Technical Mathematics Grade 10 P2 Eastern Cape November 2019 QP

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE GRADE 10 NOVEMBER 2019 TECHNICAL MATHEMATICS P2 MARKS: 100 TIME: 2 hours *XTMATE2* This question paper consists of 10 pages and a special answer book.

Downloaded from hlayiso.com 2 TECHNICAL MATHEMATICS P2 (EC/NOVEMBER 2019) INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of EIGHT questions. 2. Answer ALL the questions in the SPECIAL ANSWER BOOK provided. 3. Clearly show ALL calculations, diagrams, graphs, et cetera which you have used in determining the answers. 4. Answers only will NOT necessarily be awarded full marks. 5. You may use an approved scientific calculator (non-programmable and non- graphical) unless stated otherwise. 6. If necessary, round off your answers to TWO decimal places, unless stated otherwise. 7. Diagrams are not necessarily drawn to scale. 8. Write neatly and legibly. Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2019) TECHNICAL MATHEMATICS P2 3 QUESTION 1 In the diagram below ܲሺͶǢ ͵ሻǡ ܳሺെͶǣ െͳሻƒ†ܴሺʹǢ െ͵ሻ are vertices of the οܴܲܳ, T is a midpoint ofܴܲ. 1.1 Calculate the gradient of ܲܳ. (2) 1.2 Determine the coordinates of T, the midpoint ofܴܲ. (3) 1.3 Calculate the length of ܴܳ. (3) 1.4 Calculate the equation of the line perpendicular toܲܳ and passing through T. (4) 1.5 Calculate the coordinates ‫ܦ‬ǡ the point of intersection between the line in QUESTION 1.4 andܲܳ. (3) [15] Copyright reserved Please turn over

Downloaded from hlayiso.com 4 TECHNICAL MATHEMATICS P2 (EC/NOVEMBER 2019) QUESTION 2 2.1 Given that ‫ ݔ‬ൌ ʹ͹ǡͷo ǡ ‫ ݕ‬ൌ ͷʹo and ‫ ݖ‬ൌ Ͷ͵ǡʹo . Using a calculator, evaluate the following: 2.1.1 cos( x  y)  sin z (2) 2.1.2 cos ec x tan y  tan z (2) 2.2 If 2cot T  4 7 for T [180 ;360 ] with •‹ ߠ ൏ Ͳǡwith the aid of a sketch o o determine the value of the following: 2.2.1 •‹ ߠ (4) 2.2.2 cosT  2 tan T (3) 2.3 Solve for E if 2cos E 3  cos ec 27o for E [0o ;90o ] . (3) [14] Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2019) TECHNICAL MATHEMATICS P2 5 QUESTION 3 Mr Mampofu a local businessman who recently bought a spaza shop, decided to put a veranda on his new spaza shop. The height of the back wall for the spaza shop isͶǡʹ. He wants to place the veranda roof ‫ ܦܤ‬at an angle of ͵͹ι  from the veranda pillar ‫ܧܦ‬. The roof ‫ ܪܣ‬of the spaza shop is also at an angle of ͵͹ι to ‫ܤܪ‬. ‫ ܤ†ƒܥ‬are on  . The pillar ‫ ܧܦ‬is ͳǡͺ from the wall ‫ܨܥ‬. Below is the picture of the spaza shop with its veranda. Below is the model of the above picture: 3.1 What should be the length of roof sheet BD for the veranda? (2) 3.2 How high must he build the supporting pillar DE? (4) 3.3 His other intention is to write the name of his spaza shop on the space‫ܤܣ‬. If the length of the roof ‫ ܪܣ‬is 2,5ǡ what is the height of ‫?ܤܣ‬ (2) 3.4 Mr Mampofu wants to paint the wall represented by AFGH with a different colour. How many litres of paint must he buy to cover the whole area AFGH, if ½ litre is required to paint 1݉ଶ (round off your answer to the nearest litre). (3) [11] Copyright reserved Please turn over

