Mathematics Grade 10 KZN September Test 2024 Paper & Memo

Downloaded f rom St anmorephysics. com NATIONAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS COMMON TEST SEPTEMBER 2024 MARKS: 75 TIME: 1 hour 30 minutes This question paper consists of 6 pages and 1 separate diagram sheet Copyright Reserved Please Turn Over

Mathematics 2 September 2024 Common Test Downloaded f rom St anmorephysics. NSC –Grade 10 com INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 6 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. 5. Answers only will NOT necessarily be awarded full marks. 6. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 7. If necessary, round off answers correct to TWO decimal places, unless stated otherwise. 8. Write neatly and legibly. Copyright Reserved

Mathematics 3 September 2024 Common Test Downloaded f rom St anmorephysics. NSC –Grade 10 com QUESTION 1 An advertisement in a local newspaper reads as follows:  Buy an iPhone 14 Pro Max cell phone for only R1 029 per month.  You have 36 months to pay.  No deposit is required. 1.1 Calculate the total amount to be paid over a period of 36 months. (1) 1.2 The monthly instalment quoted in the advertisement, is calculated on a hire purchase agreement which charges interest of 8,2% p.a. on the cash price of the cell phone. Calculate the cash price of the cell phone. (3) 1.3 The cost of the cell phone is subject to inflation and increases to a cash price of R31 968, 11 after 3 years. Calculate the annual inflation rate. (4) [8] QUESTION 2 2.1 On a trip to America, Charity booked into a hotel for five days. The exchange rate at that time was $1=R18,73. The cost of the hotel per day was $104. How much did she spend, in rands, for five days? (3) 2.2 Mr Zungu from Sparks Estate Secondary takes out a loan to buy furniture for his office. The loan is repaid in ONE payment of R189 389,80 at the end of 4 years. The interest paid on the loan is 10% p.a. compounded annually. Calculate the amount of money borrowed from the bank to buy furniture. (4) [7] Copyright Reserved

Mathematics 4 September 2024 Common Test Downloaded f rom St anmorephysics. NSC –Grade 10 com QUESTION 3 3.1 Given: P  A  0,4 ; P  B   0,5 and P  A and B   0,25 . Determine the: 3.1.1 P  not B  (1) 3.1.2 P  A or B  (2) 3.1.3 P  not A and B  (3) 3.2 In a school of 70 Grade 10 learners, 32 learners take Economics (E), 43 take Mathematics (M) and 15 learners take neither of these two subjects. Let the number of learners who take both subjects be x . 3.2.1 Show that x  20 . (3) 3.2.2 Draw a Venn diagram to illustrate the above information. (3) 3.2.3 Determine the probability of a learner taking: (a) Economics and Mathematics. (2) (b) at least ONE of the two subjects. (2) (c) taking EXACTLY ONE subject. (2) 3.2.4 The probability that a Mathematics learner is also a Physical Sciences learner is 79%. Determine the number of learners that take Physical (3) Sciences. [21] Copyright Reserved

Mathematics 5 September 2024 Common Test Downloaded f rom St anmorephysics. NSC –Grade 10 com QUESTION 4 At a School Athletics Day, a stopwatch was used to find the time it took a group of athletes to run the 200m event. The results were recorded in a frequency table below. Class intervals (time in seconds) Frequency (number of athletes) 20  x  30 6 30  x  40 16 40  x  50 21 50  x  60 8 4.1 How many athletes ran the 200m event? (1) 4.2 Calculate the estimated mean. (4) 4.3 What is the modal class interval (1) 4.4   Identify in which class interval the thirtieth 30th percentile lies. (2) 4.5 Represent the data on a histogram, using the attached DIAGRAM SHEET. (3) [11] QUESTION 5 The following Life Sciences marks, for a test out of 50, were recorded from 15 grade 10 learners at a certain school. 10 13 15 17 18 20 23 24 26 28 28 29 39 48 49 5.1 Write down the median. (1) 5.2 Determine: 5.2.1 The mean of the data. (2) 5.2.2 The range. (1) 5.2.3 The interquartile range. (3) 5.3 Draw a box and whisker diagram to represent the data above. (3) 5.4 The pass mark for the Life Sciences test was 30%. How many learners passed? (2) [12] Copyright Reserved

Mathematics 6 September 2024 Common Test Downloaded f rom St anmorephysics. NSC –Grade 10 com QUESTION 6 6.1 Given: f  x   2sin x  1 and g  x   tan x , where x  [0 ;270 ] 6.1.1 Write down the: (a) period of g . (1) (b) range of 𝒇 . (2) 6.1.2 On the same set of axes provided on the DIAGRAM SHEET, sketch the graphs of f and g . Clearly indicate all intercepts with the axes, as well as turning points and end points of the graphs. (4) 6.1.3 Determine the value(s) of x where g  x   0 . (2) 6.2 A handy man attempts to reach the roof of a hall with a ladder 5 metres in length. Unfortunately, the ladder is too short, and a new ladder will be required. Suppose that the length of the ladder needed to reach the top has to be double the distance from the foot of the ladder to the wall. Also, the angle between his current ladder and the ground will need to be equal to the angle between the two ladders. The above situation is depicted in the diagram below. x 6.2.1 Calculate the value of  . (3) 6.2.2 If   30 , determine what the length of the ladder should be, to get the (4) handy man to the roof. [16] TOTAL: [75] Copyright Reserved

