Mathematics Grade 10 Paper 2 KZN November 2025 Paper & Memo

Downloaded from Stanmorephysics.com KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE MARKS: 100 TIME: 2 hours This question paper consists of 11 pages, including an information sheet. Copyright Reserved Please Turn Over

Mathes ic/rloaded from Stanmorephysics. com DBE/November 2025 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. ls This question paper consists of 9 questions. 2 Answer ALL the questions. 3) Number the answers correctly according to the numbering system used in this question paper. 4. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your answers. 3. Answers only will NOT necessarily be awarded full marks. — 6. You may use an approve stated otherwise. or (non-programmable and non-graphical), unless a If necessary, round off answ O decimal places, unless stated otherwise. 8. Write neatly and legibly. Copyright Reserved Please Turn Over

MathepsUWiiloaded from Stanmorephysics.com QUESTION 1 DBE/November 2025 The table below shows the number of public schools from the NINE provinces in South Africa. Provinces Number of public schools Eastern Cape 5 468 Free State 1214 Ll () 1.2 (2) 1.3 Write down the media qd) 1.4 Determine the interqua (3) 1.5 Due to the population: as uth Africa, 0,68% more schools will be required in the next 15 years. Determine the number of schools needed in the next 15 years. (2) 19] QUESTION 2 The following table represents the grade 10 mathematics test results at Excel Secondary School. MARKS (in %) FREQUENCY 20<x<30 6 30<x<40 ll 40<x<50 9 50<x<60 7 60<x<70 8 70<x<80 13 80<x<90 6 2.1 How many learners wrote the test? (1) 22) Calculate the estimated mean. (4) 2.3 Calculate the percentage of learners who obtained less than SIXTY PERCENT. (2) Copyright Reserved (7] Please Turn Over

Mathes ic/rloaded from Stanmorephysics. com DBE/November 2025 QUESTION 3 3.1 In the diagram below, trapezium QHFS is drawn, such that QH//SF. ry v x 3.1.1 Determine the gradient of SF. (2) 3.1.2 Determine the equation of QH. (3) 3.1.3 Calculate the value of k. (2) 3.1.4 Determine the length of HF. (2) 3.1.5 Calculate the coordinates of M, the midpoint of HS. (3) 3.2 Line segment AB is perpendicular to the segment CD. A(-5 ; 2) and B(p ;-1) are points on AB. If the gradient of segment CD is 2, calculate the value of p. (3) [15] Copyright Reserved Please Turn Over

Mathes riloaded from Stanmorephysics.com DBE/November 2025 QUESTION 4 a 4.1 if Yay: 7,7° and y=52,3°. Calculate the following correct to TWO decimal places. (2) (2) (2) 42 ( ms (correct to ONE decimal place). (3) 4.2.2 4tan0= (3) 4.3 In which quadrant d¢ e | n of the angle @ lie if: 43.1 sin@<0 and (1) 43.2 tand<0a (1) [14] Copyright Reserved Please Turn Over

Mathes riloaded from Stanmorepshysics.com DBE/November 2025 QUESTION 5 artesian plane such that XOP = 0. Siahimorephysics.com S-Lel Calculate the length of OP. (2) $112. Hence, WITHOUT the use of a calculator, determine the value of: a) tanO () b) (sind+cos0)" (3) Copyright Reserved Please Turn Over

Mathes ic/rloaded from Stanmorephysics. com DBE/November 2025 5.2 In the diagram below WMT = 90°, MS_L WT, W =70° and MW =40 units. T 5.2.1 (3) 52:2 (5) [14] QUESTION 6 Given: g(x)=cosx+1 and f(x)=2sinx for x <[0° ; 360°]. 6.1 On the grid provided in your SPECIAL ANSWER BOOK, sketch the graphs of f and gon the same set of axes for x e[0° ; 360°]. (4) 6.2 Write down the period of /. qd) 6.3 Determine the range of g. (2) 6.4 For which value of x will al itis =1? (2) 19] Copyright Reserved Please Turn Over

