Mathematics Grade 10 P2 National November 2015 QP

basic education Department: Basic Education REPUBLIC OF SOUTH AFRICA y INAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS P2 NOVEMBER 2015 TIME; 2 hours This question paper consists of 11 pages and a 16-page answer book. IA Please um over Copyright reserved

Mathematics/P2 2 Downloaded from hlayiso.com DBE/November 2015 CAPS — Grade 10 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2. 3. This question paper consists of 9 questions. Answer ALL the questions in the SPECIAL ANSWER BOOK provided. Clearly show ALL calculations, diagrams, graphs et cetera that you used to determine the answers. Answers only will NOT necessarily be awarded full marks. If necessary, round off answers to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. Write neatly and legibly. Consist resened (ANNA A Pessenumove

Downloaded from hlayiso.com , Mathematics/P2 DBE/November 2015 CAPS — Grade 10 QUESTION 1 Nineteen girls were required to complete a puzzle as quickly as possible. Their times (in seconds) were recorded and are shown in the table below. 14 15 16 16 17 17 18 18 19 19 19 20 21 21 22 23 24 24 29 Lt Identify the median time taken by the girls to complete the puzzle. qd) 1.2 Determine the lower and upper quartiles for the data. (2) 1.3 Draw a box and whisker diagram to represent the data. (2) 1.4 The five-number summary of the time (in seconds) taken by 19 boys to complete the same puzzle is (15 ; 19 ; 23 ; 26 ; 30). 1.4.1 Calculate the interquartile range for the time taken by the boys. (2) 1.4.2 If only one boy took 19 seconds to complete the puzzle, what percentage of the boys took at least 19 seconds to complete the puzzle? qa) 15 In which group, the girls or the boys, did a larger number of learners complete the puzzle in less than 23 seconds? Justify your answer. (2) {10} QUESTION 2 The table below shows information about the number of hours 120 learners spent on their cellphones in the last week. NUMBER OF HOURS (4) FREQUENCY O<h <2 10 2<h <4 15 4<h <6 30 6<h <8 35 8<hA <10 25 10<h <12 5 21 Identify the modal class for the data. (a) 2.2 Estimate the mean number of hours that these learners spent on their cellphones in the last week. (3) [4] Cops reserved UNA A Pease tam over

Downloaded from hlayiso.com Mathematics/P2 4 CAPS — Grade 10 QUESTION 3 DBE/November 2015 In the diagram, C is a point on the y-axis such that A;4, B4;-4, C and DC 4; 2) are vertices of parallelogram ABCD. K is the point [0:-25] and L isa point on AB such that KL || CB. A(0; 4) DC 4; 2) x 3.1 Calculate the length of diagonal DB. (6) 3.2 Calculate the coordinates of M, the midpoint of DB. G) 3.3 Calculate the gradient of AD. GB) 3.4 Prove that AD 1 AB. G) 3.5 Give a reason why parallelogram ABCD is a rectangle. ay 3.6 Determine the equation of KL in the form y= mx +c. (2) 3.7 Write down, with reasons, the coordinates of C. G3) [18] cree 0000080 Please turn over

Downloaded from hlayiso.com Mathematics/P2 5 DBE/November 2015 CAPS — Grade 10 QUESTION 4 APQR and ASQR are right-angled triangles as shown in the diagram below. PR=26, PQ=24, QS=8, SR=6, QR=10 and PRQ=0. P 26 24 8 6 6 Q 10 R 4.1 Refer to the diagram above and, WITHOUT using a calculator, write down the value of: 4.1.1 tanP (1) 4.1.2 sinSQR (a) 4.13 cosé () 4.1.4 secSRQ a) 7 7 cot é 4.2 WITHOUT using a calculator, determine the value of =. cosec QRS (3) 7] comet SAHA

