Mathematics Grade 10 NSC Prelim 2022 Paper & Memo

Downloaded from Stanmorephysics.com | Ce HEE Gy ) KWAZULU-NATAL PROVINCE EDUCATION REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE TIME: 1% hours This question paper consists of 7 pages.

Matewnloaded from Stanmorephysics.com KZN/September 2022 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 5 questions. Answer ALL the questions. 2. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your answer. 3. ‘You may use an approved scientific calculator (non-programmable and non- hical), unless stated otherwise. re 4. Answers only will not necessarily be awarded full marks. 2 5. If necessary, round off answers to TWO decimal places, unless Ce otherwise. 6. Diagrams are NOT necessarily drawn to scale. oe 7. Number the answers correctly according to the numieling system used in this question paper. & 8. Write neatly and legibly. xO" Copyright Reserved Please turn over

Matewnloaded from Stanmorephysics.com KZN/September 2022 QUESTION 1 11 Tyler decides to purchase a sound system which costs R 7999 on a hire purchase agreement. 1.1.1 If Tyler pays a 11% deposit, calculate the balance after Tyler has paid the deposit. (2) 1.1.2 The store charges Tyler 20% interest per year, with the loan payable over 4 years. Calculate the total amount that he will have to pay back. (3) 1.1.3 Tyler is also required to pay a monthly insurance of R30 and an administration fee of R12. How much will Tyler’s monthly repayments be? (2) 1.2 On a trip to Florida, Akwande booked into a hotel for four nights. The exiangsfona that time was $1 = R16,77. The cost per night was $450. @) How much did she spend, in Rands, for the four nights? Rey (2) 1.3 After 7 years, an investment increased to R95 798,35. If the inet rate was 8,25% per annum, compounded annually, calculate the initially invested. ge (3) 1.4 Lynda deposits R 4500 into a savings account. At tl Xi of 4 years she adds a further amount of R 2500 into the savings account. The i ‘st paid on the savings is 7,5% p.a. compounded annually. ‘) 1.4.1 Calculate how much money.is\in the account at the end of 4 years, immediately after the second deposit. 5 (3) 1.4.2 Calculate how mu wa be available in the savings account 10 years after the first deposi < (3) dS [18] Copyright Reserved Please turn over

Matewnloaded from Stanmorephysics.com KZN/September 2022 QUESTION 2 2.1 2.2 2.3 24 2.5 A bag contains yellow and blue marbles of equal size. The probability that a marble chosen at 1 random will be yellow is é . 2.1.1 If it is given that there are 102 marbles in the bag, how many of them will be blue? 2.1.2 If there are 26 yellow marbles in the bag, how many of them will be blue? Complete the following: 2.2.1 For exhaustive events: P(A or B)=.... 2.2.2 For mutually exclusive events: P(A and B)=.... Given that: e A and B are inclusive events e P(AorB)=0,9 ; P(A)=0,6 and P(B)=0,4 Calculate P(A and B). 205 Grade 10 students have a choice of 2 sports, soccer (S) and hockey (H). 86 students play soccer (S) 64 students play hockey (H) 63 play neither of the 2 sports Let the number of students that play BOTH soccer (S) and hockey (H) be x. 24.1 Draw a Venn diagram to represent the above information. 2.4.2 Calculate how many students play both soccer and hockey. 2.43 Determine the probability that a learner chosen at random plays hockey only. Given: A and B are two mutually exclusive events with P(A) =0,5 and P(B)=0,4. Determine P(B') . Copyright Reserved Please turn over Q) (2) () Q) Q) Q) 2) Q) Q) [17]

Matewnloaded from Stanmorephysics.com KZN/September 2022 QUESTION 3 The coordinates of AABD are given as: A(—5 ; 4), B(3; 5) and D(—1 ;—3) below. E is the midpoint of BD. y A(-5;4) BG;5) E Vi , D(-1:-3) 3.1 Calculate the length of BD. Leave your answer in surd form. (2) 3.2 Determine the coordinates of E , the midpoint of BD. (2) 3.3 Show that AE LBD. (4) 3.4 Determine the equation of the line parallel to BD and passing through A. (3) 3.5 Calculate the area of AABD . (3) 3.6 Determine the coordinates of a point C such that the quadrilateral ABCD is a rhombus. Q) [16] Copyright Reserved Please turn over

