Mathematical Literacy Grade 11 P1 2016 Memo

Basic Education KwaZulu-Natal Department of Education REPUBLIC OF SOUTH AFRICA MATHEMATICS P1 JUNE 2016 , : COMMON TEST : NATIONAL ) SENIOR CERTIFICATE GRADE 11 | MARKS: 100 ’ \ TIME: 2 hours | fl This question paper consists of 6 pages and 1 diagram sheet. | Copyright Reserved Please turn over

MathematicsPaper] : D Oo wn | oa d e d from h | ayiso. CO Hommon Test June 2016 NSC ~ Grade 11 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 5 questions, 2. Answer ALL the questions. 3. Clearly show ALL calculations, diagrams, graphs, et cetera which you have used in determining the answers. 4. Answers only will NOT necessarily be awarded full marks. 5. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 6. If necessary, round off answers to TWO decimal places, unless stated otherwise, C ~ 7. Diagrams are not necessarily drawn to scale, 8. ONE diagram sheet for answering QUESTION 4.1.2 and 4.1.5 is attached at the end of this question paper. Write your name in the space provided and insert it inside your ANSWER SHEET, 9. Number the answers correctly according to the numbering system used in this question paper. 10, Write neatly and legibly. Copyright reserved Please turn over

MathematicsPaper! NSC ~ Grade 11 QUESTION 1 11 Solve the following equations: | LiL ax-35 | x 1.1.2 3x?—6x+1=0 (correct to two decimal places) | ! 1.13 Sx -2(x?-6) <0 ! Ll4 2+vx+2 =6-x | LLS 3 —1=0 1.2 Solve for p if the roots of 4x? = p—5x are real. i) 1.3 Solve for x and y simultaneously if: x-3=2y and x?—y? =45 QUESTION 2 2.1 Simplify the following without using a calculator: 3 211 814 are e438, 2.1.2 3375 535° 2.2 Without using a calculator, show that: 2 8 2 a) 1+ 2 V8 Copyright reserved Downloaded from hlayiso.codtinon tes se 2016 (4) (4) (4) 6) G3) (3) (6) [29] @) G) 4) {10} Please turn over

MathematicsPaper! D own | oa d e d rem “> NSC — Grade 1 QUESTION 3 3.1 The following sequence of numbers is given: | ay is O. COLP Common Test June 2016 23.7; L257; cen 3.1.1 Write down the values of the next two terms of the sequence, (2) 3.1.2 Write down the value of the first term in the sequence that will have a value that.is greater than 107. a) 3.1.3 Determine an expression for the n" term of the sequence. (Q) 3.1.4 Which term of the sequence will be equal to 182? (2) 3.1.5 The terms of this sequence are also the first differences of a certain quadratic sequence. If the fourth term of this quadratic sequence is 22, write down its first, second and third terms. (3) 3.2 Given the following quadratic sequence: 51; 70; 95; 126; occu 3.2.1 Write the value of the next term of the sequence. (2) 3.2.2 Determine an expression for the n"” term of this quadratic sequence. (5) 3.2.3 Which term of the sequence will be equal to 4063? (4) [21] Copyright reserved Please turn over

C — Grade 11 | QUESTION 4 4.1 Given f(x) = ~x? ~2x +3. MathematicsPaper| Downl oaded from h | ay iso . CO lAnmmon Test June 2016 4.1.1 Write f in the form y=a(x+p) +q. (3) 4.1.2 Draw a neat sketch graph of f on the DIAGRAM SHEET provided. Indicate all intercepts with the axes and the coordinates of the turning point. (5) 4.1.3 Write down the range of (2) 4.1.4 Describe the transformation from f to A if A(x) =x?+2x-3 (2) 4.1.5 On the same set of axes as f, draw a neat sketch graph of gif g(x) = -2x+2, showing all intercepts with the axes. (2) ho) 4.1.6 Now use your graphs to answer the following questions: For which value(s) of x is: (a) f'(*)~ g(x) =0? (2) (6) f(x) >0? (2) 4.2 Draw a rough sketch graph of k(x) =ax’ +4x+-¢ , if it is given that e & has no real roots; e b> 0 and © c>0. (3) (21) Copyright reserved Please turn over

MattemascsPepert Downloaded from hlayiso. COFfommon Test June 2016 NSC ~ Grade QUESTION 5 The diagram below represents the graphs of f(x) = Tp +g and g(x) =f". f outs the x-axis at R (~2;0) and the y-axis at D. (2:4) is a point on the graph of g. f and -g intersect at point D, 3 ? wecececneneeeeneneeneen a ee | aennennee weteneewene aT H H ' 4 ' t ‘ i i t H 1 J 5.1 Write down the values of p and g. (2) 5.2. Determine the value of a. @G) 5.3. Determine the value of ¢ @) 5.4 Calculate the average gradient of g between x=-2 and x=2. QB) 5.5 Write down the equation of the asymptote of g. () 5.6 Write down the coordinates of D. (2) 5.7 Determine the equation of the axis of symmetry of f that has a negative gradient, 3) 5.8 _ _Point_D is reflected in the line determined in 5.7 to give point E. ne Write down the coordinates of E. Q) {19] TOTAL: 100 Copyright reserved Please turn over

TEAR — OFF SHEET ( MathematicsPaperl DIAGRAM SHEET NAME OF LEARNER: Downloaded from ~ Grade 11 hlayiso .COMommon Test June 2016 QUESTION 4,1.2 and 4.1.5 GRADE: — Copyright reserved oo a wy

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