Mathematics Grade 10 September Test 2018 Paper & Memo

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Downloaded from hlayiso.com Mathematics 2 Common Test September 2018 GRADE 10 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. Clearly show ALL calculations, diagrams, graphs, et cetera, which you have used in determining the answers. we 4. Answers only will NOT necessarily be awarded full marks. 5. You may use an approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise. 6. Ifnecessary, round off answers to TWO decimal places, unless stated otherwise. 7. Number the answers correctly according to the numbering system used in this question paper. 8. Write neatly and legibly. Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics Common Test September 2018 GRADE 10 QUESTION 1 ABCD is a quadrilateral with vertices A(5 ; 1), B(-3 3 5), C(-1 ;-5) and D(9 ; -7). B(-3;5) x ss ll Determine the distance AB. (2) 1.2 Calculate the gradient of BD. (2) 1.3 Determine the equation of BD in the form y=... (3) 1.4 Determine the co-ordinates of M, the midpoint of BD. (3) 1.5 Prove that AMB = 90°. (3) 1.6 Find the co-ordinates of E(x;) such that ABEC is a parallelogram. (4) [17] Copyright Reserved Please turn over

Mathematics Downloaded from hlayiso.com GRADE 10 QUESTION 2 2.1 2.2 2.3 2.4 Common Test September 2018 A newly married couple bought furniture and kitchen appliances, on hire-purchase, for R70 000. They paid a cash deposit of 20%. The balance will be paid off over 5 years at an interest rate of 22% p.a. and a monthly insurance fee of R120. Calculate their monthly repayments. (4) Calculate how many years it will take for an investment, earning 7.5% p.a. simple interest to triple in value. (4) In a certain country, the rate of inflation has remained unchanged for the past 8 years. Currently, a 100g bar of chocolate costs R10.98. 8 years ago the same bar of chocolate cost R7.25. What is the rate of inflation, as a percentage, in this country. Use the given exchange rates to answer the questions: $1:R910 and £1:R11,25 Calculate: 2.4.1 how many rand (R) is $ 152 2.4.2 how many pounds (£)is R3500 2.4.3. how many dollars ($) is £250 QUESTION 3 3.1 (1) (1) U5] P,Q, Rand S are the midpoints of AB, BC, CD and DA, respectively. BD is drawn. Give reasons for all statements. Prove that PS || QR Copyright Reserved (4) Please turn over

Downloaded from hlayiso.com Mathematics Common Test September 2018 GRADE 10 3.2. ABCD isa parallelogram. Let: E, =x Prove: 321 £ =F (3) 3.2.2 AAED=ACFB (4) 3.2.3. DEBF isa parallelogram (3) [14] QUESTION 4 An ice-cream vendor wants to paint the model of an ice-cream cone that is attached to the roof of his van. It consists of a hemisphere and a cone. AB = 36cm. Surface Area of Sphere = 40r° Surface Area of Cone = ar°+ ars A Jzom %em ee Lo \ 8 Calculate the total surface area of the ice-cream cone that he will need to paint [6] Copyright Reserved Please turn over

Mathematics Downloaded from hlayi so.com Common Test September 2018 GRADE 10 QUESTION 5 5.1 The table contains the maths results for Class A: Exam percentage Frequency O<x< 20 5 | 20<x< 40 _o | 40<x< 60 12 60<x< 80 15 80<x < 100 8 5.1.1 Write down the modal class. 5.1.2. Write down the interval containing the median for the data. 5.1.3. Construct a histogram to represent the information. 5.2 The data set shows the June Exam marks (in percentages) of a Grade 10 class. 73; 63; 50; 55; 79; 59 ; 66 ; 72; 72; 64; 78; 80 5.2.1 Calculate the range of the data set. 5.2.2 Determine: 5.2.2.1 the median §.2.2.2 Ist and 3rd quartiles. 5.2.3. Write down the 5 number summary. 5.2.4 Draw a box and whisker diagram for the given data set. 5.2.5 Determine in which percentile you would find the learner that obtained a mark of 73%. Copyright Reserved (2) [15] Please turn over

Downloaded from hlayiso.com Mathematics 7 Common Test September 2018 GRADE 10 QUESTION 6 The Great Pyramid at Giza is 146m high. Two people A and B are looking at the top of the pyramid the angle of elevation of the top of the pyramid from B is 12°, The distance between A and B is 25m. ry a —- —_ — aoe 146m On 18m y / oN y Y : ai see I canis Y 25m C If both A and B are |.8m tall, calculate: 6.1 the distance on the ground from B to the centre of the base of the pyramid, indicated as point C. (4) 6.2. the angle of elevation, 0 of the top of the pyramid from A. (4) 8] TOTAL MARKS: 75 Copyright Reserved

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3 Cox...000 Test September 2018 4 Common T GRADE 10 GRADE 10 Marking Guideline 1 September 2018, Downloaded from hlayiso.com QUESTION 3 ~ 1 in AABD 100 = RS6000 R56000 ¥# fiat AS = DS ¥ * both statements AP = BP A=PO iene) + PS {BD (midpt th) Y"S&R =56000(1+——x3) 100 In ABCD ¥ * both statements = R117600 7600 final amount CR = DR (given) 117600 CQ = BQ (given) Y* S&R Monthly instalments=———+ 120 60¥* no. of payments “.QR||BD — (midpt th) “™ awa R2080,00 ¥ @ answer (4) PS OR 22 Let P=x - B21 | Bax A , BE, =180°—x (adj.angles str dine) v? S&R =3F F),=180°— x (alt.angles DE || BF) ¥* S&R i Qi F.=x (adj.angles strline) Y*S&R Y * correct sub. into simple interest formula 1 . . Q) =F ¥ “simplification 3.22 | In AAED and ACFB ~ A, =6, (altangles AD || BC , =C, (ali ang! | BC) ae 19 BR 22 Fh 27 years ¥ “answer ¥? S&R (4) =BC ese v* S&R = 96.27 years AD= BC (opp.sides parm) os eer =e -A AED =ACFB(A,A,S) (a) 23 A=P(l+ 3.2.3. |DE\|BF (given) ¥* statement mer ant Y * correct sub. into compound interest DE = BF (corres. sides = As) Ye SER B= 7,251 +i) formula -. DEBF is a parm (one pair opp sides both = &|| ) v? reason (3) Y© simplification | 1 14] r= 5,33% ¥ answer 6) 24.1__[ S1S2x R910 = RI383,20 R1383,20 ¥* @) 242 £31111 ¥* answer a) 243 | 250x11,25 _ ae 50x 11,25 | 3 30X11.25 — as9907 = Se R309,07 ¥ answer Q) [15] Copyright Reserved Copyright Reserved Please turn over

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