Matewnloaded from Stanmorephysics.com KZN/September 2022 QUESTION 4 4.1 42 The data below represents the daily rainfall (in mm) during the month of September in KwaZulu-Natal. RAINFALL | FREQUENCY MIDPOINT MIDPOINT x (mm) FREQUENCY 0<x<20 A 10 20 20<x<40 4 30 120 40<x<60 5 B 250 60<x<80 6 70 420 80<x<100 8 90 720 100 <x <120 3 110 Cc 120<x<140 2 130 260 4.1.1 Determine the missing values in the table above. 4.12 Use the table above to calculate the estimated mean rainfall. 4.1.3 Represent the data on a histogram. 4.1.4 In which class interval will the following be found? (a) the median (b) the 75" percentile (c) the mode The box and whisker plot below shows the test results of a grade 10 class (in percentages. 25 31 64 80 95 — | -—— PrPErErririririteitd 30 40 50 60 70 80 90 = 100 Use the box and whisker plot above to determine: 4.2.1 the lowest and highest marks obtained by students in the test. 4.2.2 what percentage of the class achieved above 31%. 4.2.3 the median mark. 4.2.4 what percentage of the class achieved between 64% and 80%. 4.2.5 the interquartile range. Copyright Reserved Please turn over Q) Q) (3) Q) Q) Q) Q) Q) () Q) (2) [18]

Matewnloaded from Stanmorephysics. com KZN/September 2022 QUESTION 5 Two buildings are 45 metres apart (length ED), separated by a park. A person on the top of the shorter building, at point A, calculates the angle of elevation of B from A to be 30° and the angle of depression of D (the base of the taller building) from A to be 50°. 5.1 5.2 Copyright Reserved B oO oLJe ae Pam 50° a AAA ayaa COE (0 Oo(00)(00 2 OO}44)/(00 strate ha a ae (T) |S amma E park D Determine the size of ADE. () Calculate the length of BD, the height of the taller building. (5) [6] TOTAL [75]

Downloaded from Stanmorephysics.com Education KwaZulu-Natal Department of Education REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE GRADE 10 MARKS: = 75 TIME 1% hours NOTE Ifa candidate answered a QUESTION TWICE, mark only the FIRST attempt. If a candidate crossed out an answer and did not redo it, mark the crossed-out answer. Consistent accuracy applies to ALL aspects of the marking guidelines. Assuming values/answer in order to solve a problem is unacceptable. This marking guideline consists of 6 pages.

MaiPewnloaded from Stanmorephysics.com KZN/September 2022 NSC - Memorandum QUESTION 1 1.1.1 ; 11 deposit Deposit : — x R7999 = R879,89 100 answer Balance: R7999 — R879, 89 = R7119,11 (2) 112 | 4=P(+in) A=P(1+in) A=R7119,11(1+0,2 4) (1+0,2x4) A=R12814,40 answer G) 1.1.3 Monthly payment : ee = R266,97 + additional : + R42 per month adding services answer -, R266,97 + R42 = R308,97 per month @) 1.2 4 nights = 4x $450 = $1800 (for R1800) $1=R16,77 answer (2) .. $1800 = R30186 13 A=P(+i)" substitution into = A correct formula d+)" _ 95798,35 95798, 35 ~ (1+0,0825)" (1+0,0825)’ CA P= R55000 3) 14.10) 4=P(+i" a 4 substitution into A= 4500(1+ 0,075) correct formula A=R6009,61 R6009,61 R6009,61+ R2500 = R8509, 61 CA G) 1.4.2 A=P(1+i)" substitution into correct formula A=8509,61(1+0,075)° n=6 A= R13132,89 CA G3) [18] Copyright Reserved Please turn over

