Mathematics Grade 10 Paper 1 KZN November 2025 Paper & Memo

Downloaded from Stanmorephysics.com KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE tanmorephysics. com MARKS: 100 TIME: 2 hours This question paper consists of 8 pages, including an information sheet.

Bawnloaded from Stanmorephysics.com DBE/November 2025 CAPS — Grade 10 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. Ll. This question paper consists of 7 questions. 2: Answer ALL the questions. 3s 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. — $; Answers only Wi be awarded full marks. 6. You may use an apj unless stated othe calculator (non-programmable and non-graphical), Ti If necessary, round off answers correct to TWO decimal places, unless stated otherwise. 8. Write neatly and legibly. Copyright reserved Please turn over

Bawnloaded from Stanmorephysics.com DBE/November 2025 Cc S — Grade 10 12.3 593-4 0 1.3 Calculate the value of the following, WITHOUT the use of a calculator: 2010 (2013? —9)x 2012 2016x (2011? —1) Copyright reserved Please turn over (2) (3) (3) (2) (3) (3) (4) [20]

Bawnloaded from Stanmorephysics.com DBE/November 2025 Cc 'S — Grade 10 QUESTION 2 2.1 Solve for x without using a calculator: 2.2 Ataschool event, tickets are sold at two different prices: R20 for adults and R12 for learners. A total of 20 tickets were sold, collecting R320 in total. How many adult tickets and learner tickets were sold? Let the number of adult tickets be x and the number of learner tickets be y. QUESTION 3 3.1 The n" term of an 3.1.1 Determin ri of the sequence. 3.1.2 Which term is equal to 683? 3.2 A grade 10 learner wrote the word WHEAT over and over again on a piece of paper as follows: d position, the second H is in the seventh position, the osition, and so forth. Determine in which position the 1;-7x4;-11x7;-15x10. Determine the 62"! term of the above pattern. Copyright reserved Please turn over (3) (4) (6) [13] (1) (3) (1) (3) (3) (4) [15]

Bawnloaded from Stanmorephysics.com DBE/November 2025 CAPS — Grade 10 QUESTION 4 Amanda is planning a trip to England in 2 years. She considers two different ways to save her money. meena Option 2 She invests RS 000 at 6% She invest R8 000 at 5,5% per annum simple interest per annum compound —— interest for 2 years. 4.1 Calculate the total man ill have after 2 years if she chooses the 2" option. (2) a 4.2 Which option gives aa com return after 2 years? Show calculations to support your answer. (3) 4.3 If the exchange rate is £1 = R22,50. How many British pounds (£) will she have after 2 years if she chooses the better option? (2) 4.4 Suppose instead she wants to use option 1, but save monthly. If the bank agrees to let her save a fixed amount every month for 2 years, and she wants a total of R9 000, calculate the fixed monthly payment. (Assume the interest is only calculated on the total of all deposits at the end of 2 years) (3) [10] Copyright reserved Please turn over

Bawnloaded from Stanmorephysics.com DBE/November 2025 CAPS — Grade 10 QUESTION 5 5.1 Sketched below are the graphs of f(x) = 2s and g(x)=—2x—-1. Points A and B are x x-intercepts of f and g respectively. E is the y-intercept of g. C and D are the points of intersection of f and g. 5 g& x any S74 | ee f 5.1.1 Write down: a) the y-coordinate of E. b) the equation of the vertical asymptote of 5.1.2 Determine the coordinates of B. 5.1.3. Calculate the length of AB. 5.1.4 Determine the coordinates of C and D. 5.1.5 Determine the value(s) of x for which: a) f is increasing. g(x) b 2—<0 £0) 5.1.6 If h(x) = f(—x)+3. Describe in words the transformation from f to h. Copyright reserved Please turn over (1) Q) (2) (4) (5) (1) (3) (2)

Bawnloaded from Stanmorephysics.com DBE/November 2025 Cc 'S — Grade 10 5.2 Use the following properties to sketch the graph of p if p(x)=axb'+q: ea>0 °0<b<l +q<0 (3) [22] QUESTION 6 Given: m(x) =—2x’ +8 6.1 Determine the x — intercepts of m. (2) 6.2 Sketch the graph of m. (3) 6.3 Determine the value(s) of k for which m(x)=k will have no solution. (1) 6.4 Determine the maximum value of sn (2) [8] QUESTION 7 7.1 If P(D)=0,25 ; P( P(D or K) = 0,625 7.1.1 Calculate | (2) 7.1.2 Are eve nts D entary? Give a reason. (2) 7.2 A survey was conducted among 100 learners to determine their participation in two subjects: Maths (M) and Life Orientation (LO). The following results were obtained: e 42 learners participate in Maths. e 35 learners participate in Life Orientation. x learners participate in both subjects. re nt the above information. (3) s who participated in both subjects. (2) learner selected at random participates in: (1) (1) () [12] TOTAL MARKS: 100 Copyright reserved Please turn over