Mathes i/rloaded from Stanmorephysics. com DBE/November 2025 In the next TWO questions, ensure you give reasons for each statement you make. QUESTION 7 7.1 In the diagram below, ABCD is a parallelogram with AB//EG//DC. B v G Zz Cc Talal Determine the es of and w and x. (4) 71.2 Calculate the values of y and z. (4) 7.2 Given AABC, where AM = MB and AN=NC. A N B. C 5 Prove the theorem which states that MN =5BC 6) Copyright Reserved Please Turn Over

Mathes riloaded from Stanmorephysics. com DBE/November 2025 73 In the diagram below KR//CP, PX//RC , MP =PR =9cm and CK =15cm. K yr = x M 99cm jf U s -_ U 73.1 Prove that M (3) 73.2 Calculate tahmore chess Co: (2) 7.3.3. Hence, prove that MRK = 90° (2) [20] Copyright Reserved Please Turn Over

Mathes ic/rloaded from Stanmorephysics. com DBE/November 2025 QUESTION 8 In the diagram below, OB bisects ABC. O is the centre of the circle and ABC = 60°. 8.1 Determine the size of (1) 8.2 Calculate the size of 0, ue (3) 8.3 Hence, prove that AOAB= AOCB. (3) [7] QUESTION 9 A globe of the world, spherical in shape, is placed in a geography classroom. The globe has a radius of 21 cm. 91 Calculate the volume of the globe, correct to ONE decimal place. (2) 9.2 Determine the area of the globe, correct to ONE decimal place. (2) 9.3 If the radius is doubled, what would be the ratio of the volume of the original sphere to the volume of the new sphere? (1) [5] TOTAL MARKS: 100 Copyright Reserved Please Turn Over

MathepsUWiiloaded from Stanmorephysics.com DBE/November 2025 INFORMATION SHEET: MATHEMATICS D=bEND’ —4ac 2a A= P(1+ni) A=P(1-ni) A=P(1-i)" A=P(1+i)" T, =a+(n-l)d S, =Sea+(n—nd] T,=ar™" Ss _ alr" -1) ;r#l S,=—¢; -ler<l . r-1 1-r pa+i' = past-0+9"] j ; 7 xt+h)—f(x P(x) = im LEADS) h>0 h y=mxt+e 2a Ns m=tan@ In AABC: snA sinB sinC a =b° +c? —2be.cosA area AABC = 5absinC sin(@ + #) =sina cos B+ cosa@sin # cos(a + #) =cosacos # —-sinasin B cos’ a-sin’ @ cos2a@ =41—2sin> @ 2cos* a1 Copyright Reserved sin(a@ — #) =sin acos B —cosasin B cos(a — #) =cosa cos B+ sina sin B sin2@ =2sina.cosa 9 2 De 3) of = n P(A ot B) = P(A) + P(B) — P(A and B) De-*O-H) = *"Se-a Please Turn Over

Downloaded from Stanmorephysics.com KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA TO: DIRECTOR: CURRICULUM GRADES 10 - 12 DISTRICT DIRECTORS DISTRICT HEADS OF CURRICULUM GRADES: 10 - 12 DISTRICT HEADS OF EXAMINATIONS AND ASSESSMENT DISTRICT HEADS OF CIRCUIT MANAGEMENT CIRCUIT MANAGEMENT MATHEMATICS SUBJECT ADVISORS PRINCIPALS OF SECONDARY SCHOOLS ADDENDUM TO THE PROVINCIAL COMMON EXAMINATION FOR GRADE 10 MATHEMATICS PAPER 2 NOVEMBER 2025 Please note that question 7.2 from this question paper has to be removed and replaced as shown below: Remove question 7.2: Given AABC, where M, y (5) Prove the theorem which states that MN=>BC B c Replace question 7.2 with: Given quadrilateral ABCD as shown below, with AD=BC and AD || BC. Prove that ABCD is a parallelogram. PLEASE NOTE: THIS QUESTION MUST BE ANSWERED ON PAGE 16 UNDER ADDITIONAL SPACE Your, eration in this regard is highly appreciated. (oe 04% 41.2025 DRC PENNISTON DATE CHIEF DIRECTOR EXAMINATIONS, ASSESSMENT AND QUALITY ASSURANCE Scanned with SJ CamScanner’

Downloaded from Stanmonepnixgics.com KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE MARKS: 100 This marking guideline consists of 10 pages.