Downloaded from hlayiso.com 6 TECHNICAL MATHEMATICS P2 (EC/NOVEMBER 2019) QUESTION 4 Given: f ( x) 2sin x and g ( x) cos x 1 4.1 Draw the graph of ݂and gon the same system of axis provided in your ANSWER BOOK, using the interval x [0 ;360 ] . o o (5) 4.2 Write down the amplitude of݂. (1) 4.3 Write down the period of ݂. (1) 4.4 Write down the range of g. (2) 4.5 For which value(s) of ‫ ݔ‬will ݂ሺ‫ݔ‬ሻ െ gሺ‫ݔ‬ሻ ൌ Ͳ. (3) [12] Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2019) TECHNICAL MATHEMATICS P2 7 QUESTION 5 ‫ ܱܰܯܮ‬below is a kite such that ‫ ܰܯ‬ൌ ܱܰǡ ‫ ܮܯ‬ൌ ‫ܱܮ‬and the diagonals intersect at ܲ. It ෡ܲ ൌ ͵͵o and ܱ‫ܮ‬෠ܲ ൌ ͷʹo . is also given that ܱܲ ൌ Ͷܿ݉ǡ ‫ܰܯ‬ 5.1. Calculate the length of MN to the nearest whole number. (2) 5.2 Calculate the length of LN to the nearest whole number. (3) 5.3 ෡ ‫ܮ‬. Calculate the size of angle ܰ‫ܯ‬ (4) [9] Copyright reserved Please turn over

Downloaded from hlayiso.com 8 TECHNICAL MATHEMATICS P2 (EC/NOVEMBER 2019) QUESTION 6 In the diagram below HIJK is parallelogram with J‫ܮ‬෠‫ ܭ‬ൌ ͻͲo , ‫ܮܪ‬෠‫ ܫ‬ൌ ͵ͷo and ෡ ‫ ܫ‬ൌ ʹͳo . Point ‫ ܯ‬is the intersection on the diagonals ‫ ܬܪ‬and ‫ܭܫ‬. ‫ܭܮ‬ 6.1 Calculate the sizes of ‫ݓ‬ǡ ‫ݕ†ƒݔ‬ሺ‰‹˜‡”‡ƒ•‘•ˆ‘”›‘—”ƒ•™‡”ሻǤ (5) 6.2 Classify the quadrilateral‫ܮܭܬܫ‬. (2) 6.3 Show that ο‫ ؠ ܪܯܫ‬ο‫ܭܯܬ‬. (3) [10] Copyright reserved Please turn over

Downloaded from hlayiso.com (EC/NOVEMBER 2019) TECHNICAL MATHEMATICS P2 9 QUESTION 7 7.1 ෡ ‫ ܧ‬ൌ ‫ܤܦ‬෠‫ ܥ‬ൌ  ͻͲo . Given: ‫ ܦܣ‬ൌ ‫ܦܣ †ƒܤܦ‬ 7.1.1 Give the reason why ‫ ܧܣ‬ൌ ‫ܥܧ‬. (1) 7.1.2 If ‫ ܧܦ‬ൌ ͺ ƒ†‫ ܧܣ‬ൌ ͳͶ Ǥ Calculate the length of: ሺ݅ሻ ‫ܥܤ‬ (3) ሺ݅݅ሻ ‫ܤܣ‬ (4) 7.2 Two isosceles triangles ο‫†ƒܥܤܣ‬οܻܼܺ of different sizes have both an apex angle equal to ‫ݔ‬Ǥ 7.2.1 Show that these two triangles are similar. (4) 7.2.2 If x 40o what are the sizes of the other two angles inοܻܼܺ? (2) [14] Copyright reserved Please turn over

Downloaded from hlayiso.com 10 TECHNICAL MATHEMATICS P2 (EC/NOVEMBER 2019) QUESTION 8 8.1 The alignment done on a car showed the following results: Front caster: 28 34'62'' Rear camber: 131, 42 Using the above information convert: 8.1.1 Front caster to degrees (3) 8.1.2 Rear camber to degrees, minutes and seconds. (3) 8.2 Simplify the given expression and write answer in radians: 4S 63o   100o 3 (3) 2S 8.3 A circle with radius ͹ܿ݉ and central angle . Calculate the arc length of the 3 sector. (3) 8.4 The diagram below shows the floor plan of a house. Calculate the area of the floor plan and give your answer in m 2 . (3) [15] TOTAL: 100 Copyright reserved Please turn over

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