Bawnloaded from Stanmorephysics. .com DBE/November 2025 'S — Grade 10 INFORMATION SHEET: MATHEMATICS ~b+tAb° —4ac xa 2a A=P(1+ni) A= P(1-ni) A=PQ-i" A=P(1+i)” n T, =a+(n-Nd 8, = 5 a+ (-Dd] I, =r" Ss _ alr -1) 3;r#l S,=—";-l<r<l . r-1 l-r a (+1) 1 p= sls)" t I xth x f= im a F(x) m=tand In AABC: gg On snA sinB sinC a =b? +c? —2be.cosA area AABC = 5 absin c sin(a + B)=sin acos 8 +cosa@sin B sin(a@ — 8) =sin acos B-cosasin B cos(@ + 8) = cosacos f-sinasin B cos(a — 8) = cosa cos #+sinasin B cos? a—sin? @ cos2@ =41-2sin’?a sin2@ = 2sina.cos a 2cos*a-1 n 2 2s >, -¥) x= oe o =a n nA) _ P(A)= “AS) P(A orB)=P(A) + P(B) — P(A and B) . p_ 80-7) p=atbx LG-3" Copyright reserved Please turn over

Downloaded from Stanmerephysicsicom INAL KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE MARKS: 100 This marking guideline consists of 9 pages.

Bewnloaded from Stanmorephysics.com DBE/November 2025 CAPS — Grade 10 Marking Guideline QUESTION 1 1.1.1 2 -6x— v SEI Ps - 62-9 Answer only; Award Full Marks 1 products * A answer 4x°-9 2) 1.1.20) §5(4x? 4x41) +43 YA 4x°-4x41 —20x° +20x° —5x+3 YCA ~20x° + 20x? ¥CA 5x43 @) 11.3 _ 23% ¥ A prime bases pgs wa ad =29x3° ¥CA simplification =] ¥ CA answer GB) 1.2.1 | 2p+5)\(p-3) VA(2p+5)¥ A(p-3) (2) 1.2.2 | =y—-1+by by-b-1 v A rearranging =(y-)+b-D +b)—(b+1) V A factors =(y-l(i+d) b\(y-1) v A answer : GB) ¥ A common factor VA (m-2) VA (m>+2m+4) G3) Answer Only; 0/4 OR v A numerator (factors) vA denominator ¥ A simplification v A answer Copyright reserved Please turn over

Bawnloaded from Stanmorephysics.com 'S — Grade 10 Marking Guideline DBE/November 2025 let 2010 =x 3[(+3)'-9 (+2) (e+) =a] v A numerator (factors) bal oA 6)(x° + 2x) ¥ A denominator _ xx(x+2)(x+6) ~x(x+6)(x+2) vA simplification 6ie = 2010 v A answer (4) [20] QUESTION 2 2.1.1 | 234-99 YA2° 3x-4=-9 ¥CA equating exp. 5 x= “3 ¥CA answer GB) 212; 4 10 2 VA x(x-5) x-5 x x(x-5) ¥ A restrictions LCD = x(x-5) x#00rx#5 restrictions : x #0 or x #5 4x-10(x-5) =2 ¥ A simplification 6x =-48 x=8 ¥CA answer (4) 2.2 X+Y=20 ore (1) vA Equation 1 20x +12y =320......(2) YA Equation 2 y=20-x aes (3) ¥CA_ Equation 3 20x +12(20-x) =320 YCA substitution 20x + 240 -12x =320 8x =80 z= 10 ¥CA_ x-value pail ¥CA_ y-value Copyright reserved Please turn over

Bawnloaded from Stanmorephysics. com DBE/November 2025 CAPS — Grade 10 Marking Guideline OR vA Equation | a w th, Wapato 20x+12y =320 oe) YCA_ Equation 3 x=20-y sseene(3) ¥CA substitution 20(20- y)+12y =320 400-20) +12y =320 8y=80 YCA_ x-value y=10 ¥CA_ y-value on=i0. (6) -. 10 adult tickets and 10 learner tickets were sold. [13] QUESTION 3 SiLel T, =4 VA 4 dQ) 3.1.2 | 683=7n— VA equating 686=7n YCA simplification n=98 YCA answer (néN) GB) S21, |'T vA answer qd) 3.2.2 | 508 VA dividing by 5 5 =101,6 0,6x5=3 93 ibrar v A remainder times 5 v A answer OR OR 510 —e 7 — (510 is divible by 5) VA any number nearest =102 to 508 & divisible by 5 510 or 505 510 to 508 =3 steps backwards 7x method => 3" letter (backwards or forward) iE v A answer GB) Copyright reserved Please turn over

