Mathematics Grade 11 P2 KwaZulu Natal June 2015 Paper & Memo

Nawnloacde dc om Nia ‘a alae Basic Education KwaZulu-Natal Department of Basic Education REPUBLIC OF SOUTH AFRICA a * ' MATHEMATICS pP2 " | rn 1” | iW i # COMMON TEST ' w 4 i" JUNE 2015 ‘ K ” ‘oem meen meee ene ne neem ee eee eee ene? NATIONAL SENIOR CERTIFICATE GRADE 11 MARKS: 100 , TIME: 2 hours This question paper consists of 10 pages, an information sheet and Diagram Sheets. Copyright reserved Please turnover

Mathematics P2 D Oo wn | oaded feo m h | ay iSO . co (Pjamon Test June2QQis ~ INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1, Answer ALL the questions. 2, Clearly show all calculations and diagrams that you have used in determining your answers. 3. You may use an approved scientific calculator (non-programmable and non-graphical). 4. If necessary round off answers to TWO decimal places, unless stated otherwise. 5. Answers only will not necessarily be awarded full marks. 6. Diagrams not necessarily drawn to scale. 7. Number the answers correctly according to the numbering system used in this question paper. 8, Write neatly and legible. Copyright reserved Please turnover

ken edi Department: Education KWAZULU-NATAL Downloaded from hlayiso.com TO: THE CHIEF INVIGILATOR(S) OF ALL CENTRES OFFERING NATIONAL SENIOR CERTIFICATE —- COMMON TEST JUNE 2015 GRADE 11: MATHEMATICS P2 ERRATA: MATHEMATICS P2 ERROR CORRECTION Page 3 Page 3 Question 1: Question 1: 1.1.7 inthe formof y = mx+x... 1.1.7 inthe form of y = mxtc... QUESTION FIVE: PAGE 10 ERROR CORRECTION Kindly ensure that all candidates are informed of the Errata. , “ re. MR R.C. PENNISTON SENIOR MANAGER 2% | VOLS DATE PROVINCIAL EXAMINATION ADMINISTRATION KWAZULU-NATAL DEPARTMENT OF EDUCATION Postal Address; Privcite Bag X01 ° EAST END * 4018 » Republic of South Affica Physical Address: 72 Stalwart Simeiane Sireet > Maigate Building + Durban » 4000 Tels +27 31 327 0462 9 Web:www.kzneducation.goy.za .. Together moving South Africa forward through quality education and skills development

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Mathematics P2 Downloaded geom hlayiso.cakMnen Test June 2015 QUESTION ONE 1.1. In the diagram below A(0;8), B(8;2), C(2;-6) and D (x ; y) are the vertices of a parallelogram. M is the midpoint of AC. ACB = 0. Pe A(0:8) B(8:2) j M Dey), 8 CQ+6) 1.1.1 Calculate the lengths of AB and BC. (4 1.1.2 Determine the coordinates of M. (3) 1.1.3 Prove that BM is perpendicular to AC. (4) h "11.4 Prove that ABC = 90° (4) 1.1.5 What type of triangle is AABC? (2) 1.1.6 Determine the area of A ABC. (2) 1.1.7 Determine the equation of BM in the form y = mx + x. @) 1.1.8 Calculate the size of angle@. (A) 1.1.9 Determine the coordinates of D. (2) 1.2 Prove that the point (-4;11) lies on the line 3x + 4y = 32 (3) 1.3. Given the points P(6;5); Q(3;2); R (Qm ; m+ 4) and T (2 is} Calculate the value of m if PQ is parallel to RT. Copyright reserved Please turnover (4)

Mathematics P2 Downl oaded from h | ay iso . COGommon Test June 2015 1.4 Inthe diagram below P is a point (-3;0) and Tis (2a ; 0).The inclination of the line PR is 108,4° and R is the y-intercept of PR. ¥ 108,4° T (2a: 0) P (-3: 0) Calculate: 1.4.1 the gradient of PR, to the nearest integer value. 1.4.2 the equation of PR inthe form y = mx +c. 1.4.3 the coordinates of R. 14.4 If TQa;0); Q (a:b) and R lie on the same straight line. Prove that b = = Copyright reserved 2) Q) (2) (4) [45] Please turnover

| | | { i i Mathematis P2 Downloaded som hlayiso. Corson ts: sune 2015 5 QUESTION TWO 2.1 Complete the following statement: The line drawn from the centre of a circle, perpendicular to a chord » (2) 2.2 ‘In the diagram BOM is a diameter of a circle with centre O. OD is perpendicular to the chord XY. OY= 12,5 cm and XY = 24 cm. B oO : 2,5 om D Y M Calculate the lengths of: 2.2.1 MD. (4) 2.2.2 BX. (4) [10] Copyright reserved Please turnover

watemise — Downloaded fram hlayiso.cortonen tes ime 2015 QUESTION THREE 3.1 Complete the statement: The angle subtended by an are at the centre of the circle is . (2) 3.2 Inthe diagram A, B, C and D are points on the circle with centre O. OBC = 40°, BD=DC, A B 40° Cc D Calculate, with reasons, the value of: 3.2.1 BAC. (4) 3.2.2 BDC. (2) 3.23 DCB. (2) [10] Copyright reserved Please turnover

