Mathematics Grade 11 KZN March Test 2026 Paper & Memo

| KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE GRADE 11 MARKS: 75 TIME: 1% hours This question paper consists of 4 pages and an answer book of 8 pages. Copyright reserved Please turn over

““"SSWhloaded from Stanmorephysi¢s.com March 2026 INSTRUCTIONS AND INFORMATION Read the following instructions and information carefully before answering the questions. iF Va This question paper consists of 3 questions. Answer ALL the questions in the SPECIAL ANSWER BOOK provided. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your answers. Answers only will NOT necessarily be awarded full marks. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise. If necessary, round off answers to TWO decimal places, unless stated otherwise. Write neatly and legibly. Copyright Reserved Please Turn Over

“"3SWnloaded from Stanmorephysi¢s.com QUESTION 1 L2 Solve for x and y simultaneously: V36-24m L3 The roots of a quadratic eg A Calculate the values of m- 18 | fig—-2N2 2.1.3 a 2.2 Solve for x, WITHOUT using a calculator: 221 a= 92 2.22 12.3" +1=0 Copyright Reserved ts of the equation will be real. March 2026 (2) (4) (4) (4) (6) (6) (2) [28] (3) (4) (3) (2) (5) [17] Please Turn Over

Mathers nloaded from Stanmorephysics.com March 2026 QUESTION 3 3.1 oll If 3tan0+2= 0 and sin@>0, evaluate the following with the use of a diagram and ) > without using a calculator: 312 — 1Bcos?@-Vi3sind 3.2 Simplify the following expression to a single term: cos (360° — x). tan (—x).cos(90°+x) sin (x +720°) , 33) Evaluate without the use tan 120°.sin 115° cos 240°.cos 205°" 3.4 Given: — (cosx+ tan) tan % of x in the interval x €[0°;360°) is in x) undefined? for Be [1 80° ; 270°]. Calculate, without the use sible e(s) of k, leaving your answer in surd form. Copyright Reserved (4) (3) (6) (7) (4) (2) (4) [30]

Downloaded from Stanmorephysics.com KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA PROVINCIAL STANDARDISED ASSESSMENT GRADE 11 Marks: 75 Time: 1% hours Question Marks 1 2 3 TOTAL N.B. This answer book consists of 8 pages. Copyright Reserved Please Turn Over

March 2026 ““"Fownloaded from Stanmacephysias.com Marks Q) (4) 1.1.3 ; fmorephfales com (4) 1.1.4 (4) Please Turn Over

“"e"ownloaded from Stanmacephysics.com March 2026 Solution Marks Ts — (6) 1.2 1.3: [28] Copyright Reserved Please Turn Over

March 2026 “""ownloaded from Stanmacephysias.com QUESTION 2 Solution Marks 211 GB) 212 (4) 23 G3) Copyright Reserved Please Turn Over

March 2026 “""ownloaded from Stanmacephysias.com 2.2.1 2) 2.2.2 (5) (17] Copyright Reserved Please Turn Over

“""ownloaded from Stanmacephysias.com March 2026 QUESTION 3 Solution Marks 3.1.1 (4) 3.12 GB) 3.2 (6) Copyright Reserved Please Turn Over

March 2026 ““"Fownloaded from Stanmacephysics.com 3.3 (7) 3.4.1 (4) 3.4.2 (2) 38. (4) [30] Copyright Reserved Please Turn Over

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Downloaded from Stanhor enn .com ¥ ‘i > 4 J KWAZULU-NATAL PROVINCE ss fL. EDUCATION ea REPUBLIC OF SOUTH AFRICA NATIONAL TOR CERTIFICATE MARKS: 75 These marking guidelines consist of 10 pages. Copyright Reserved Please turn over

