NATIONAL SENIOR CERTIFICATE GRADE 10

Transcription

1 NATIONAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS P1 EXEMPLAR 01 MARKS: 100 TIME: hours This question paper consists of 6 pages.

2 Mathematics/P1 DBE/01 NSC Grade 10 Eemplar INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions This question paper consists of 7 questions. Answer ALL the questions. 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 nongraphical), unless stated otherwise. If necessary, round off answers to TWO decimal places, unless stated otherwise. 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.

3 Mathematics/P1 DBE/01 NSC Grade 10 Eemplar QUESTION Simplify the following epressions fully: ( m n)( m 6mn n ) () () 1. Factorise the following epressions fully: () 1.. a + a ab b () 1. Determine, without the use of a calculator, between which two consecutive integers 1 lies. () 1. Prove that 0, is rational. () [19] QUESTION.1 Determine, without the use of a calculator, the value of in each of the following:.1.1 = 1 () = ().1. R = () S. Solve for p and q simultaneously if: 6q + 7 p = q + p = () [1]

4 Mathematics/P1 DBE/01 NSC Grade 10 Eemplar QUESTION ; ; 7.. are the first three terms of a linear number pattern..1.1 If the value of is three, write down the FIRST THREE terms. ().1. Determine the formula for T n, the general term of the sequence. ().1. Which term in the sequence is the first to be less than 1? (). The multiples of three form the number pattern: ; 6 ; 9 ; 1 ;... Determine the 1 th number in this pattern that is even. () [11] QUESTION.1 Thando has R 00 in his savings account. The bank pays him a compound interest rate of,% p.a. Calculate the amount Thando will receive if he decides to withdraw the money after 0 months. (). The following advertisement appeared with regard to buying a bicycle on a hirepurchase agreement loan: Purchase price R 999 Required deposit R600 Loan term Only 18 months, at 8% p.a. simple interest..1 Calculate the monthly amount that a person has to budget for in order to pay for the bicycle. (6).. How much interest does one have to pay over the full term of the loan?. The following information is given: 1 ounce = 8, g $1 = R8,79 Calculate the rand value of a 1 kg gold bar, if 1 ounce of gold is worth $978,. () [1]

5 Mathematics/P1 DBE/01 NSC Grade 10 Eemplar QUESTION.1 What epression BEST represents the shaded area of the following Venn diagrams? A B.1.1 A.1.. State which of the following sets of events is mutually eclusive: A B C Event 1: The learners in Grade 10 in the swimming team Event : The learners in Grade 10 in the debating team Event 1: The learners in Grade 8 Event : The learners in Grade 1 Event 1: The learners who take Mathematics in Grade 10 Event : The learners who take Physical Sciences in Grade 10. In a class of 0 learners the following information is TRUE: 7 learners are left-handed 18 learners play soccer learners play soccer and are left-handed All 0 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...1 How many learners in the class are right-handed and do NOT play soccer?.. Draw a Venn diagram to represent the above information. ().. Determine the probability that a learner is: (a) (b) Left-handed or plays soccer Right-handed and plays soccer () () [1]

6 Mathematics/P1 6 DBE/01 NSC Grade 10 Eemplar QUESTION 6 Given: f ( ) = + 1 and g ( ) = 6.1 Sketch the graphs of f and g on the same set of aes. () 6. Write down the equations of the asymptotes of f. () 6. Write down the domain of f. () 6. Solve for if f ( ) = g( ). () 6. Determine the values of for which 1 g () <. () 6.6 Determine the y-intercept of k if k() = g(). () 6.7 Write down the coordinates of the - and y-intercepts of h if h is the graph of g reflected about the y-ais. () [0] QUESTION 7 The graph of f ( ) = a + q is sketched below. Points A( ; 0) and B( ;,) lie on the graph of f. Points A and C are -intercepts of f. y B( ;,) f C O A( ; 0) 7.1 Write down the coordinates of C. 7. Determine the equation of f. () 7. Write down the range of f. 7. Write down the range of h, where h ( ) = f( ). () 7. Determine the equation of an eponential function, g() = b + q, with range y > and which passes through the point A. () [10] TOTAL: 100

7 NATIONAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS P1 EXEMPLAR 01 MEMORANDUM MARKS: 100 This memorandum consists of 7 pages.