Bawnloaded from Stanmorephysics. .com DBE/November 2025 Grade 10 Marking Guideline ar n-3 YA 5Sn-3 hia 5(103)—3 YCA subst. n = 103 Ls 12 ¥CA answer Ir md (3) 3.3 lah +1)3d —2) Vv AV A(-4k +1)(3d -2) iz ; (62) + 1][3(62) —2] ¥CA substitution |= +247x184 ¥CA answer Accept: —45448 as the final answer (4) [15] QUESTION 4 4.1 A=P(1+i)" = 8000(1 40,0 vA subs. into correct formula =R8904 ¥CA answer OR A= eft + 1 mai imorephysies.com r vA subs. into correct = s000( 33 } formula 00 ¥ CA answer =R8904,20 (2) 4.2 A=P(1+ni) 7 ae 8000(1 +2 0,06) v A subs. into correct | teal ' formula ¥CA future value ¥CA answer OR vA subs. into correct formula ¥CA future value | ¥ CA answer LL @) Copyright reserved Please turn over

Bawnloaded from Stanmorephysics. com DBE/November 2025 CAPS — Grade 10 Marking Guideline 43 R8960x £1 ¥CA dividing by 22,5 R22,50 =£398,22 ¥ CA answer (2) 44 A=P(i+niy 9000 = P(1+ 20,06) VA if wrong formula used P=R8035,71 Y A value of P 8035,71 Y A dividing P by 24 Fixed monthly payment= 24 Y CA answer =R334,82 (3) [10] QUESTION 5 5.1.1a)] y=-l * VA y=-l (1) 5.1.1b) | x=0 VA x=0 (1) 5.1.2 0=-2x- v A equating to 0 x=-t 7 wer only; Award Full marks Y CA answer (in a(-5:0] coordinate form) (2) 513 [5 2, VA f(x)=0 x BeAr x Y CA x, x=-2 A(-2;0) 1 Y CA difference ee 1 Sunt AB 53 +2=1,5units Y CA answer OR OR rynor‘en YA f()=0 ee = x Y CA x, x=-2 A(-2;0) 1 2 5 Y CA using the AB= [-3+2] +(0-0) distance formula v CA answer (4) =1,5units Copyright reserved Please turn over

Bawnloaded from Stanmorephysics. com DBE/November 2025 CAPS — Grade 10 Marking Guideline Slt 2 = 2x-] VA equating x ud =-2x x x -1=0 V A std. form Y CA factors +1)(x-1)=0 rea) Y CA both values of x=-l or x=1 % y=l or y=-3 C11) Y CA both values of D(1;-3) y (5) 5.1.5a)| xeR;x¥0 VA OR x>0 or x<0 VA OR 4 xe(-20 ; 0) or VA Q) 5150) | oan VCAYCAVA GB) OR x€(-0;-2) or xe|-3:0) ¥CAYCAVYA 2 G3) 5.1.6 | - Reflected about the y — axis or line x = 0. vA - Shifted or translated 3 units up. YA Q) 5:2 ¥ vA shape (decreasing function) ¥ A both intercepts ax x with the axes < 0 | Rec, VA horizontal al asymptote < 0 GB) Copyright reserved Please turn over

Bevwnloaded from Stanmorep CAPS — Grade 10 Marking Guideline hysics.com DBE/November 2025 OR Copyright reserved ¥ vA shape (decreasing function) YA point of origin ¥ A horizontal asymptote < 0 A shape (decreasing function) YA both intercepts with the axes ¥ A horizontal asymptote < 0 [22] Please turn over

Bewnloaded from Stanmorephysics..com DBE/November 2025 CAPS — Grade 10 Marking Guideline QUESTION 6 6.1 0==2x7 +8 0=x’-4 vA factors or square root on (&+2)(x—2)=0 both sides x= -2 or x=2 v A (both values of x) Q) 6.2 Y A turning point 5 " | ¥ CA both x - intercepts v A shape (concave down) GB) 6.3 k>8& or keE(8;0) ¥CA (from the graph in 6.2) Q) 6.4 Max value of m=8 8-5=3 YA3 3 «. The maximum value is 27. v A answer Q) [8] Copyright reserved Please turn over

Bawnloaded from Stanmorephysics.com APS — Grade 10 Marking Guideline QUESTION 7 DBE/November 2025 Tedel P(Dand K) = P(D) + P(K)—P(D or K) =0,25+0,5-0,625 vA substitution = 0,125 v CA answer (2) 7.1.2-~1.No, vA - Events are not mutually exclusive / P(Aand B) #0 _OR vA reason - events are not exhaustive / P(A)+P(B) =1 (2) Toul ¥ A x on the intersection vA both 42 —x& 35 —x YA 38 (3) 7.2.2 vA equating ¥ CA answer 2) 7.2.3 VA dd) vA dd) vA Q) [12] Copyright reserved TOTAL: 100 MARKS Please turn over