Mathematics Grade 10 KwaZulu Natal June 2017 Memo

____-hownloaded from hlayiso.com Education KwaZulu-Natal Department of Education REPUBLIC OF SOUTH AFRICA Gen RGR R RR SRR RT Re * MATHEMATICS = nm COMMONTEST = 8 NATIONAL SENIOR CERTIFICATE MARKS: 100 TIME: 2 hours This question paper consists of 10 pages and 2 DIAGRAM SHEETS.

Mathematics Downloaded from hlayiso.com June 2017 Common Test NSC INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions: L. 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 7.1, QUESTION 7.2, QUESTION 7.3, QUESTION 8.1 and QUESTION 8.2 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

Downloaded from hlayiso.com Mathematics 3 June 2017 Common Test NSC QUESTION 1 1.1 Factorise the following expressions fully: y LLL 7414 ve (1) 1.1.2 2x? +2ax—3bx-3ab (3) 1.2 Determine the product of the following expression: ~2(x+D00? ~x +1) (3) 1.3 Calculate the value of the following expression without using a calculator: (0,072)? ~ (0,028)? Lo (2) 14 — Simplify the following expression fully: 5x? + 14x —3 ; x? -9 (3) 15 Evaluate the following expression: get gx? Gagat . Write your answer as a fraction in its simplest form, 6) verre (17). Copyright Reserved Please turn over

Mathematics QUESTION 2 Downloaded from hlayiso.Cartr commonest 2.1 Solveform: 4% =1 2.2 Given: a+ Ss 5x 2.2.1 Solve for x. 2.2.2 Write the answer to QUESTION 2.2.1 in interval notation. 2.3 Solve simultaneously for x and y: x-2y=3 37 where xeR and = 4x+3y+10=0 (2) (3) 68) 6) 24 Arectangular garden is made up of a square lawn of side x m and two paths 1,5 m wide, as shown in the diagram below. The total area of the garden is 88 m_. Write down an equation in terms of x and solve the equation to find the dimensions of the lawn. Copyright Reserved 1,5 m i I I a [ I I I [ I I + I 15m CT [I TT NOT J TO SCALE T I (5) [16] Please turn over

Downloaded from hlayiso.com Mathematics 5 June 2017 Common Test NSC QUESTION 3 3.1 The nth term ofa pattern is given as T, =12n—~7. 3.1.1 Write down the first three terms of this pattern. (2) 3.1.2 Is 356 a term in this pattern? Explain your answer. Q) 3.2 Consider the following sequence of Es: 3.2.1 How many blocks are needed to make the next E? qd) 3.2.2 Write down the general term, T,,, for the number of blocks used in each E. (2) 3.2.3 Calculate how many blocks will be needed to make the 100" E, (2) 3.2.4 Calculate which E can be made from 116 blocks. (3) [12] QUESTION 4 The following functions are given: f(x) =x~-2 and g(x)= 4 ~2 x Sketch the graphs of f and g on the same set of axes, clearly showing all intercepts with the axes and asymptotes where applicable, [6] Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics June 2017 Common Test NSC QUESTION 5 Sketched below are the graphs of f(x)=-4x° +9 and g(x)=2x+3. The graph of f intersects the x-axis at A and B. The graph of g intersects f at A and D and the y-axis at C, DE // y-axis. ty g Cc A x A N EB > 5.1 Write down the coordinates of C. qd) 5.2 Calculate the length of AB. Q) 5.3 Calculate the length of DE if AE =2 ; units. (2) 5.4 For which values of x will s(x) > g(x)? (2) 5.5 Calculate the length of AD. (2) [10] Copyright Reserved Please turn over

Mathematics NSC QUESTION 6 Sketched below are the graphs of g and hf. g(x) =b* +c and A(x) = k : x A, the point of intersection of g and A, is (1; 1). Downloaded from hlayiso.c Use the graphs and the information above to answer the following : 6.1 Write down the values of k, ¢ and d. 6.2 Write down the equation of the asymptote of g. 6.3. Write down the domain of h. 6.4 Determine the equation of f if f is the reflection of g in the y-axis, Copyright Reserved June 2017 Common Test (4) G) (2) (2) 19] Please turn over

Mathematics NSC QUESTION 7 Downloaded from hlayiso.com June 2017 Common Test In this question, you must give a reason to justify each of your statements. 71. Inthe diagram below, the diagonals of parallelogram ABCD intersect in M. AB = 13cm, ABC=76° and COM=28°. 13cm 28° D Cc 7.1.1 Write down, giving a reason, the length of DC. 7.1.2 Calculate, giving reasons, the size of ADM 7.2 %n the diagram below, PR is a diagonal of square PORS. Point E lies on SR and QE is drawn, PR and QE intersect at T. SET =120°. P Q 1209 E 7.2.1 Giveareason why SPR = 45°, 7.2.2 Calculate, giving reasons, the size of PTE Copyright Reserved 76°, (2) Q) 13) Q) Please turn over ”

