Mathematics P1 GR 10 Exemplar 2012 Eng hlayiso.com

Downloaded from hlayiso.com NATIONAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS P1 EXEMPLAR 2012 MARKS: 100 TIME: 2 hours This question paper consists of 6 pages. Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 2 DBE/2012 NSC – Grade 10 Exemplar INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 7 questions. 2. Answer ALL the questions. 3. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining your 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. 7. Diagrams are 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 Mathematics/P1 3 DBE/2012 NSC – Grade 10 Exemplar QUESTION 1 1.1 Simplify the following expressions fully: 1.1.1 (m − 2n )(m 2 − 6mn − n 2 ) (3) x3 + 1 4 x 2 − 3x − 1 1.1.2 − (5) x2 − x +1 4x + 1 1.2 Factorise the following expressions fully: 1.2.1 6 x 2 − 7 x − 20 (2) 1.2.2 a 2 + a − 2ab − 2b (3) 1.3 Determine, without the use of a calculator, between which two consecutive integers 51 lies. (2) 1.4 Prove that 0,2 4 5 is rational. (4) [19] QUESTION 2 2.1 Determine, without the use of a calculator, the value of x in each of the following: 2.1.1 x 2 − 4 x = 21 (3) 5 2.1.2 96 = 3 x 4 (3) 2 x 2.1.3 R= (2) 3S 2.2 Solve for p and q simultaneously if: 6q + 7 p = 3 2q + p = 5 (5) [13] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 4 DBE/2012 NSC – Grade 10 Exemplar QUESTION 3 3.1 3x + 1 ; 2x ; 3x – 7….. are the first three terms of a linear number pattern. 3.1.1 If the value of x is three, write down the FIRST THREE terms. (3) 3.1.2 Determine the formula for T n , the general term of the sequence. (2) 3.1.3 Which term in the sequence is the first to be less than – 31? (3) 3.2 The multiples of three form the number pattern: 3 ; 6 ; 9 ; 12 ; ... Determine the 13th number in this pattern that is even. (3) [11] QUESTION 4 4.1 Thando has R4 500 in his savings account. The bank pays him a compound interest rate of 4,25% p.a. Calculate the amount Thando will receive if he decides to withdraw the money after 30 months. (3) 4.2 The following advertisement appeared with regard to buying a bicycle on a hire- purchase agreement loan: Purchase price R5 999 Required deposit R600 Loan term Only 18 months, at 8% p.a. simple interest 4.2.1 Calculate the monthly amount that a person has to budget for in order to pay for the bicycle. (6) 4.2.2 How much interest does one have to pay over the full term of the loan? (1) 4.3 The following information is given: 1 ounce = 28,35 g $1 = R8,79 Calculate the rand value of a 1 kg gold bar, if 1 ounce of gold is worth $978, 34. (4) [14] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 5 DBE/2012 NSC – Grade 10 Exemplar QUESTION 5 5.1 What expression BEST represents the shaded area of the following Venn diagrams? A B 5.1.1 (1) A 5.1.2 (1) 5.2 State which of the following sets of events is mutually exclusive: A Event 1: The learners in Grade 10 in the swimming team Event 2: The learners in Grade 10 in the debating team B Event 1: The learners in Grade 8 Event 2: The learners in Grade 12 C Event 1: The learners who take Mathematics in Grade 10 Event 2: The learners who take Physical Sciences in Grade 10 (1) 5.3 In a class of 40 learners the following information is TRUE: • 7 learners are left-handed • 18 learners play soccer • 4 learners play soccer and are left-handed • All 40 learners are either right-handed or left-handed Let L be the set of all left-handed people and S be the set of all learners who play soccer. 5.3.1 How many learners in the class are right-handed and do NOT play soccer? (1) 5.3.2 Draw a Venn diagram to represent the above information. (4) 5.3.3 Determine the probability that a learner is: (a) Left-handed or plays soccer (3) (b) Right-handed and plays soccer (2) [13] Copyright reserved Please turn over

Downloaded from hlayiso.com Mathematics/P1 6 DBE/2012 NSC – Grade 10 Exemplar QUESTION 6 3 Given: f ( x) = + 1 and g ( x) = −2 x − 4 x 6.1 Sketch the graphs of f and g on the same set of axes. (4) 6.2 Write down the equations of the asymptotes of f. (2) 6.3 Write down the domain of f. (2) 6.4 Solve for x if f ( x) = g ( x) . (5) 6.5 Determine the values of x for which − 1 ≤ g (x ) < 3 . (3) 6.6 Determine the y-intercept of k if k(x) = 2g(x). (2) 6.7 Write down the coordinates of the x- and y-intercepts of h if h is the graph of g reflected about the y-axis. (2) [20] QUESTION 7 The graph of f ( x ) = ax 2 + q is sketched below. Points A(2 ; 0) and B(– 3 ; 2,5) lie on the graph of f. Points A and C are x-intercepts of f. y f B(−3 ; 2,5) C A(2 ; 0) x O 7.1 Write down the coordinates of C. (1) 7.2 Determine the equation of f. (3) 7.3 Write down the range of f. (1) 7.4 Write down the range of h, where h( x) − = f ( x) − 2 . (2) 7.5 Determine the equation of an exponential function, g(x) = bx + q, with range y > – 4 and which passes through the point A. (3) [10] TOTAL: 100 Copyright reserved