MathemPewnloaded from Stanmorephysics.com November 2025 GRADE10 Marking Guideline QUESTION 1 1. x =2083 AY answer () 1.2 _ 23718 9 mean =2635,33 | ANSWER ONLY: FULL MARKS AV’ answer PENALISE HERE FOR ROUNDING (2) 1.3 Mpumalanga ALSO ACCEPT 1725 CAY answer (1) 14 IQR = Q,-Q, CAY Q, and Q, IQR = 4667,5—1332 CAY correct subst = 3335,50 CAY answer (B) 1.5 Number of schools = 23718(0,68%)e= AY = 161,28 ‘ = 162 schools AY ALSO ACCEPT Number of schools = 2 5 AY = 23879,28 = 23880 schools Av Q) 19] QUESTION 2 21 A ¥ answer (1) .7) + (65.8) +(75.13)+(85.6) | A ¥ correct midpts CAY 60 CAY 3330 CAY R ONLY: FULL MARKS answer —_ 3330 BS" B80 60 CAY 60 ¥=55,50 CAY answer (4) Copyright Reserved Please turn over

MathemPewnloaded from Stanmorephysics.com November 2025 GRADE10 Marking Guideline v 2.3 naa. «100 AVY 33 | 605) CAY answer [55% (2) uif 17] QUESTION 3 | 3.1.1 = 5 = fig y27)1 x, —% O+1 AY - subst into Msp = 3-0 correct formula Mp =; ANSWER ONLY: FULL MARKS __ | CAY answer (2) CAY may = Me CAY correct subst fafimorephysies.com CAV answer CAY Moy = Msp CAV correct subst CAV answer (3) Piet 3 k=-2 OR CAY correct subst CAV answer k<0 Copyright Reserved Please turn over

MathemPewnloaded from Stanmoreph ics.com November 2025 GRADE10 Marking Guideline AY correct subst CAY answer k<0 (2) 3.1.4 AY — correct subst CAY answer (2) 3:15 AY correct subst CAV 2 cay 3 2: (3) 3.2 1 AY my = “3 CAY equate toM,, CAY answer (3) [15] QUESTION 4 4.1.1 sin x 2 _ sin 67,7° AY correct subst 2 CAY answer =0,46 (2) 4.1.2 cos(3y) _ cos(3(52,3°)) AY correct subst v =-0,92 CAY answer (2) Copyright Reserved Please turn over

MathemPewnloaded from Stanmorephysics.com GRADE10 Marking Guideline November 2025 AY correct subst ad CAY answer (2) 3+cos40 = 3,706 AV cos 40 = 0,706 cos 40 = 0,706 40 = 45,08961075° CAY @=T11,3° 40 = 45,08961075° CAY answer (3) 4.2.2 4tan0=7-—4tan 8tand=7 AY 8tan0=7 tand=7 CAY tano= 6 8 O=41,2° CAY answer (3) 4.3.1 Third quadrant AY (l) 4.3.2 Fourth quadrant AY (l) [14] QUESTION 5 5.1.1 a? +y =r Pythagoras v (-12)’ +(5)° = OP? AY — correct subst OP = 13units ANSWER ONLY: FULL MARKS CAY answer (2) vo 512 2) wd=— is A 12 a) Copyright Reserved Please turn over

