Mathematical Literacy Grade 11 P1 2017 Memo

ownloaded from hlaviso.com G SHIVIN LED Education KwaZulu-Natal Department of REPUBLIC OF SOUTH AFRICA SARA AN EERE ERA E ELE AER ERE BS 4) # a " *" * = * = a «i cf “ ts MATHEMATICS P1 COMMON TEST ix i in i is i i i B 5 CALE EJ at errs JUNE 2017 NATIONAL SENIOR CERTIFICATE | GRADE of MARKS: = 100 TIME: 2 hours This question paper consists of 6 pages. Copyright Reserved . Please turn over

Mathematics /P1 Downloaded from hlayiso.com NSC — Grade 11 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. 2, Copyright Reserved This question paper consists of 6 questions. Answer ALL the questions. Number the answers correctly according to the numbering system used in. this question paper. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your 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. Diagrams are NOT necessarily drawn to scale. Write neatly and legibly, Common Test June 2017 Please turn over

Downloaded from hlayiso.com NSC — Grade 11 Mathematics /P1 QUESTION 1 1a Solve for x: Lil (x+3\x-5)=9 1.1.2 x-V2x-1=2 113 1<(2x~3) 1.2 Given: 3x? = 3x+5 1.2.1 Solve for x (correct to TWO decimal places). 1.2.2 Hence, or otherwise, solve for y if 3(y +l) =3(y+ 1) +5. 13 Describe the nature of the roots of 3x7 = 3x+ 5 1.4 Solve for x and y in the following simultaneous equations: Qx+y=l and 2x?~xyey? =4 QUESTION 2 2.1 Solve for x, without the use of a calculator: 24.1 VI-V2 peg x 3 21.2 553 256 = a)x? 2.2 Simplify without the use of a calculator: 2.2.1 Fraxal 10” 45 Copyright Reserved Please turn over Common Test June 2017 (3) (4) (5) (4) (2) (2) (6) [26} 4) (4) Q) (4) [14]

Downloaded from hlayiso.com Mathematics /P1 Common Test June 2017 NSC — Grade 11 QUESTION 3 3.1 4; 10; 18; 28; ..... isa quadratic number pattern. 3.14 Write down the next term in the pattern. qd) 3.1.2 Determine an expression for the n'” term of the pattern. (4) 3.1.3 Calculate the value of the first term of the pattern that will be greater than 460, (4) 3.1.4 Determine an expression for the n® term of the sequence of first differences of this quadratic number pattern. (2) 3.1.5 Between which two terms of the quadratic number pattern will the first difference be equal to 64? (3) 3.2 The first 4 terms of a quadratic sequence are 133; «; 29; x+24;...... Calculate the value of x. (5) [19] QUESTION 4 Given: A(x)=2°* +1 4.1 Determine the y-intercept of A, (2) 4.2 Write down the equation of the asymptote. qd) 43 Draw a sketch graph of fh. Show clearly any intercepts with the axes and the asymptote. (3) 4.4 Determine the average gradient of i between x=-2 and x=0, (3) 45 Solve for xif h(x)>5. - (2) [i] Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics /P1 Common Test June 2017 NSC ~ Grade 11 QUESTION 5 The graphs of f(x) = fg q and the straight line g are sketched below. x+p The asymptotes of fintersect at (- 3;- 2). The points of intersection of fand g are (- 5;0) and (1;- 3). | y i 0 | eo H x roerreennennnnrcnanennns Ca — EEE I iit 5.1 Determine the values of p, g and a. (4) 5.2 Write down the domain of f (2) 5.3 The equation of one of the axes of symmetry of fis y =x + k. (2) Calculate the value of k. 5.4 Use the graphs to solve for x, if (x) 2 g(x). (3) 5.5 Determine the equation of g. (2) [13] Copyright Reserved Please turn over

Mathematics /P1 ~ Downloaded from hlayiso.com — NSC - Grade 11 QUESTION 6 The sketch below represents the graphs of two parabolas: f and g. Pa)=-58 ~x+4, B is the turning point of f A(- 23 4) is a point of intersection between f and g, and C is the y-intercept of f D and E are the x-intercepts of f D is also the x-intercept of g. K isa point on f and La point on g, such that KL is parallel to the y-axis, and three units to the left of the y-axis. 6.1 6.2 6.3 6.4 6.5 6.6 y Calculate the coordinates of 6.1.1 B 6.1.2 Cc Calculate the coordinates of D and E. Determine the equation of g. The graph of gis reflected about the y-axis to obtain the graph of 4. Determine the equation of h, Determine the value(s) of k such that - * ~x+4=k will have no real roots. Calculate the length of KL. TOTAL Copyright Reserved Common Test June 2017 3} () (3) G3) (2) (2) (3) (17) 100

