Mathematics Grade 11 KZN Prelim 2025 Paper & Memo

Downloaded from Stanmorephysics.com KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL 1% hours This question paper consists of 7 pages and 2 DIAGRAM SHEETS. Copyright reserved Please Turn Over

matPewnloaded from Stanmorephysics.com September 2025 Test Grade 1 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2. This question paper consists of 5 questions. Answer ALL the questions. Number the answers correctly and according to the numbering system used in this question paper. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your answers. Answers only will NOT necessarily be awarded full marks. You may use an appro graphical), unless s lator (non-programmable and non- If necessary, round off ans\ TWO decimal places, unless stated otherwise. TWO DIAGRAM SHEETS fo ON 3.2.2, QUESTION 3.2.4, QUESTION 5.1 and QUE attached at the end of this question paper. Detach the DIAGRAM SHEETS and hand them in together with your ANSWER BOOK. Diagrams are NOT necessarily drawn to scale. Write neatly and legibly. Copyright reserved Please Turn Over

matPewnloaded from Stanmorephysics.com September 2025 Test Grade 1 QUESTION 1 1.1 1.2 1.3 1.4 15 A’school bought a brand-new data projector for R20 000. The value of the machine depreciated annually at the rate of 13% per annum, on a reducing balance. 1-1-1 — Calculate the book value of the data projector 7 years after it was bought. (2) 1.1.2. The exchange rate between America ($) and South Africa (R ) was $1 =R18,45. Calculate the book value of the data projector 7 years after it was bought in American dollars. (2) An investment earns interest a p.a., compounded quarterly. Calculate the effective interest rate (3) The value of a flat increases a e rate of 12% per annum on a straight-line basis. Calculate the current f it will be valued at R500 050 in 60 months’ time. (2) Three years ago, the selling price of a dozen of eggs was R16,25. The selling price of a dozen of eggs is currently R18,00. Calculate the average yearly inflation rate at which the price of eggs increased over the three years. (4) Mr Mavundla invested R12 000 in an account that earned interest at the rate of 11,35% p.a.. He had forgotten what the compounding period of the investment was. After 20 unequal amounts of interest were added to the original investment, the accumulated amount was R36 193,15. How many years did it take for the original investment to accumulate to R36 193,15? (5) [18] (2) iven that events A and B are mutually exclusive. (3) Copyright reserved Please Turn Over

matPewnloaded from Stanmorephysics.com September 2025 Test rade | 2:2 A SuEICY was conducted among 140 workers about the category of salary they earned i ey worked. The results are summarised in the Moderate Bad : : Total environment | environment 15 17 55 3 Pp 60 12 9 25 30 61 140 Write down the values of m and p. (2) 2.2.2 Calculate the prob electing a worker from this group who worked in a good ose salary was in the R25 000 < x < R40 000 cate (1) 2.2.3. Are the events worki rate environment and earning a salary above R40 000 independent? Fustif ir answer with relevant calculations. (4) 2.3. Mr Van der Merwe rolls an ordinary fair dice in a game. The rules are as follows: e if number | is rolled, he wins; e ifnumber 2 or 3 is rolled, he loses; e if number 4,5 or 6 is rolled, he rolls again. If Mr Van der Merwe rolls again and: e anumber from | to 4 is rolled, he loses; e number 5 or 6 is rolled, he wins. The game stops when Mr Van der Merwe wins or loses. 2.3.1 Represent the above information in a tree diagram. Show the probabilities associated with each branch and the outcomes of this game. (4) 2.3.2 Write down the probability that Mr Van der Merwe wins on the first roll of the dice. q) 2.3.3 Calculate the probability that Mr Van der Merwe will lose at this game. Write your answer as a percentage. (3) [20] Copyright reserved Please Turn Over

matPewnloaded from Stanmorephysics.com September 2025 Test Grade 1 QUESTION 3 ca! 3.2 The table below shows the number of learners who participated in a Maths Olympiad at a school over the past 9 years. 5 8 15 20 25 27 31 36 75 3.1.1 Calculate the mean of the data. (2) 3.1.2 Write down the standard deviation of the data. dd) of learners who participated in the Maths 3.1.3. For how many years wa 1 ation below the mean? (2) tbe number )f learners waited one afternoon before orded. The information was summarised The amount of time, in mi they were helped by a schoo in the frequency table below. 3.2.1 Write down the modal class of the data. (dd) 3.2.2 Complete the cumulative frequency column of the table provided in DIAGRAM SHEET 1. (2) 3.2.3. Write down the total number of learners who waited to be helped by the librarian () that afternoon. 3.2.4 On the grid provided in DIAGRAM SHEET 1, draw the cumulative frequency graph (ogive) of the data. (3) 3.2.5 Use your graph to estimate the interquartile range of the data. (3) [15] Copyright reserved Please Turn Over