Mathematics 7 September 2024 Common Test Downloaded f rom St anmorephysics. NSC –Grade 10 com DIAGRAM SHEET Learner’s Name : _____________________________ QUESTION 4.5 QUESTION 6.1.2 Copyright Reserved

Downloaded f rom St anmorephysics. com MATHEMATICS COMMON TEST SE PT E M BE R 202 4 M AR K I NG G U I D E L INE NATIONAL SENIOR CERTIFICATE GRADE 10 MA R K S: 75 This marking guideline consists of 5 pages. Copyright Reserved Please turn over

Downloaded f rom St anmorephysics. com Mathematics 2 September 2024 Common Test NSC-GRADE 10 Marking Guideline QUESTION 1 1.1 T otal am ou n t  R 1 0 2 9  3 6 = R 37 044 Answer (1) 1.2 A  P 1  i  n  formula substitution 3 7 0 4 4  P  1  0, 0 8 2  3  P  R 2 9 7 3 0, 3 4 answer (3) 1.3 A  P 1  i  n formula 3 3 1 9 6 8, 1 1  2 9 7 3 0, 3 4  1  i  substitution 3 1 9 6 8, 1 1 i  3 1 3 1 9 6 8, 1 1 2 9 7 3 0, 3 4 i3 1 2 9 7 3 0, 3 4 i  2, 4 5 % p .a answer (4) [8] QUESTION 2 2.1 $1  R 18, 73 $104 = x  R 1 9 4 7 , 9 2 x  R 1 9 4 7 , 9 2 p er d ay total sp en d i n g = R 9 7 3 9 , 6 answer (3) 2.2 A  P 1  i  n formula 4 1 8 9 3 8 9 .8 0  P  1  0, 1   substitution P  R 129 355, 78 answer (4) [7] QUESTION 3 3.1.1 P  n ot B   0, 5 answer (1) 3.1.2 P  A or B   P  A   P  B   P  A an d B  formula = 0, 4 + 0, 5  0, 2 5 answer = 0, 65 (2) 3.1.3 P  n ot A an d B   0, 5  0, 2 5  0, 5  0, 2 5 answer = 0, 25 (3) Copyright Reserved Please turn over

Downloaded f rom St anmorephysics. com Mathematics 3 September 2024 Common Test NSC-GRADE 10 Marking Guideline 3.2 32  x  x  43  x 15  70  32  x  x  43  x 15 x  20 equating to 70 answer (3) 3.2.2 12 20 23 15 (4) 3.2.3 20 2 answer (a) P  E an d M     0, 2 9 70 7 (2) 3.2.3 55 11 answer (b) P  A t l east on e     0, 7 9 70 14 (2) 3.2.3 12  23 35 1 answer (c) P  E x actl y on e      0, 5 70 70 2 (2) 3.2.4 P h y si cal sci en ce  4 3  7 9 %  4 3  7 9 %  3 3, 9 7 answer  3 4 l earn ers Answer only: full marks (3) [21] QUESTION 4 4.1. 51 athletes answer (1) 4.2 ( 6  2 5)  (1 6  3 5)  ( 4 5  2 1)  (5 5  8) numerator M ean  x   51 denominator  2095 2095 = 51 answer = 41, 08 (4) 4.3 40  x  50 answer (1) 4.4 30  x  40 answer (2) Copyright Reserved Please turn over

Downloaded f rom St anmorephysics. com Mathematics 4 September 2024 Common Test NSC-GRADE 10 Marking Guideline 4.5  20-40 40-50 50-60 (3) [11] QUESTION 5 5.1 Median = 24  answer (1) 5.2.1 387 387 M ean =  15 15 = 25, 8 answer Answer only: full marks (2) 5.2.2 ran g e = 4 9  1 0 answer = 39 (1) 5.2.3 I Q R = 29  17  2 9  1 7 = 12 answer (3) 5.3  10 and 49 24 17 and 29 (3) 5.4 15 pass mark is the pass mark. answer 50 ∴13 learners passed. Answer only: full marks (2) [12] Copyright Reserved Please turn over

Downloaded f rom St anmorephysics. com Mathematics 5 September 2024 Common Test NSC-GRADE 10 Marking Guideline QUESTION 6 6.1.1 a) P er i od = 1 8 0  answer (1) 6.1.1 b) Range : y   1; 3  notation OR values Range: 1  y  3 (2) 6.1.2 shape of f shape of g asymptotes of g turning point of f (4) 6.1.3 0   x  9 0  OR 1 8 0   x  2 7 0   0  x  90  180  x  270 (2) 6.2.1 x 1 x 1 cos 2    cos 2   2x 2 2x 2 2  60  2  60  = 30 answer (3) 6.2.2 x x cos 3 0    cos 3 0   5 5 x  4, 3 3 value of x answer L en g th of th e l ad d er = 8 , 6 6 m (4) [15] TOTAL: [75] Copyright Reserved Please turn over