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Downloaded from hlayiso.com 3 ‘Mathematics P1 (Marking Guideline) NSC June 2017 Common Test 122 |y+1=1,88 OR y+1=—0,88 y= 0,88 or yp=-1,88 2CA for answers Q) 13 | 3 269 6 _ . oe 1CA for irrational ‘The roots are real, irrational and unequal. 1CA for unequal @) 14 ys-2xt1 equation 1 1A for making y the subject of the wWe-wyty=4 equation 2 formula Substitute equation 1 into equation 2: 2x? —x{-2e4l)+(C2x41f =4 1CA for substitution 2x? 42x? —x+4x? ~4x+1=4 82° —5x-3=0 ICA for standard form (x+3)e-1)=0 ICA for factorization 3 macy or eel ICA for both x-values | 1CA for both y-values 4 6 ©) [26] Please Turn Over Copyright Reserved Mathematics P1 (Marking Guideline) NSC June 2017 Common Test QUESTION 2 211) J75—Vi2 _ ge x 1A for 5¥3 -2V3 5y3-2y3 Saal 1A for 43 W345 we ai43 x ICA for simplification wed a3 =3 ICA for answer 4 4) 2i2/|_ 2 3 z 5x? -256 = x? 1A for x? 3 4x2 = 2 r= 256 1A for 4x4 x? =64 2 2 2 x= 642 1A for (64)5 =2* 7 LCA for answer =1 @ 321 2 1 Lit en") 1 =—+24+2 1 A for i 2 2 wal 2 1A for answer (2) 2221 [eraser 10" +5" _ [27.3" 453" , OV 5" 2" 455" 1 A for expanding =A” b" +5) 1CA for factorisation 5° QQ" 45 =a . ” 2) 1 CA for simplification 3 1 CA for answer “5 4) U4] Copyright Reserved Please Tum Over ¥

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% Downloaded from hlayiso.com 7 Mathematics P1 (Marking Guideline) NSC Jane2017 Common Test Mathematics P1 (Marking Guideline) June 2017 Common Test QUESTION 5 QUESTION 6 SL | p=3 1A for p=3 611 [nb qa 1A for g=-2 2a a -(1 y=—-2 = ct xt3 = 1A for substitution Substitute (—5;0): OR Substitute (5-3): 1CA for substitution 3 a a =-1 1A for answer (x-coordinate) ne ae 3377 7 l 1 7 * fC D=-2 C1 -Ciesaas ICA for y-coordinate qa -1=4 2 2 —2 4 cial a=-4 a=-4 1CA for answer 2 @) @) 612 | (4) TA for answer 52 xe RK, but x#-3 e) OR (3) oF (35e0) 2A for answer 87) ak eaneano tAfor-Lit-xe4=0 C32) 2 x +2x-8=0 5.3 Substitute (-3;-2) in yox+k: 78s -2=-3+k 1A for substitution (e+4x-2)=0 1A for factors k=l 1A for answer @ x=—4 or x=2 34 |—-SSx<-3 or x2]. D-4; 0) EQ; 0) 2CA for answers © OR 2A for —S£x<-3 - [-5;-3) UIt~) 1Afor x21 63 | ymalx+ay 1A for y=ale+4F 3 4ea(-24+4F 1A for substituting (—2; 4) 35 | Gradient 4=aQy _-3-0 1A for gradient a=l 1+5 1 ya(et4y ICA for answer 6) “2 64 =(e- > 1 5 1CA for answer an & ay (x-4Y OR x? -8x +16 a hay Q) =x? —8x +16 2A for answer Q) [13] 65 ke ah 2A for answer 2 @) 66 | #&)-2&) 12 2 -4 2 xa4—(x 44h lap xt oxtd- (er) ie —x+4—x°-8x-16 2-32 -9x-12 LA: simplification 2 fC3)-2-3) $037 —9(-3)-12 -3 ICA: answer 2 @ 117) . TOTAL: 100 Copyright Reserved Please Tum Over ‘Copyright Reserved Please Tum Over ed