Mathematics P2 Downl oaded feom hlayiso. COW mon Test June 2015 QUESTION FOUR 4.1 In the diagram below, O is the centre of the circle. Use the diagram to prove the theorem which states that : If PORS is a cyclic quadrilateral then POR + PSR =180°. (6) P Copyright reserved Please turnover

matnematsP2 Downloaded Trem hlayi$O.COrBemmon Tes tune 2015 4.2 Complete this statement: The angle between a tangent to a circle and a chord is . (2) 4.3 Inthe diagram below, AOD is a diameter of the circle and EDF is a tangent to the circle at D. ADB = 62° and BC = CD, E Calculate, with reasons, the numerical value of: 43.1 BCD. (4) 43.2 CDF. (4) Copyright reserved Please turnover

Mathematics P2 Down | oaded fee m h layiso CO Mommon Test June 2015 4.4 Inthe diagram, A, B and C are points on the circumference of a circle. PCT is a tangent to acircle at C and also parallel to AB. Prove that AC = BC (5) [21] Copyright reserved Please turnover

Mathematics P2 Downloaded fagom h layiso .CO amon Test June 2015 10 QUESTION FIVE In the diagram below, PQRT is a cyclic quadrilateral. PB is a tangent. RQB is a straight line.. PT // BOR, PT=QTand , =x. 5.1 Write down, with teason, R in terms of x. (2) 5.2. Write down, with reasons, FIVE other angles each equal to x. (10) 5.3. Prove that QP = BP Q) [14] - TOTAL: 100 Copyright reserved Please turnover

Mathematios P2 Downloaded fscom hlayiso.Comnon-res: une 2015 Ih INFORMATION SHEET: MATHEMATICS INLIGTINGSBLAD: WISKUNDE xe ~btvb? ~4ac 2a A=P(l+ni) A= P(l~ni) A= P(~iy" A= P(+i)" ft yn Mien yin ee T, =a+(n—Nd S, = @a+(n-1d) isl dal T, =ar™ Ss aay" al ; rel S, = -y-ler<l "pl 1-r me (Co | past 0+9") i i Va) = tim LTDA LO) FG) = jim, h x, +X. + d=\(%) — x1)? +04 -y,)" Seared 2 yemxte yry =m(x—-x,) m= 222 m= tand Lo mma | (x-a) +(y-by¥ =r? in AABC: 4. Fe a a* =b* +¢* —2be,cosA area MABC =~ ab.sinC sind sinB sinc 2 sin(a + £) = sina.cos B + cosa.sin f sin(a ~ 8) = sina.cos f — cosa.sin £ cos(a + 8) = cosa.cos f - sina.sin B cos(a — 8) = cosa.cos 8 + sina.sin cos’ @~sin? a cos2e =41-2sin? a sin 2a = 2sina.cosa@ 2cos? a -1 (x; y) > (xcos0 + ysin®@ ; ycosd— xsind) (x3 9) > (xcos@ ~ ysin 8; ycos@ + xsin 8) x= oe = 48 n n P(A) = iG) P(A or B) = P(A) + P(B) ~ P(A and B) Dien 5y Copyright reserved Please turnover

Mathematics P2 Downloaded firem hlayi$O.COrBmmon Test une 2015 12 DIAGRAM SHEETS Pe Question 1.1 A(0:8) B(8:2) Dey) mx C(2:-6) Question 1.4 —r . 108,4° px T (2a: 0) P (-3; 0) Copyright reserved Please turnover

Mathematics P2 Question 2.2 Question 3.2 Copyright reserved Downloaded fisom h layiso .cCO (Bommon Test June 2015 oO 2,5 cm D Y M A 40° Cc D Please turnover

Mathematics P2 Downloaded feo h layiso .CO Ammon Test June 2015 Question 4.1 Question 4.3 Copyright reserved Please turnover

Mathematics P2 Do Ww nl oad ed sero m h | ay is O. CQ@bMnon Test June 2015 Question 4.4 A P. B Cc ) T Question 5 Copyright reserved

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