Downloaded from hlayiso.com Mathematics/P2 6 DBE/November 2015 CAPS — Grade 10 a QUESTION 5 5.1 In the diagram below, P(x ; y) is a point in the third quadrant. ROP=f and 17 cos 8 +15=0. y CN aX oO R r P(x; y) v $.1.1 Write down the values of x, y and r. (4) 5.1.2 WITHOUT using a calculator, determine the value of: (a) sin B q) (b) cos’ 30°. tan B (3) 5.13 Calculate the size of ROP correct to TWO decimal places. (2) 5.2 In each of the following equations, solve for x where 0° <x<90.. Give your answers correct to TWO decimal places. 5.2.1 tan x = 2,22 Q) 5.2.2 sec(x +10) =5,759 @) sinx —2=1,24 5.2.3 02 G3) [18] aes LAA A ical AN

Downloaded from hlayiso.com Mathematics/P2 7 DBE/November 2015 CAPS — Grade 10 QUESTION 6 In the diagram below, the graph of f(x) =—2cosx is drawn for the interval 0° < x < 360°. 6.1 Write down the amplitude of f 03) 6.2 Write down the minimum value of /(x)+3. qa) 6.3 On the same system of axes, draw the graph of g, where g(x)=sinx+1 for the interval 0° < x < 360°. (3) 6.4 Use the graphs to determine the following: 64.1 The value of (180°)— g(180°) (2) 6.4.2 For which value(s) of x will f(x).g(x) > 0 (2) 6.5 The graph of /f is reflected about the x-axis and then moved 3 units downwards to form the graph of A. Determine: 6.5.1 The equation of A (2) 6.5.2 The range of h for the interval 0° < x < 360°. 3 Consiahi mses (OMAN Messe tun ove

Mathematics/P2 Downloaded from hlayiso.com 8g DBE/November 2015 CAPS — Grade 10 QUESTION 7 A concrete gate post comprises a right rectangular prism as shown in the diagram below. The length of the sides of the base is 30cm and the top, having a square base and a pyramid at the height of the rectangular section is 150 cm. The perpendicular height of the pyramid section is 8cm. sem] 150 cm 30 cm 30cm Volume of a pyramid= sae of the base x height Total surface area of a pyramid = area of the base + ; (perimeter of the base x slant height) TA 7.2 73 Calculate the volume of concrete required to make ONE post. (3) Calculate the surface area of the pyramid section of the post. @) If the length of the sides of the base is halved, how many posts, having the same design as the original, can be made with the same volume of concrete as the original post? (2) (8] ee

Downloaded from hlayiso.com Mathematics/P2 9 DBE/November 2015 CAPS ~ Grade 10 Give reasons for your statements in QUESTIONS 8 and 9. QUESTION 8 In the diagram, ABCD is a rhombus having diagonals AC and BD intersecting in O. ADO =3687° and DO =8 em. A B ) 36,872 8cm D Cc 8.1 Write down the sizes of the following angles: 8.1.1 cbo 8.1.2 AOD 8.2 Calculate the length of AO. 8.3 If E isa pointon AB such that OE|| DA, calculate the length of OE. Conighreserved (ANAT nas eso (1) () (2) (4) {8}

Downloaded from hlayiso.com Mathematics/P2 10 DBE/November 2015 CAPS — Grade 10 QUESTION 9 91 In the diagram below, D is the midpoint of side AB of AABC. E is the midpoint of AC. DE is produced to F such that DE= EF. CF || BA. A F D Cc B OAL Write down a reason why AADE = ACFE. (1) 9.1.2 Write down a reason why DBCF isa parallelogram. ql) 9.1.3 Hence, prove the theorem which states that DE = pBc. (2) comiaeenet ELH

Downloaded from hlayiso.com “ Mathematics/P2 il DBE/November 2015 CAPS — Grade 10 9.2 In the diagram below, PQRS is a parallelogram having diagonals PR and QS intersecting in M. B isapointon PQ such that SBA and RQA are straight lines and SB=BA. SA cuts PR in C and PA is drawn. S > R M P BU Q A 9.2.1 Prove that SP = QA. (4) 9.2.2 Prove that SPAQ isa parallelogram. Q) 9.2.3 Prove that AR = 4MB. (4) {14} TOTAL: 100 Cone resves UA AA