Mathematics Grade 10 September 2015 Paper & Memo

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Mathematics Downloaded from hlayiso.com 2 Common Test September 2015 NSC INSTRUCTIONS AND INFORMATION Read the following instructions carefully before. answering the questions: 1. 2. This question paper consists of 6 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. 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 Common Test September 2015 NSC QUESTION 1 1.1 In which quadrant will @ lie if 0°<@ <360° and sind >0 and tan? <0? Q) 7 O io 1.2 Determine, without using a calculator, the value of sin A?.cosen 90" | () /3cos0°. tan 60° 1.3 If 13 cos@=—5 and 180°<6 <360°, determine, using a suitable diagram and without the use of a calculator, the value of: 13.1 coté (4) 13.2 sin?@—cos*é (3) [14] QUESTION 2 In the diagram below, AD = 13 units, AB = 12 units and DC =3 units, DBA and DCB are two right angles in quadrilateral ABCD. D “ A 12 B 2.1 Calculate the length of DB and BC. ) 2.2 Hence determine the value of the following, without the use of a calculator: 2.2.1 tanA qd) 2.2.2 sec ADB +sin DBC (3) 23 Use you calculator to determine the size of angle A, correct to ONE decimal (2) place. 110 Copyright Reserved Please turn over

Downloaded from hlayiso.com - Mathematics Common Test September 2015 NSC QUESTION 3 ‘The following graphs have been drawn below for x €[0°;360°]: J (x) = tanx and g(x) = asinx+q Ne ---> tn nn nnn ep ee Use the graphs to answer the following questions for x € [0° ; 360°] : 3.1 Determine the value of a and q. (2) 3.2 Write down the period of f. ql) 3.3. Write down the range of g. (2) 3.4 Write down the values of x for which / is undefined. (2) 3.5 Determine the values of x for which g(x) = 1. 10) Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 5 Common Test September 2015 NSC QUESTION 4 Ayanda plans to travel to New Zealand. Her flight has been paid for by her parents. However, she will need spending money of about NZ$ 150. 4.1 If the exchange rate is currently 8,8595 Rand to the NZ$, how much will she need in South African Rand in order to have enough spending money? (2) 4.2 Ayanda has just received a gift of R500 from her grandmother and her grandmother promises to give her another R500 in a year’s time. Ayanda decides to invest this money in an account which pays 8,5% p.a. compounded annually. How much will she have in her account after two years? (6) 4.3 How much additional money will she have to add to her investment after two years if she withdraws all the money for her trip? (2) [10] ) QUESTION 5 5.1 A bag contains 7 red marbles and 5 green marbles. One marble is drawn out of ‘the bag at random. Calculate the probability that it is: 5.1.1 ared marble qd) 5.1.2 an orange marble qd) 5.1.3 ared ora green marble a) 5.1.4 notared marble qa) 5.2 There are 120 grade 10 learners at a school. 55 learners take Mathematics and 80 (2 learners take Life Sciences. There are 25 learners who do not do Mathematics or . Life Sciences and the number of learners who take both Mathematics and Life Sciences = x. 5.2.1 Represent this information in a Venn diagram. Let M = {learners who take Mathematics}, LS = {learners who take Life Sciences}. (3) 5.2.2 Calculate the value of x (2) Use the Venn Diagram to calculate the probability that a randomly chosen learner: 5.2.3 takes Mathematics only (2) 5.2.4 takes Mathematics and Life Sciences (2) 5.2.5 takes Mathematics or Life Sciences (2) [15] Copyright Raserved Please turn over

Mathematics Downloaded from hlayiso.com 6 Common Test September 2015 NSC QUESTION 6 In the diagram below A(-3 ; 7), BC-8 ; 2) and C(4 ; 6) are the vertices of triangle ABC. AD is drawn such that D(-2 ; 4) is the midpoint of BC. Ay A(-3 37) C4 ; 6) DA2;4 BC8 ; 2) x a > 6.1 Calculate the gradient of BC. 6.2 Calculate the length of BC. 6.3 Determine the value of k. 6.4 Determine the equation of a line that is parallel to BC and passes through A(-3;7). 6.5 Ifthe value of kis 4, prove that AD 1 BC. 6.6 Hence, calculate the area of AABC, TOTAL: Copyright Reserved @) (2) (2) (3) 6) (4) [16] wh)

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