8 Mathematics/P1 DBE/01 NSC Grade 10 Memorandum QUESTION ( m n)( m 6mn n ) = m 6m n mn m n + 1mn + n = m 8m n + 11mn + n ( + 1)( + 1) ( + 1)( 1) = + 1 = + 1 ( 1) = = ( + )( ) a + a ab b = a( a + 1) b( a + 1) = ( a + 1)( a b) Since 7 = 9 and 8 = 6 and 9 < 1 < 6, 7 < 1 < 8 i.e. 1 lies between 7 and 8 1. Let = 0, Then 1000 =, i.e. 999 = i.e. = 999 Therefore is a rational number. epansion m ; + n 8m n + 11mn ( + 1)( + 1) ( + 1)( 1) + 1 ( 1) answer ( + ) ( ) grouping (1 + a) a b ( ) 9 < 1 < 6 introduce variable 1000 =, 999 = = 999 () () () () () () [19]

9 Mathematics/P1 DBE/01 NSC Grade 10 Memorandum QUESTION.1.1 = 1 1 = 0 ( + )( 7) = 0 standard form factors = 0 = 96 = = = = ( ) ( ) = = 16 or 7 = 0 = 7 s = = ( ) R = Multiply by S and S divide by RS = Squaring both sides 9R S () = 6q + 7 p =...Equation 1 q + p =...Equation () () 6q+ 7 p =...Equation 1 1q+ 7 p =...multiply Equation with 7...Equation Equation Equation 1: 8q = q = ( ) + p = p = 1 q + 7 p = 8 q = q = substitution p = () [1]

10 Mathematics/P1 DBE/01 NSC Grade 10 Memorandum QUESTION ; 6 ; d =.1.. QUESTION T n = n + 1 n + 1 < 1 n < n > 11, n = 1 T n = 6n T1 = 6( 1) = 78 OR T n = n T6 = ( 6) = 78 () n 1 () n + 1 < 1 n >11, () 6n substitution of 1 () OR n substitution of 6 () [11].1 n A = P(1 + i).. = = R Loan amount = R 999 R600 = R 99 Total amount owed = 99[1+(0,08)(1,)] = R6 06, Monthly instalment = 18 = R,9.. R6 06,88 - R 99 = R67,88. 1 kg = g 1000 =,76861 ounces 8,, , 8,79 = R0 7,16 n =. substitution answer y = 0 99 n = 1, Substitution R6 06,88 18 R,9 conversion division multiplication answer () (6) () [1]

11 Mathematics/P1 DBE/01 NSC Grade 10 Memorandum QUESTION.1.1 A B OR A and B.1. A / OR not A. B learners are right-handed and do not play soccer... 1 S L 1 19 () 19.. (a).. (b) P(L OR S) = 0 1 = 0 1 P(R AND S) = 0 7 = () () [1]

12 Mathematics/P1 6 DBE/01 NSC Grade 10 Memorandum QUESTION y shape of f g 6 f -int of f -intercept of g y-intercept of g f () 6. = 0 and y = 1 6. ( ; 0) (0 ; ) values notation = = = + + = 0 ( + )( + 1) = 0 = or = 1 1 < < 7 1, >,, < 1, OR (, ; 1,] k( ) = ( ) = 8 y-intercept: (0 ; 8) 6.7 -intercept: ( ; 0) y-intercept: (0 ; ) () () + 1 = standard form factors s () 1 < < 7 () equation of k() () -intercept y-intercept () [0]

13 Mathematics/P1 7 DBE/01 NSC Grade 10 Memorandum QUESTION C( ; 0) 7. f ( ) = a f ( ) = a, = a(( ), = a a = 1 ( ) ) ( ) 1 f ( ) = 7. Range of f: [ ; ) + q f ( ) = a ( 16 ) substitution of ( ;,) 7. Range of h: ( ; 0] notation critical values 7. g ( ) = b 0= b = b b = g ( ) = g ( ) = b substitution () () () [10] TOTAL: 100