Mathematical Literacy Grade 11 P2 2016 Memo

Basic Education KwaZulu-Natal Department of Basic Education REPUBLIC OF SOUTH AFRICA MATHEMATICS P2 COMMON TEST pa JUNE 2016 " * y eee errr re er eet eee Te ee ee eee ee eee re eer ‘ NATIONAL ; SENIOR CERTIFICATE [ GRADE 11 ] MARKS: 100 TIME: 2 hours | This question paper consists of 8 pages and 3 diagram sheets. Copyright Reserved Please turn over

Mathematics P2 Downloaded from hlayiso.com Common Test June 2016 NSC INSTRUCTIONS AND INFORMATION Read the following instruction carefully before answering the questions. 1, The question paper consists of 6 questions. 2. Answer ALL the questions. 3. Clearly show all calculations and diagrams that you have used in determining your answers. 4, You may use an approved scientific calculator (non-programmable and non-graphical). 5. If necessary round off answers to TWO decimal places, unless otherwise stated. 6. Answers only will not be awarded full marks. ( ! 7. Diagrams not necessarily drawn to scale. 8. Number the answers correctly according to the numbering system used in this question paper. 9. Write neatly and legibly. Copyright Reserved Please turn over

Downloaded from hlayiso.com NSC Mathematics P2 Common Test June 2016 QUESTION 1 1.1 In the diagram below PQRS is a square with sides of 5 units. The coordinates of R is (1;-2). PQ is parallel to the x-axis. y a Q 5 units x sc RA; ~2) 1.1.1 Write down the coordinates of Q. (qt) 1.1.2. Write down the coordinates of S. (1) 1.1.3 Write down the equation of PQ, (1) 1.1.4 Write down the equation of QR. 43) 1.2 Inthe sketch below A(0;4), B(-4;-3) and C(4;~2) are the vertices of AABC. K is the midpoint of AC. AT is drawn with T a point on the x-axis, such that the acute angle between AT and the x-axis is equal to 26,6°. S(p; 1) is a point on AT. ¥ a0; 4) K (p3 1) 26,6: ~~ x C(4; -2) B(-4; -3) 1.2.1 Determine the coordinates of point K, (2) 1.2.2 Calculate the length of AC, correct to.2 decimal places. (2) 1.2.3 Calculate the gradients of BK and AC and then show that BKC = 90°. (6) 1.2.4 Determine the equation of line BK. @) 1.2.5 Calculate the area of AABC, correct to 2 decimal places, (5) 1.2.6 Calculate the value of p. (5) [26] Copyright Reserved Please turn over

Mathematics P2 NSC QUESTION 2 2.1 PORS is a parallelogram. The equation of PQis y =is . The gradient of SP is equal to ~1. R is the point (3; 2). Downloaded from hlayiso.com (3 52) 'Q @&y) PO; 2) 2.1.1 Write down the gradient of RQ. 2.1.2 Determine the equation of RQ. 2.1.3 Calculate the coordinates of point Q. 2.1.4 Calculate the size of SPQ. 2.2 Given A(6;7), B(O;—1) and C (4; p). Calculate 2.2.1 The length of AB. 2.2.2 The value of p if AB=2 BC, p <0 . Copyright Reserved Common Test June 2016 () (2) ) 6) (2) 6) (19] Please turn over

Downloaded from hlayiso.com NSC Mathematics P2 ‘common Test June 2016 N.B: Give reasons for your statements and calculations in Questions 3 — 6. QUESTION 3 3.1 COMPLETE: The line drawn from the centre of a circle to the midpoint of a chord cscerssunssvevevssacaestvevsvisessvavsevevevavsuevivevivevavececanstsevanenevaes (1) 3.2 O is the centre of the circle. AB is a chord and OP LAB. OP is extended and intersects the circle at N. AB = 16 cm and PN= 2 om. oO Let oP = x, P N 3.2.1 Calculate the length of AP. (2) 3.2.2 Calculate the length of the radius of the circle. (5) [8] Copyright Reserved Please turn over

Mathematics P2 Downloaded from, hlayiso.com NSC Common. Test June 2016 QUESTION 4 4.1 Inthe figure below O is the centre of the circle and A, B and C are three points on the circumference of the circle. Use the figure and prove the theorem that states that BOC =2A,. 4.2. In the figure O is the centre of the circle and ABCD is a cyclic quadrilateral. DA is produced to F such that FA = AC and CB is produced to meet DF at F. oO ¢ F 4.2.1 If f =x, write down, with reasons, in terms of x, an (a) the size of A OO (C) (b) the size of 6,. (2) 4.2.2 Ifitis further given that FA = DA, find with reasons, the size of A, . (6) [18] Copyright Reserved Please turn over

Downloaded from hlayiso.com NSC Mathematics P2 QUESTION 5 5.1. In the diagram below O is the centre of the circle. G, H, J and K are points on the circumference of the circle. GOH is a diameter. Chords GH, JH, KH, KJ and GK have also been drawn. H, =26°. x J G 0 Calculate, with reasons, the size of S11 K,. 512 49, 5.2. GAFE and FCDE are two circles, Chords GA, AF, EF, CF, CD and DE aie drawn. GFC isa straight line. DC produced meets GA produced at B, Ey = 28° and B, = 64°, Calculate, with reasons, the size of 521 G 5.2.2 B Copyright Reserved Common Test June 2016 (1) 3) (2) (4) [10] Please turn over

Downloaded from hlayiso.com NSC Mathematics P2. Common Test June 2016 QUESTION 6 In the figure PR and PQ are two tangents drawn from point P to circle AQR. The straight line drawn through P parallel to AR meets QR produced at 8, and QA produced at T. The tangent PR cuts QT at B. Let R, =x 6.1 Prove that PTRQ is a cyclic quadrilateral. (3) ( ' 6.2 If itis further given that QA = RA, prove that: 621 S=x (3) 62.2 PQ=RS (5) 6.2.3 PTS is atangent to circle TAR. (6) . (19) oS POTAL MARKS: [100P > Copyright Reserved Please turn over

Mathematics P2 Downloaded from hlayiso.co DIAGRAM SHEETS: HAND IN WITH YOUR ANSWER BOOK [ i I I I | NAME: GRADE: \ QUESTION 1.2 t | i | | | 1 1 j i 1 ! 1 ! ‘ C(4; ~2) | B(-4; -3) BI cal il ¢| 4 QUESTION 2.1 | | (3 5 2) i 8 | i] \ C4 Q wy) PO;2) * QUESTION 3.2 i t i | | | ( | if | t i [ | | ! | | | | ! | | | \ | | ( Copyright Reserved Common Test June 2016 Please turn over

Downloaded from,hlayiso.com Mathematics P2 Comution Test June 2016 NSC QUESTION 4.1 A B (ei QUESTION 4,2 QUESTION 5.1 Copyright Reserved Please turn over

Downl oaded from hlayiso. co 1 Test June 2016 Mathematics P2 NSC QUESTION 5.2 QUESTION 6 Lads ddOUVAL Copyright Reserved

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