Downloaded from hlayiso.com Mathematics June 2017 Common Test NSC 7.3 Inthe diagram below, ABCD is a kite having diagonals AC and BD intersecting at O. AO = 8cm, BO = 2x cm and DO = 5x A 8 Sx 2x D B ie) Cc cm, 7.3.1 Write down, giving a reason, the length of OC. (2) 7.3.2. Write down the area of ABCD in terms of x. (2) 7.3.3. Ifthe area of ABCD is 168cm’, calculate the value of x (2) - 73.4 Calculate, giving a reason, the length of AB. (3) [16] QUESTION 8 In this question, you must give a reason to justify each of your statements. 8.1 In the diagram below, ABCD is a quadrilateral having AB = DC and AB || DC. A +4 B D 1 2 mn 1 D or Cc Use the diagram on the DIAGRAM SHEET to prove that ABCD is a parallelogram. (5) Copyright Reserved Piease turn over

Downloaded from hlayiso.com Mathematics June 2017 Common Test NSC 8.2 In APQR, A is the midpoint of QR and B is the midpoint of PA. C and D are points on PR such that QBC || AD. G is a point on QB such that GB = BC. A 8.2.1 Give a reason why PGAC is a parallelogram. qd) 8.2.2 Prove that PC = CD = DR. (4) 8.2.3 Prove that GCDA is a parallelogram (4) [4] TOTAL MARKS: 100 Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics June 2017 Common Test NSC | NAME: ! DIAGRAM SHEET 1 ! QUESTION 7.1 A 13cm B M 28° : D i C %| QUESTION 7.2 Bip —Q 5! RY é | 2! E ' T Be ' o s 120' R : E ! QUESTION 7.3 A 5x 2x D r) B C Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics June 2017 Common Test NSC : NAME: | DIAGRAM SHEET 2 | QUESTION 8.1 A ~ B No QUESTION 8.2 PLEASE TEAR ON DOTTED LINES Copyright Reserved

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Downloaded from hlayiso.com Mathematics 3 June 2017 Common Test GRADE 10 Marking Guideline QUESTION 2 Zl 4 =] 4 =4 v1=4 x=0 ¥ answer 2 2.2.4 2415 sto 4 3 3x+180 <20x—24 vmultiplying by 12 -17x S-204 Y simplification x212 v answer @) OR x Sx 4° 15< 3 2 3% 445< 202 5 mom RB 12” ¥ common denominator Vix forx aps Y simplification x212 ¥ answer @) 222 | xe [12;<) @ 23 x—2y= x=2yt3 VY x=2y43 A(2y +3) +3y +10 =0 Y substitution 8y+1243y+10=0 ~ multiplying out lly =-22 yo v y—value x= 2(-2)+3 ze] ¥ x~value (5) 24 Area of rectangle = [xb 88 = x(x +3) Y x(x+3) ¥ equating to 88 x? +3x-88=0 Y standard form (~-8)(x411) =0 Y factors x=8vx#-11 - The lawn is 8 m by 8 m Y answer 6 [16] Copyright Reserved Please turn over Mathematics 4 June 2017 Common Test GRADE 10 Marking Guideline QUESTION 3 3.11 ‘The sequence is: 5 ; 17; 29; ... v5 ¥17 and 29 (2) 3.12 )No v answer 12n-7=356 363 is not exactly divisible by 12 ¥ reason OR 12 is not a multiple of 363 Q) 3.21 17 blocks au ie) 322 | TL =3n+5 ¥3n +5 (2) 3.23 | No. of blocks required to make the 100°E: 3(100)+3 j ¥ substitution =305 Y answer (2) N.B. Answer only: full marks. 3.24 3n+5=116 ¥ 3n+5=116 3n=111 Y simplification n=37 The 37" E can be made from 116 blocks Y answer G) {12} QUESTION 4 f)=x-2 and g(a)= 4-2 v x-intercepts of f (2; 0) y-intercept of f: (0 ;-2) v x-intercept of g: (2 : 0) Y asymptote of g: y=~2 ¥ another point ong eg. (132), 43-0, (2; 4), (1; 6), etc. Please turn over 2;4) Y shape of g ie. hyperbola predominately in quadrants 1 and 3. [6t Copyright Reserved

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Mathematics. 7 June 2017 Common Test GRADE 10 72 P iQ T 120) (eo) 5 R O E © (721 _ J The diagonals of a square bisects the vertex angles. Y reason 12) @) —~ 722 ) pfE+45°+90° +120°=360° (gum of angles in quad) vSIR PTE =360°—255° io} =i0s° Y answer, = fp " 7. A fo} 8 ; a bx on Qu D ray B TW AY) Q S ° © [734 [0C=8em (diagonals of @ kite) YSYR t (2) = 732 |p ceaof ite = (ACNBD) 1 g 120° 1 ==(16)(7: R 1 B FOOT) E ¥ 50072) = Y answer = 56x 2) 733 | 36x=168 VS x=3 Y answer 2) 734 [OB=6em VS AOB =90° (diagonals of a kite) vse AB’ =67 +8 ‘Theorem of Pytha; =100 ‘ of Fythagorss) Y answer with AB=10 reason. (3) [16] Copyright Reserved Please turn over « Mathematics 8 June 2017 Common Test GRADE 10 Marking Guideline QUESTION 8 8.1 A B : (NI Y 2 D t 4 Constr: Draw diagonal AC Proof: In AABC and ACDA @ = ACis common @ aB=DC (given) Gi) AC, (alt angles AB {[ DC) AABC=ACDA (8323S) oA, =O, ‘These are alternate angles <-AD || BC :. ABCD isa parallelogram (both pairs of opp sides are parallel) Y constr Y AABC=ACDA (S;2;8) YA, =¢, “AD || BC YR G) Copyright Resexved Please tum over

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