserved Please turn over

Dawnleaded from Stanmorephysics.com ORTCD/March 2026 NSC QUESTION 5 a(x -p)y +q by completing the square. (3) (2) (3) 5.3. Sketch the graph of f (3) 5.4 Write down the y-intercepts of f (2) 5.5 Write down the domain of f"! (2) 5.6 If f(x) is shifted 2 units to the rig up, write down the new (2) equation , [17] QUESTION 6 6.1 Simplify without using a calculator: sin(x—180°).tan(x+180°).cos(90+x) (6) sin? (180° + x) 6.2 If cos25° = V1—k? , determine the following in terms of k: 6.2.1 sin 25° (2) 6.2.2 sin50° (3) 6.2.3 cos70° (5) Prove that we ae aes = = 2, (5) sin0d cos@ m+n (3) If cos(4+B)=m and cos(4-B)=n, prove that cos 4.cos B = [24] Copyright reserved Please turn over

Dawnleaded from Stanmorephysics.com NSC QUESTION 8 Given APQR with PQ=8units, QR= P 8.1 Calculate the area of APOR 8.2. Calculate the length of PR Copyright reserved hat a’ =b’ +c? —2becos A ORTCD/March 2026 (4) [4] (2) (3) 5] TOTAL 100 Please turn over

Dawnleadaed from Stanmorephysics.com ORTCD/March 2026 NSC 3.3 a 49. (Fs | aH Copyright reserved Please turn over

Dawnleaded from Stanmorephysics.com ORTCD/March 2026 NSC 5.3 o cy & Copyright reserved Please turn over

Dawnleaded from Stanmorephysics.com NSC ORTCD/March 2026 dfimorephysles.com Copyright reserved Please turn over

Dawnleaded from Stanmorephysics.com ORTCD/March 2026 NSC INFORMATION SHEET A= Pil—ni) A= Pii-i)" A= Pil+i)" . =F ba tn—pa] T.=ar"' s, -4=!) jrel S. pont -l<ral Pes = 3 t+ iy po tt-t+)"] i — im LEt-I@) es se d= (x, =P +, —¥F y=mrrc Ia mew m-=tan@ (x~ of +b) =r? a? =b? +c7 ~2becos A area MABC = jebsinc sin(a + 8)=sin a.cos 8 +cosa.sing sinla—$)=sina.cos B—cosa.sinB cos(a+ f)=cosa.cos f-sina.sin# cos(a—£)=cosa.cos B+sina.sinB cos’ a-sin? a cos2a = <1~2sin* a sin 2a = 2sina.cosa 2cos’ a=1 Le, ~xy a n P(A) = P\A or 8) ~ PCA) + P{B) ~ PUA and B) ; _Le-70-P) prath 6 Sa-3 Copyright reserved Please turn over

Downloaded from Stanmorephysics.com ee Province of the heed EASTERN CAPE EDUCATION — OR TAMBO COASTAL DISTRICT NATIONAL SENIOR CERTIFICATE GRADE 12 TERM 1 CONTROLLED TEST 2026 MATHEMATICS MARKING GUIDELINES This marking guidelines consist of 8 pages. NOTE e Ifacandidate answers a question TWICE, only mark the FIRST attempt. e Ifacandidate has crossed out an attempt of a question and not redone the question, mark the crossed out version. ¢ Consistent accuracy applies in ALL aspects of the Marking Guidelines. Stop marking at the calculation error. e Assuming answers/values in order to solve a problem is NOT acceptable.

DRawnleaded from Stanmorephysics.com ORTCD/March 2026 QUESTION 1 1.1 V value of a (4) ¥ value of b ¥ value of c Y equation T, =1.n' +4.n+0 T, =n +4n ma (Ry P4425) Y answer (2) T,, = 725 13 T, =n +4n=1152 ¥ substitution (4) Vv ; n? +4n-1152=0 ‘awe (n—32)(n+36)=0 Y answer n#-36 n=32 Ty =1152 14 T,.,-T, = (n+l) +4(n41)-(n? +4n) ¥ substitution (3) ¥ simplification T,,,-T, =n’ +2n+1+4n+4-n? —4n v answer TT, =2n45 2n is always an even number adding 5 to any even number gives odd number T,,, -T,, =2n+5 is always an odd number [13] Copyright reserved Please turn over

DRawnleaded from Stanmorephysics.com ORTCD/March 2026 QUESTION 2 211 \Anay 311 —5(1 Y first term @) RFS, = 30) -5() =-l ¥ second term UTI) 5 4 v third term WAT? 3(2) —5(2) 30) -S5(U1 ipa, -5, 222-52) 300-500, — 3(3) -5(3) 3(2) -5(2 Fass, 50) 30¥ 50) 17255355 ae 3(20)° —5(20) 3(19)° -5(19) Y Sip GB) Dy = Sry — Sto = 2 ~ 2 =56 Y Sy v¥ answer 2.2 -l<k-1<1 . V¥-1<k-1<1 (3) -l+l<k<14l \ 7 VY —-141<k<14+1 -l<k<2 i. V-1<k<2 Y Soy (5) 1 bs vS,,-S, ahimorephysics.com ¥ factor“ —_ Y factor r” ¥ simplification [14] Copyright reserved Please turn over