matPawnloaded from Stanmorephysics.com September 2025 Test le 1 QUESTION 4. In the diagram below, the graphs of f(x)=sinbx+gq and g(x) =cos(x+p) are shown for the interval 90° < x <180°. 4 z= oN 15 re — 7 LZ, -° 60° oe Yea? 055 r 4.1 Write down the amplitude of f () 4.2 Write down the period of g. (1) 43 Write down the values of b, q and p. (3) 44 Determine the value(s) of x in the interval —90° < x <180° for which: 4.4.1 x.g(x) 20. (2) 44.2 — f(x)—sin30°= g(x)+1 (3) 45 Given that A(x)=g(x+k), determine the value(s) of k in the interval —90° <k <180°where h(x) =sin(—x). (2) [12] Copyright reserved Please Turn Over

matPawnloaded from Stanmonephysics.com September 2025 Test le 1 QUESTIONS 5.1 Inthe diagram below, AABC is sketched. B is an acute angle. A sinB _ sinC Use the sketch provided on D! 2 to prove that = (5) e 5.2 In the diagram below, AB is a vertical pole. The angle of elevation from C to the top of the pole is @ and the angle of elevation from M to the top of the pole is @. CM is x metres. B x ain a@.sin@ (5) sin(O-a) [10] TOTAL: 75 MARKS Copyright reserved Please Turn Over

TEAR OFF matPewnloaded from Stanmorephysics.com September 2025 Test Grade 1 NAME: DIAGRAM SHEET 1 QUESTION 3.2.2 Time waiting Number of | Cumulative (in minutes) learners frequency O<x<4 6 4<x<8 12 20 16 6 QUESTION 3.2.4 10 ll 12 Time waiting (in minutes) 14 15 16 17 18 19 20 Copyright reserved Please Turn Over

September 2025 Test Grade 1 matPawnloaded from Stanmorephysics.com DIAGRAM SHEET 2 QUESTION 5.1 QUESTION 5.2 Copyright reserved AHO YUVAL

NATIONAL SENIOR CERTIFICATE MARKS: 75 These marking guidelines consist of 7 pages.

Matheownloaded from Stanmorephysics.com September 2025 Test Grade 11 CAPS — Marking Guidelines QUESTION 1 1.1.1 | A=P(1-i)" B/D incorrect formula A=20-000(1-0,1 3)’ vA correct subst. into correct formula fal Only penalize here for RG 45,10 incorrect rounding off. ¥CA answer Q) 1.1.2 | Vaiuein dotlars = 87 545.10 va Book value R18,45/$1 18,45 =$408,95 | Answer only: Full marks ¥CA answer Q) 1.2 tig = ( + ba] YA correct formula m 4 ltig = (: + 0, a vA correct substitution into formula 4 r=9,31% per annum ¥CA answer G3) 13 | 4=P(+in) 500050= P(1+0,12x 5) vA correct subst. into correct formula _ 500050 (1+0,12x 5) P=R312531,25 B/D incorrect formula ¥CA answer (2) 14 A=P(I+i)' (red) ; VA P= 16,25; A= 18; n=3 18=16, 25(1 +i ) vA subst. into correct formula . 18 i= te 25 ol YCA simplifying using ¥..... im B/D incorrect formula and a r=3,47% if A and P are swopped CA answer “) vA correct subst. of A and P vA correct subst. of i and exponent 20 ¥CA simplification ¥CA value of compounding period ¥CA answer (5)