Mathemewnloaded from Stanmorephysics.com GRADEI 0 Marking Guideline November 2025 b)-(sind +cos0)° isla) =| —+| — 13 13 (UB =o 169 OR =sin’ 0+2sin@cos@+ cos’ @ CAY Y correct subst CAY answer AY simplification CAY correct subst _ 25, =120 144 169 169 169 a _ 49 CAY answer 169 (3) 5.2.1 §, = 90° angles on str line AY S,=90° 70° = WSs AY correct subst costae = “40. into trig ratio WS = 13,68 units CAY answer (3) P Y tri i Ded cos W = WM AY trig ratio WT cos.70° = 40° AY correct subst WT CAY BNE opeekie WT=116,952176 ST=116,952176 -13,68 CAV difference ST =103,27 units CAY answer OR T=20° sumofA AY SIR in20°= 40 CAY correct subst sa WT into trig ratio WT =116,952176 cay ST=116,952176-13,68 WT=116,952176 ST =103,27 units CAY difference CAY answer [14] Copyright Reserved Please turn over

MathemPewnloaded from Stanmorephysics.com GRADE1L 0 Marking Guideline November 2025 QUESTION 6 6.1 g(x) Av shape AV Tpt wae) Av shape AY x int (4) 6.2 360° (1) 6.3 O<y<2 or ye[0;2] (2) 6.4 a(x)— SQ) =3 x=270° ANSWER ONLY: FULL MARKS (2) 19] Copyright Reserved Please turn over

MathemPewnloaded from Stanmoreph ics.com November 2025 GRADE10 Marking Guideline QUESTION 7 711 | 2y4210=70° corr Zs AB//EG AY S/JR w=30° AV answer 5x+45°+70°=180° sum Zs in A AVY S/R x=DBF AY answer (4) 7.1.2 | y+70°+45°=180° sum Zs inA AV SJR y=65° AY answer z=70° opp Zs of parm YSYR (4) 72 A i D B In AABC and AADC AC is common vS Ce Ay alt Zs AD|IBC vS/IR BC=AD given vs . AABC=AADC SAS vS/R A,=C, congruent As vS -. AB|| DC alt Zs equal «. ABCD is a parm 2 pairs of opposite sides parallel ALTERNATIVELY AD=BC given vS AD || BC given vs -. ABCD is a parm vs One pair of opposite sides equal and parallel vYR (5) Copyright Reserved Please turn over

MathemPewnloaded from Stanmoreph ics.com November 2025 GRADE10 Marking Guideline 7.3.1 |MC=KC line through midpt // to 2nd side AY S/R MG =15 Av 15 MX=CX Line through midpt // 2nd side AY SIR MC=+=MX+CxX 2MxX=15 MX = os. 2 (3) 7.3.2 KR= 16 5 KR= 16 x 15 AY correct subst 5 2 RB- 24 AY answer (2) 7.3.3 | MK* =30° MK’ =900 AY MR? +KR? = 187 +24? MR? +KR? =900 CAY MRK=90° _convers (2) [20] QUESTION 8 8.1 ABO = 30° OB bisects ABC AVS (1) 8.2 A=ABO Zs opp equal sides AY S/R A=30° AY A=30° 0, =ABO+A Ext Zs of A AY answer O, = 60° OR A=ABO Zs opp equal sides AV SIR AOB = 120° sum of A AY SIR Bs 0, = 60° Zs onastr line AY SIR (3) Copyright Reserved Please turn over

MathemPewnloaded from Stanmoreph ics.com November 2025 GRADE1 0 Marking Guideline 8.3 In AABO and ACBO 1) BO is common AVY S/R 2) ABO =CBO=30° —OB bisects ABC AY SIR 3) A=ABO=30° Zs opp = sides C=CBO=30° Zs opp = sides A=C :. AOB = COB sum of A AABO =ACBO SAA Av SAA @) [7] QUESTION 9 9.1 V= 4 ar AY correct subst 4 3 V=—2(21 7 (21) V =38792,4 cm’® CAPanswer Provided z and r used (2) in the formula 9.2 A=4ar? A=42(21) AY correct subst . CAY answer A=5541,8 em Provided and r used in the formula Q) 9.3 1 CAY answer 1:8 or — 8 qd) [5] TOTAL MARKS: 100 Copyright Reserved Please turn over