MATHS 2015-JUNE-QP-and MEMO_hlayiso.com_.pdf

Basic Education KwaZulu-Natal Department of Education REPUBLIC OF SOUTH AFRICA est R RRA RRR RRR RRR a Coe. ee ee MATHEMATICS COMMON TEST JUNE 2015 ¢ y MTT rTTTTrrrrerrrericrecrrerrrrrrrrrrerrrrrirri NATIONAL ] SENIOR CERTIFICATE GRADE 10 | } MARKS: 100 TIME: 2 hours This question paper consists of 8 pages and a 2 page diagram sheet.

Mathematics Downloaded from hlayiso.com Common Test June 2015 NSC INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions: 1. 2. 10. This question paper consists of 8 questions. Answer ALL the questions. Clearly show ALL calculations, diagrams, graphs, et cetera, which you have used in determining the answers. Answers only will NOT necessarily be awarded full marks. ‘You may use an approved scientific calculator (non-programmable and non- graphical), unless stated otherwise. (. If necessary, round off answers to TWO decimal places, unless stated otherwise. TWO diagram sheets for answering QUESTION 6.1, QUESTION 6.2, QUESTION 7, and QUESTION 8 are attached at the end of this question paper. Write your name on these sheets in the spaces provided and insert the sheets inside the back cover of your ANSWER BOOK. Diagrams are NOT necessarily drawn to scale. Number the answers correctly according to the numbering system used in this question paper. Write neatly and legibly. Copyright Reserved Please turn over

Mathematics QUESTION 1 1.1 If ke {0; 152; 3}, determine the value of & such that ih 1.1.1 is an integer 1.1.2 is irrational 1.1.3 is undefined 1.2 Determine the product of the following and simplify fully: (x+3y)(9y? +x? —3xy) ij 1.3. Factorise the following completely: xi4x?—x-1 1.4 Simplify the following expression fully: 2x? ~2y? + 4x? + 4xy x -Qxyty? xp-y? QUESTION 2 2.1 The volume of a cone is given by V = anh iy Write down the value of r, the radius of the cone, in terms of V, 2 and h. 2.2 Solve simultaneously for x and y: 3xe=y-4 and 2ye5+3x 2.3 Solve the following inequality: -3<3+2x<13. Henee, illustrate your answer on a number line if x is a real number. 24 Solveforx: 2.3%" =162 2.5 The sides of a kite are x7 +3 and x? +3x~-3 units respectively. Downloaded from hlayiso.com Common Test June 2015 NSC 2.5.1 Calculate the value of x for which the kite will be a rhombus. 2.5.2 Hence, determine the length of the sides of the rhombus. Copyright Reserved qd) (@) (1) (2) (4) 6) [14] (2) 1) (4) (4) GB) 2) [19] Please turn over

Mathematics Downloaded from hlayiso.com Common Test June 2015 NSC QUESTION 3 3.1 Consider the following sequence: 9 ; 16 ; 23 ;30;... 3.1.1 Write down the next term in the sequence. 3.1.2 Write down the general term (nt term) of the sequence. 3.1.3 Which term in the sequence has the value of 408? 3.2 Write down the fourth term in terms of x in the following linear sequence: 2x +4; 4x43; 6x45... 3.3. The following pattern is given: Row I 1 Row 2 1 3 5 Row 3 3 5 7 9 Row 4 § 7 9 Wk 13 Row 5 13 5 7 9 <1 13 15 17 3.3.1 Determine the last term in Row 6. 3.3.2 Write down the rule to calculate the last number in the n™ row. 3.3.3. Hence write down the last number in Row 70. 3.3.4 Calculate the sum of the numbers in Row 15. QUESTION 4 The following functions are given: f(x) = (4) where xe R and g(x) = 3 where x<0 x 41 4.2 4.3 44 Copyright Reserved Sketch the graphs of f and g on the same set of axes. Show all intercepts with the axes and asymptotes where applicable. Write down the range of & if k(x) = f(x) -2. Write down the equations of the asymptotes of h if A(x) = g(x)+3. Write down the values of x for which f(x) < g(x). a) 2) @) (2) (1) (2) (2) 3) (15) (5) @) Q) (2) (14) ’ Please turn over

Downloaded from hlayiso.com Mathematics Common Test June 2015 NSC QUESTION 5 Sketchedbeloware the graphsof f(x)=2x? -2 and g(x)=-2x+2. The graph of / intersects the x-axis at A and B and the y-axis at C. The graph of g intersects the x-axis at B and the y~axis at D. f and g intersect at H and B. » y x > Use the graphs and the information above to determine the following: 5.1. The coordinates of A and B, (4) } 5.2 The coordinates of C. qd) 5.3. The coordinates of D. (1) 1 5.4 The length of EG if OF = J unit and E lies on g andG lies on f (3) (1 Copyright Reserved Please turn over

Mathematics Downloaded from hlayiso.com . Common Test June 2015 NSC QUESTION 6 In this question, you must give a reason to justify each of your statements. 6.1 6.2 Copyright Reserved In the diagram below, ABCD is a rectangle, Use the diagram to prove the theorem which states that the diagonals of a rectangle are equal. THIS QUESTION MUST BE ANSWERED ON THE DIAGRAM SHEET. A B re “ef ee we an ae ° SS N i at (6) In the diagram below, PQRS is a rectangle with E being the point of intersection of the diagonals. QSR = 35°, Calculate the size of RPS ie. Py. P Ss rm L <4 1 4 3 2 E 2 14 i Q R (4) [10] Please turn over

Downloaded from hlayiso.com Mathematics 7 Common Test June 2015 NSC QUESTION 7 In this question, you must give a reason to justify each of your statements. 7.1 Complete the following statement: The line drawn from the midpoint of one side of a triangle, parallel to the second side... q) 7.2 In the figure below, BCE is a right-angled triangle. F is the midpoint of BE and D is a point on CE. FD is produced by its own length to G and forms parallelogram BCGF, FD = 30 mm and DE = 25 mm. toh E y pnp G B Cc uo 72.1 Why is ED=DC. Q) 7.2.2 Prove that EFCG is a rhombus. (2) 7.2.3 Calculate the area of parallelogram BCGF. (2) 7.2.4 Prove, by calculation, that: the area of rhombus FCGE * the area of parallelogram BCGF. (2) 19] Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics Common Test June 2015 NSC QUESTION 8 In this question, you must give a reason to justify each of your statements. In the diagram below, PQRS is a parallelogram with diagonals PR and QS. QY and XS are drawn such that QY // XS Q R Use the diagram to prove each of the following: 8.1 AQPY = ASRX (6) 8.2 QYSX isa parallelogram (3) 8.3 YM=MX (2) a TOTAL MARKS: 100 ¢; Copyright Reserved Please turn over

Downloaded from hlayiso.com Common Test June 2015 9 Mathematics NSC DIAGRAM SHEET 1 QUESTION 6.1 Marks (6) Solution QUESTION 6.2 SUNIT GALLOG NO YVEL ISVAId Please turn over ight Reserved Copyr'

Common Test June 2015 Downloaded from hlayiso.com Mathematics NSC i tT DIAGRAM SHEET 2 QUESTION 7 QUESTION 8 SUNIL @GLLOG NO UV4L ISVATd Copyright Reserved

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