“aheB8ivnloaded from Stanmonephysics.cam QUESTION 1 KZN/March 2026 Tle (x+1)(2x-6)=0 x=-l or x=3 vA answer YA answer (2) 1.1.2 | 3x°+8x=4 3x7 +8x-4=0 YA standard form —= =b+Vb° —4ac YCA correct subst. into quadratic formula YCA answer ¥CA answer (4) YA correct factors YCA critical values (accept if shown on a sketch or number line) imorephysics.com s-ll<x<-8 OR xe(-11;-8) VCAYCA answer (4) 1.1.4 | ¥36—5x? -2x=0 VAG , 36-5" aie A isolation of surd 2 * 2 (V36-5x7) =(2x) 36-5x? =4x° ¥YCA squaring both sides 36 =9x° 9x* -36=0 gin hal YCA standard form (x+2)(x-2)=0 OR x =4 x#—2 or x=2 OR x#-2 or x=2 ¥CA answer with selection (4) Copyright Reserved Please turn over

“aheB8inloaded from Stanmonephysics.Gam KZN/March 2026 LL. x(¥>4)+ l(x-2) =2 i re re x=2=x+4 x°-6x+8 x 1 2 + = =D X-4 (x-2)(x-4) ¥-2)(x-4) X(x—4)+1(x—2) _ (x-2)(x-4) x? —4x+%-2 _ (=2)(=4) x -3x-2 2 (x-2)(x-4) (x-2)(x-4) wx? -3x-2=2 Award mark for standard form x -3x-4=0 aan ; ' only if it is a quadratic equation (x+1)(x-4)=0 x=-l or x#4 vA factoring denominator on RHS YA writing as a single fraction YCA simplification YCA standard form YCA both x-values ¥CA valid answer (6) OR YA factoring denominator on RHS vA LCD on LHS ¥YCA equating numerators YCA standard form ¥CA both x-values ¥YCA valid answer (6) 1.2 2x+y=3 VHB 2WNvrrrrccrssereeeed equ.(3) 2 Hy y vay x? -(3-2x)° =-x—-(3-2x) x? =(9-12x-4+4x7) = -v-3 42x x? -94+12x-4x? =x-3 3x? +11x-6=0 3x? —11x+6=0]| B/D if standard form is NOT quadratic (3x-2)(x-3)=0 x== or x=3 yo or y=-3 wilnr wlry vA expressing y in terms of x YCA substitution YCA simplification (after removing all brackets) YCA standard form YCA values of x YCA values of y (6) Copyright Reserved Please turn over

“aheBBinloaded from Stanmonephysics.Gam KZN/March 2026 —3y° -6y+9=-2y +6 3y? +4y-15=0 YA expressing x in terms of y YCA substitution YCA simplification (after removing all brackets) YCA standard form YCA values of y or x= 2 x= 7 or x=3 YCA values of x (6) 1.3 36-—24m20 YA 36-24m>0 —24m = -36 msa Y¥CA answers Q) [28] Copyright Reserved Please turn over

“aheB8inloaded from Stanmonephysics.cam QUESTION 2 KZN/March 2026 2 RSP =3'2%54 3 “3 ss 125 Answer only, award 0 marks VA writing 0,125 as = 1000 YA applying exponent / surd law YCA answer (3) OR VA rewriting 0,125 as (0,5) “A applying exponent / surd law ¥CA answer (3) = BPH2PHl gp pt2tp-2-2p 5 p-2-p-l vA rewriting as prime bases VA applying the law of exponents YCA simplification ¥CA answer (4) Copyright Reserved Please turn over

“aheB8inloaded from Stanmonephysics.cam KZN/March 2026 2.1.3 | —LOghk -2./2 v2 18-2) -= ti Wa) N2 =x? 22 YA rationalising denomin. i.e. x A = a -3V2 -2,2 VA 3V2 =9/2-52 = 4/2 Answer only, award 0 marks || “CA answer (3) OR VA 3V2 YA LCD = 38 Answer only, award 0 marks || /, GA answer a GB) 2.2.1 | 2°* =32 2 =2° YA 32=2° -3x=5 — OR exile vA answer 3 @) OR OR 2332 1 PR, Pres 9% Be 25* oF 3x=-5 a OR x=-l= vA answer 3 2) Copyright Reserved Please turn over

