Gr10 Math P2 (English) November 2018 Question Paper_hlayiso.com_.pdf

Downloaded from hlayiso.com basic education Department: Basic Education REPUBLIC OF SOUTH AFRICA NATIONAL SENIOR CERTIFICATE GRADE 10 a eS ee ee ee ee 7 MATHEMATICS P2 Hi uw uu Ww u A NOVEMBER 2018 " . See ee BB BB BB BB EEE BP BREE EEE RB e eee y MARKS: 100 TIME: 2 hours This question paper consists of 9 pages and a 12-page answer book. | Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 2 DBE/November 2018 CAPS — Grade 10 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1, 2. This question paper consists of EIGHT questions. Answer ALL the questions in the SPECIAL ANSWER BOOK provided. Clearly show ALL calculations, diagrams, graphs, etc. that you used to determine the answers. Answers only will NOT necessarily be awarded full marks. Tf necessary, round off answers to TWO decimal places, unless stated otherwise. Diagrams are NOT necessarily drawn to scale. You must use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. Write neatly and legibly. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 3 DBE/November 2018 CAPS — Grade 10 QUESTION 1 The line graph below shows test marks out of 10 obtained by a Grade 10 class. oe Frequency 1.1 Complete the frequency column in the table provided in the ANSWER BOOK. (2) 1.2 How many learners wrote the test? qd) 1.3 Calculate the: 1.3.1 Range for the data (2) 1.3.2 Mean for the test (3) 1.4 Determine the median for the data. (3) 1.5 Draw a box and whisker diagram for the data. tia ] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 DBE/November 2018 4 CAPS — Grade 10 QUESTION 2 In the diagram below, P(i ; 0), Q(6 ; 3) and R (9; —2) are the vertices of a triangle such that PQ=QR and PQ 1 QR. T isa point on PQ such that T is the midpoint of PQ. S is the point of intersection of RQ and the x-axis. V isa point on the x-axis such that QSV=121°. QPS =0 - y Q66 ; 3) vi ©] pa :0) : RQ; -2) 2.1 Determine the: 2.1.1 Length of PQ. Leave your answer in surd form. (2) 2.1.2 Gradient of PQ (2) 2.1.3 Coordinates of T (2) 2.2 Calculate the: 2.2.1 Area of AQTR G3) 2.2.2 Size of ®, with reasons (2) 2.2.3 Coordinates of S @) 2.3 Determine, with reasons, the gradient of the line through T and the midpoint of PR. (3) [17] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 5 DBE/November 2018 CAPS — Grade 10 QUESTION 3 3.1 In the diagram below, AQPR is a right-angled triangle with QPR = 90°. Q P R 3.1.1 Use the sketch to determine the ratio of tan(90°-R). (1) . ; oi, . QR 3.1.2 Write down the trigonometric ratio that is equal to oP , (1) 3.2 SC3 ; -4) is a point on the Cartesian plane such that OS makes an angle of 8 with the positive x-axis. ty (| \_, 7) > S(-3 ; -4) Calculate the following WITHOUT using a calculator: 3.2.1 The length of OS (2) 3.2.2 The value of sec 0 +sin? @ (3) 3.3 Determine the value of the following WITHOUT using a calculator: cosec 45° sin 90°. tan 60° 4) (11) Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 6 DBE/November 2018 CAPS - Grade 10 QUESTION 4 4.1 In the diagram below, ABC, ACD and ADE are right-angled tirangles. BAE = 90° and BAC =30°. BC=20 units and AD = 60 units. A E 30° 60 D B 20 Cc Calculate the: 4.1.1 Length of AC (2) 412 Sizeof CAD (2) 4.1.3 Length of DE (3) 4.2 Solve for x, correct to ONE decimal place, where 0° <x <90°: 4.2.1 tan x = 2,01 (2) 4.2.2 Scosx+2=4 GB) 4.23 = =3 6) [15] QUESTION 5 5.1 Consider the function /(x) =—-3 tan x. 5.1.1 Sketch, on the grid provided in the ANSWER BOOK, the graph of f for 0° <x < 360°. Clearly show ALL the intercepts and asympotes. (3) 5.1.2 Hence, or otherwise, write down the: (a) Period of f Q) (b) Equation of h if h is the reflection of f about the x-axis (1) Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 7 DBE/November 2018 CAPS — Grade 10 5.2 Sketched below is the graph of g(x) =a.cos 50 y 2 g 1 x 0 ° 180° 2 360° +1 -2 5.2.1 Write down the values of a and 3b. (2) 5.2.2 Use the graph to determine the value(s) of x for which g(x) >0. (1) 5.2.3 Determine the range of # if A is the image of g if g is shifted down TWO units. (2) 5.2.4 Determine, using the graph, the value of: — 2(cos 0° + cos 1° + cos 2° +... + cos 358° + cos 359° + cos 360°) (2) [12] QUESTION 6 The diagram below shows a cup with a volume of 117mcm? and an inner diameter of 60 mm. Ignore the thickness of the cup. 60 mm SO h Calculate the: 6.1 Height of the cup (3) 6.2 Total surface area of the water that touches the cup if the cup is 80% full with water (4) [7] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 8 DBE/November 2018 CAPS — Grade 10 Give reasons for ALL geometry statements in QUESTIONS 7 and 8. QUESTION 7 71 Complete the statement so that it is TRUE: The line drawn from the midpoint of the one side of a triangle, parallel to the second side, ... qd) 7.2 ACS isatriangle. P isa pointon AS and R isapointon AC such that PSRQ is a parallelogram. PQ intersects AC at B such that B is the midpoint of AR. QC is joined. Also, CR=PS, fon =50° and BP=60 mm. A Q B P Ss Cc 724 Calculate the size of A. (5) 7.22 Determine the length of QP. GB) 19] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P2 9 DBE/November 2018 CAPS — Grade 10 QUESTION 8 8.1 ABCD isa parallelogram. E and F are pointson AB and DC respectively such that AE=CF. DE is producedto J and CJ is drawn. BF is produced to K and AK is drawn. A 4 G B 2° 3 1 J 3\2 43) 1 H\1 l/F K Prove that: 8.1.1 DJ || BK (5) 81.2 ££, =F (4) 8.2 In the diagram below O is the centre of the circle. A and B lie on the circumference of the circle. AP = BP. P A fe) B Prove that: 8.2.1 AT=BT (5) 8.2.2 OTA =90° (ep) [15] TOTAL: 100 Copyright reserved