MATHEMATICS GRADE 12 SESSION 38 (LEARNER NOTES)
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1 EXAM PREPARATION PAPER (A) Leane Note: In this session you will be given the oppotunity to wok on a past examination pape (Feb/Ma 010 DoE Pape ). The pape consists of 1 questions. Question 1, and will be dealt with in this session. Stuctue of Pape TOPIC APPROXIMATE MARK ALLOCATION Coodinate Geomety 40 Tansfomations 5 Tigonomety 60 Data Handling 5 TOTAL 150 Befoe witing the maths examination, it is essential fo you to have at least two blue pens, a pencil, a ule and a wokable scientific calculato (non-pogammable and non-gaphical). You will be given time to ead though the pape pio to stating. It is essential that you ead the instuctions caefully and ensue that the pape is complete. Don t waste time on a specific question. If you cannot do that question, athe move on to the next question. Remembe to numbe the questions coectly. You might wish to stat with Question. This is fine, povided that the question is clealy indicated. SECTION A: TYPICAL EXAM QUESTIONS (QUESTION 1, AND ) Impotant infomation egading Question 1, and It is impotant fo you to evise the gade 10 and 11 Data Handling concepts including quatiles, ange, mode, inte-quatile ange, standad deviation, cumulative fequency cuves, outlies, mean, box and whiske diagams, scatte plots and lines/cuves of best fit. Page 1 of 7
2 QUESTION 1 The gaph below shows the monthly maximum tempeatues in a cetain city. 1.1 What is the ange of the monthly maximum tempeatues? () 1. Calculate the mean monthly maximum tempeatue. () 1. Calculate the standad deviation of the monthly maximum tempeatue. () 1.4 It is pedicted that one hunded yeas fom now, global waming is likely to incease the city s monthly maximum tempeatue by 5 C in Decembe, Januay and Febuay. It will also esult in an incease of 1 C in the othe months of the yea By how much does the mean incease? () 1.4. Descibe the effect that the pedicted inceases in tempeatue will have on the standad deviation. Justify you answe. () Page of 7
3 QUESTION.1 A study was conducted amongst socce playes in South Afica. The numbe of goals scoed in a season was measued against the numbe of hous each playe tained each week. The table below displays the esults. Hous tained (x) Numbe of goals (y) Daw a scatte plot fo the data on the diagam below:.1. One of the data points is an outlie. Indicate this point on the diagam. (1).1. Use you gaph to pedict the numbe of goals scoed by a playe who tains fo 10 hous a week. (). Leanes at Phambili High School tavel fom thee diffeent neighbouhoods, neighbouhood A, B and C. The table below shows the numbe of leanes fom each neighbouhood, and thei mean tavelling times fom home to school. Neighbouhood A B C Numbe of leanes Mean tavelling time (in mins) 4 x The mean tavelling time fo leanes living in neighbouhood C is the same as the mean tavelling time fo all 560 leanes. Calculate the mean tavelling time fo neighbouhood C. Page of 7
4 QUESTION The time taken (to the neaest minute) fo a cetain task to be completed was ecoded on 48 occasions and the following data was obtained: Time (in minutes) Fequency 11t t t 1 t t Complete the cumulative fequency table povided below: Time (in minutes) Fequency Cumulative fequency 11t t t 1 t t 0 8. Daw an ogive fo the given data. Use the diagam povided. (4). Detemine, fom the ogive, the median, lowe quatile and uppe quatile. () Page 4 of 7
5 .4 Daw a box and whiske diagam of the data. Use the diagam povided. ().5 Comment on the spead of the time taken to complete the task. (1) SECTION B: SOLUTIONS AND HINTS TO SESSION 7 QUESTION V h 00 h 00 h 8. Suface Aea h 00 S( ). 400 S( ) 8. 1 S( ) 400 ds 400 d ds At minimum : 0 d ,99 cm V h 00 h () S h 00 S( ). () 1 S( ) 400 ds 400 d ,99 cm (5) Page 5 of 7
6 QUESTION ; a;10 ; b; 1;... (10 a) ( a ) 1 10 a a 1 a 1 a 6 (1 b) ( b10) 1 1 b b10 1 b 0 b 15 (10 a) ( a) 1 a 6 (1 b) ( b10) 1 b 15 (4) 9. ; 6 ;10 ;15 ; 1;... a 1 1 a ab 1 b b a b c 1 c c 1 1 Tn n n1 ; 6 ;10 ;15; 1;... 1 a b c 1 1 Tn n n 1 (5) n n 1 ( n 1) ( n 1) n n 1 ( n n 1) n n n 1 n n n 1 n 4n 4 ( n ) T T n n1 expanding n ( n ) 4n 4 (4) Page 6 of 7
7 QUESTION x See diagam x y x 100y See diagam x40y P 40y 0x P P y x 4 40 cuts on y-axis 4 cuts on x-axis 10.5 Seach line Maximum at (00;00) (00;00) Page 7 of 7
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