“aheB8ivnloaded from Stanmonephysics.gam KZN/March 2026 2.2.2 2h" +1=0 9* VA 9 =37* YA correct standard form ¥CA factors ¥CA both equations with base 3 vA both answers (5) 27 _193*41=0 9 27, = gr 7123" +1=0 VA 9° =3" 27.37 -12.3* +1=0 “A correct standard form (9.3 -1)(3.3* -1)=0 CA factors 9.3*-1=0 or 3.3*- 3° =i or 3*= u 9 3 3°%=3° or 3*=3" YCA both equations with base 3 x=2 or x=1 YA both answers (5) [17] QUESTION 3 3.1.1 | 3tand+2=0 tan@=—2 vA — 3 3 Paxgy? v A diagram in the correct 3 quadrant =(-3) +(2) =13 r=VB VA r=Ni3 cos @ = _s ve Vis CA answer (4) 3) D 3.1.2 | 13cos?0-Vi3 sino=13(-5] -Vi3) (F) YCA substitution 13 vi3 = (2 -2 ¥CA simplification =7 ¥CA answer (@) Copyright Reserved Please turn over

MateDs8ivnloaded from Stanmorenlysigaigem KZN/Mareh 2026 3.2. | £98(360°-x).tan(—x).cos(90°+ x) sin(x+720°) _ (cos.x)(—tan x)(—sin x) > (sin x) cosx sinx sinx ¥A cos(360° — x) = cosx vA tan(—x) =—tanx VA cos(90°+ x) =—sinx YA sin(x + 270°) =sinx OR eee ee eee sinx soll “cosx’ 1 "A sinx =sinx YCA answer (6) 3.3. | tan120°.sin115° cos 240°.cos 205° vA tan120° =—tan 60° SK es Ot ° (—tan 60°)(sin 65°) StS Sens ~ (—cos 60°)(—cos 25°) vA cos 240° =—cos 60° ¥ Acos 205° =—cos 25° __ xi 65°) OR - Y CA special angles z (sin 65°) Y CA co-ratio =-2y3 ¥CA answer 2) 3.4.1 LHS= | (cosx+ tan x.sin x) tanx = Sts S088 sins sins) VA tany = Si sinx\ 1 cosx 1 cos x cos’x sinx . = = v A removing brackets sinx 1 = cos* x+sin* x YA writing as a single fraction sin x —s v A cos’ x+sin? x=1 sinx (4) =RHS OR Copyright Reserved Please turn over

KZN/March 2026 —— (cos x#tan x; “aheB8iinloaded from Stanmonenhysics.cam 1 v A removing brackets sin YA tany = 0* cos x YA writing as a single fraction Y A cos’ x+sin? x=1 =RHS (4) 3.4.2 | (i) If sinx=0 “x =0° or x =180° YA 0° and 180° and (ii) If. tan. x is undefined “x =90° or x =270° ¥A 90° and 270° (2) 3.5 | cosB=k and sinf= sin’ B+cos’ B=1 YA sin? B+cos* B=1 2 2 2 (2k) +(k) =(1) ¥ A substitution 4k +k? =1 5k’ =1 2_l 1 == VA k?=— 5 ik 1 fi 5 5 (4) OR OR Copyright Reserved Please turn over

“aheB8inloaded from Stanmonephysics.cam KZN/March 2026 sin B =2cos 8 4 tan Z == an 2 { sx=s1 and y=-2 Pax y =i) 4-2) r=NV5 k=cos Pp cosB=k and sinf=2k v Asin B =2cos 8 VA tan p == v A diagram in the correct quadrant Copyright Reserved TOTAL MARKS: 75