Dawnleaded from Stanmorephysics.com ORTCD/March 2026 wl. Yx=l (1) 3.1.2 : Vy=3 (1) 3.2 3 4 2 ¥ substitution for | (3) lf (3) at 3 x-intercepts for x—int let y=o vsimplly 0O= a +3 x-1 -3(x-1)=2 v¥asymptotes (4) vy-intercepts ¥ point fixing graph v¥ shape v ¥ answer (2) [11] Copyright reserved Please turn over

Dawnleaded from Stanmorephysics.com ORTCD/March 2026 QUESTION 4 41 [g(x)e ax’ r substitution (2) ; r answer 8=a(2) =4a @=2 g(x)=2x° 4.2 | h(x) =log, x ¥ substitution (2) ¥ answer 3=log,8 b=8=2° b=3 h(x) =log, x 43 | y=log,x vinterchange (2) x=lo variable. ey v¥ answer yah yas 4.4 Domain =x/x > 0 diimorephYsles.com v V answer (2) 4.5.1 | 0<x<1 v VY answer (2) 4.5.2 | x21 ¥ ¥ answer (2) [12] QUESTION 5 5.1 v factor 2 (3) ¥ complete square ¥ answer 5.2.1 vx-value (2) vy-value 5.2.2 vy=0 (3) Y factorisation v Values of x (x-3)(x+1)=0 x=30rx=-1 (3:0), (-10) Copyright reserved Please turn over

Dawnlaaded from Stanmorephysics.com ORTCD/March 2026 v intercepts with (3) axis v indication of y- intercepts v shape =, | 7 (03) 2) anmorepn com 4 (0;3), (0;-1) 4 ¥ (0;-1) 4.5 | Domain=x/x>-8 ¥ value (2) ¥ notation 5.6 | f'(x)=f(x-2)+5 ¥ substitution Q) 2 v answer f'(x)=2(x-2) -6+5 f'(x) = 2x? -8x+8-1 f'(x)=2x? -8x+7 [17] Copyright reserved Please turn over

Dawnleaded from Stanmorephysics.com ORTCD/March 2026 QUESTION 6 6.1 | sin(x—180°).tan(x+180°).cos(90+x) ¥-sinx (6) sin’ (180° +x) vtanx (=sin x).(tan x).(—sin x) v-sinx = 7 _\2 ¥ simplification (-sinx) Y answer _ (-sin.x)' (tan.x) (-sinx)" = tanx 6.2 cos25°= MITA _ ah 1 Iyp opp =? (np)’ =(opp)" +(adj)° (1)? =opp'+ (VIF) opp? =K* opp=k 6.2.1} . 1. opp _k ¥ substitution (2) a hyp 1 Y answer sin 25° =k ¥sin2(25) (3) v double angle v Answer ¥cos(45°+ 25°) | (5) ¥ compound angle formular ¥ substitute first term ¥ substitution in second term ¥ Simplification Copyright reserved Please turn over

Dawnleaded from Stanmorephysics.com ORTCD/March 2026 6.3 | LHS v¥ sinxcosx (5) 'sin30. cos30_ sin3@cos@—cos36sin0 ¥ numerator | sind) cosO sin @cosO v’simplification a v express Ne (30-9) denominator as ta double angle —(2sin0cos0 2. panrang) ¥ simplification =2. gn 20 =2 sin 20 LHS = RHS 6.4 | cos(4+B)=cos Acos B-sin Asin B = m.....(1) 7 eauetion 4 (3) cos(A—B)=cos Acos B +sin Asin B = n......(2) PR saliieton (1) +(2) 2cos AcosB=m+n cos Acos B= mean [24] afimoreph 4 ics.com QUESTION 7 AB=c and BC=a | construction —_| (4) Copyright reserved Please turn over

Dawnleaaded from Stanmorephysics.com ORTCD/March 2026 RTP: =b° +c’ —2becos A v Pythagoras Construction: draw perpendicular height h from vertex Hiseieae for both @ dicular to B. ranges aati lad teular'to ¥ substitute by BD=c-AD ~ B2— B2 2 AACD: b° =h’ + AD YcosA ABCD : a? = h? + DB? =h? +(c- AD) @=h’ +c —2c.4D+ AD* @ =h? + AD? +c? —2cAD a@ =b’ +c —2cAD cos A= adj. = ae hyp b — AD =becosA a =b> +c’ —2becos A QESTION 8 2 8.1 1 . of ¥ substitution (2) Area of APQR=- (8)(12)sin 110% Japiswer Area of APQR = 45.11 square unit 8.2 PR? =(8 2 AL12 2 ~2(8)(12)cos! ¥ substitution (3) ; hay ey 2] ¥ simplification PQ* = 273.67 v answer POQ=16.54 [5] TOTAL 100 Copyright reserved Please turn over