Matheewnloaded from Stanmorephysics.com September 2025 Test Grade 11 CAPS — Marking Guidelines QUESTION 2 2.1.1 | P(B)=1—P(not B) =1-0,67 Agesier Galyt 2 vA subst. into correct rule = 0,33 2 v A answer (2) 2.1.2 | P(A or B)= P(A) + P(B)—P(A and B) 0,57 = P(A) +.0,33 —0 P(A) = 0,24 B/D if P(A and B) #0 OR P(A or B)= P(A) + P(B) 0,57 = P(A) + 0,33 ¥ A correct rule ¥CA substitution ¥CA answer (3) OR v A correct rule ¥ CA substitution P(A) = 0,24 ¥ CA answer (3) 2.2.1 |m=4 YA 4 p=35 VA 35 (2) a2) | P= 140 11 ll P= — vA — 1 70 70 qd) 2.2.3 | P(moderate and R40 000 < x3 3 vA — OR 0,09 35 P 30. 25 (moderate )xP (R40 000 < x < R65 000) VA ax 140 140 140 140 15 15 =—— OR 0,04 vA — OR 0,04 392 392 P( moderate and > R40 000) # P(moderate)xP(> R40 000) ..the events are NOT INDEPENDENT ¥CA conclusion (4) 2.3.1 1* roll 24 roll OUTCOMES , ' vA both branches correct Wins Wins ¥ A correct probabilities: x Zor! i 3orl on I* roll Loses, Loses 6 6 3 6 2 4 Loses Rolls Again & Loses | vA correct probabilities: ree : : OR : : : OR ; on 2™ roll : Wins Rolls Again & Wins | YA outcomes (4) 2.3.2 P(win on the first roll) == OR 0,17 OR 16,67% vA z (1) 2.3.3 | P(loses)= P(L) + P(Rolls Again and Loses) 5 P(loses)= 2 + exe vCA 6 OR ; 6 Copyright Reserved Please turn over

Mathefawnloaded from Stanmorephysics.com September 2025 Test Grade 11 CAPS arking Guidelines 11 3.4 1.2 moe ¥CA >x— OR=x= P(loses) : oC as P(loses)= 66,67% YCA answer (3) [20] QUESTION 3 31.1 | x22” F VA 242 9 Answer only: = = 26,89 2 ¥CA answer Note: CA only if divided by 9 (2) 3.1.2 | o=19,56 VA 19,56 dl) 3.1.3 | ¥-o =26,89-19,56 = 7,33 (no. of learne on below the mean) YCA x-o -. | year ¥CA answer (2) 3.2.1 | 8<x<12 v A answer qd) 8.2: - 7 Time waiting (in minutes) O0<x<4 1 2 an VA 6; 18 20 38 16 54 6 60 YCA 38; 54; 60 (2) 3.2.3 | 60 learners ¥CA answer (1) Copyright Reserved Please turn over

Matheewnloaded from Stanmorephysics.com September 2025 Test Grade 11 CAPS — Marking Guidelines 3.2.4 60 58 | 56 54 4 re! YCA points plotted Pa a at upper limit 44 Es a ¥ A shape: smooth = 38 curve 36 out v : 32 A grounding at 23 (0:0) £ 26 5 24 2 2 20 18 16 14 12 10 8 6 > ri Vv SS (3) 13. 14 15 16 17 18 19 20 e inutes) 3.2.5 | Q#7,5 YCA Q, =7,5 (accept 7 to 8) Q, 13,5 YCA Q, =13,5 (accept 13 to 14) IQR = 13,5-7,5 =é ¥CA answer (accept 6 to 7) (3) [15] QUESTION 4 4.1 | Amplitude of f =1 vA 1 da) 4.2 | Period of g =360° YA 360° Q) 43 | b=2 VA b=2 q=l VA q=1 p=30° VA p=30° GB) 44.1 | xe [oe ; 60°] OR 0°<x <60° v A critical values/endpoints V : If xe (0°; 60°) OR 0°<x <60°: 1 mark shnofation 6 4.4.2 | f(x)-sin30°= g(x)+1 1 ae a i vA sin30°= 3 OR 0,5 F(x) = g(x) +15 vA manipulation *x=90° Also accept: x =34,4° or x=166,4° || vA answer GB) Copyright Reserved Please turn over

Mathesownloaded from Stanmorephysics.com Grade 11 CAPS — Marking Guidelines September 2025 Test 45 | h(x)=sin(—x) =Ssinx ~=cos(90°+x) YA cos(90°+x) =cos(x+30°+60°) rs 1k =60° Answer only: — VA k=60° p : 2 ! Q) [12] QUESTION 5 5.1 Construction: Draw perpen YA construction In AABD: sing =" vA ana c VA h=csinB VA h=bsinC FA csinB _ bsinC be be (5) OR Copyright Reserved Please turn over

Mathedownloaded from Stanmorephysics.com Grade 11 CAPS — Marking Guidelines September 2025 Test A(ccosB ; csinB) csinB —— ry B D Cc % Construction: Draw perpendicular height AD. In AABC: h=csinB In AADC: sinC=4 csinB _ bsinC be be sinB_ sinC —= ahimorephysics.com b e YA construction YA y, orh=csinB YA sinc at b YA h=bsinC vA equating and + by be (5) 52 sin(O—a) _ _xsina sin(@-a) In AAMB: sind AM -. AB= AMxsin@ _ xsina.sinO sin(@-a) VA CAM=60-a@ ¥ A correct subst. into sine rule TOTAL MARK: 75 Copyright Reserved