MatPewnloaded from Stanmorephysics.com KZN/September 2022 NSC - Memorandum QUESTION 2 2.1.1 5 P(blue) = 6 method an > x102=85 answer (2) 6 212 | 4 allow) — 26 method - (blue) > 26x5=130 answer 6 (2) OR I xx=26 6 method “x =156 blue = 156-26 = 130 answer @) 2.2.1 P(A or B)=1 answer qd) 2.2.2. | P(A and B)=0 answer (1) 2.3 P(A and B) = P(A) + P(B)— P(Aor B) method: formula P(A and B)=0,6+0,4-0,9 substitution P(A and B)=0,1 answer (3) OR method: Venn diagram A B solving regions answer 0,1 (3) 2.4.1 S = 205 Ss H 86-—x : 63 outside 64—x 63 3) Copyright Reserved Please turn over

MatPewnloaded from Stanmore ysics. com KZN/September 2022 NSC - Memorandum 24.2 | (86—x)+x+(64—x)+63=205 equation 213—x= 205 answer (2) x=8 243 P(hockeyonty) = 29 56 ockey only) = —— yonly 305 205 (2) 2.5 P(B') = 0,6 answer qd) [17] QUESTION 3 3.1 2 2 substitution into aBD = (5 + 3) + (3 + 1) correct formula dBD= 4s answer (2) 3.2 3-1 5-3 substitution into E: Ty correct formula E(:1) answer (2) 3.3 4-1 1 substitution into mAE = “5-1. 2 correct formula mAE p 5-3) _> mBD 3-(-)) mAE x mBD =~-1 mAE x mBD=-1 (a) “. AE | BD 3.4 y=mxte m=2 Cc m=2 y=2xte sub A(—5;4): 4=2(-5)+e sub A(—-5;4) c=14 y=2x+14 c=l4 G) 3.5 dAE = (-s-1) + (4-19 =3N5 length of AE 1 Area of AABD = my BDx AE substitution into 1 correct formula Area of AABD = B75 x5 Areaof AABD = 30 units” answer (3) 3.6 A>D: (x+43; y-7) method BoC: (3+4; 5-7) “.C(7;-2) bysymmetry answer (2) [16] QUESTION 4 Copyright Reserved Please turn over

MaiPewnloaded from Stanmorephysics.com KZN/September 2022 NSC - Memorandum 4.1.1 A=2 v answer B=5S0 v answer C =330 v answer (3) 4.1.2 . 20 + 120 + 250 + 420 + 720 + 330 + 260 estimated mean = 30 _ 2120 v 2120 30 v 30 = 70,67 mm vy answer (G3) 4.1.3 Histogram showing rainfall (in mm) for September 8 7 6 v shape z g 5 E 4 v y-axis 3 2 v x-axis 1 O<x520' 20<x=40" 40 <x 60 '60<x<80 | 80 <x < 100" 100<x = 120" 120<x= 140 (3) Rainfall (mm) 4.14a | 60<x<80 answer qd) 4.1.4b | 80<x<100 answer qd) 4.1.4c | 80<x<100 v answer qd) 4.2.1 Lowest: 25% Highest 95% v both values ql) 4.2.2 | 75% v answer (1) 423 | 64% Y answer () 424 | 25% v answer qd) 4.2.5 IQR = 80% — 31% v 80% — 31% IQR = 49% v answer (2) [18] QUESTION 5 Copyright Reserved Please turn over

MatPewnloaded from Stanmorephysics.com NSC - Memorandum = - KZN/September 2022 A 30° Cc HH 50° u WAY a 400 colo i CO} 400 rf ae = LH} Fl nl Q (T) Q E park D 5.1 | ADE=50° (alt Zs; ACO ¥ answer (1) 5.2 | In AADE: v tan 50° Y —— AE=53,63m In AABC: tan 30° = BC Y tan 30° 45 BC =25,98m Y AE =53,63m -, BD=53,63m +25,98m =79,61m vo CA 6) [6] TOTAL: | [75] Copyright Reserved