### Transcription of GR 10 MATHS – EXAM QUESTION PAPERS Q - The …

1 Gr 10 **MATHS** National Exemplar **paper** 1. Q. GR 10 **MATHS** EXAM **QUESTION** **PAPERS** . 1. **QUESTION** 2 FINANCE & GROWTH [14]. NATIONAL EXEMPLAR **paper** 1. Determine, without the use of a calculator, **QUESTION** 4. the value of x in each of the following : Clearly show ALL calculations, diagrams, graphs, etc. Thando has R4 500 in his savings account. that you have used in determining your answers. x2 - 4x = 21 (3). The bank pays him a compound interest rate 5 of 4,25% Calculate the amount Thando Answers only will NOT necessarily be 96 = 3x 4 (3) will receive if he decides to withdraw the awarded full marks. 2 x money after 30 months. (3). You may use an approved scientific calculator R = (2). 3S. (non-programmable and non-graphical), The following advertisement appeared with unless stated otherwise. regard to buying a bicycle on a hire-purchase Solve for p and q simultaneously if : If necessary, round off answers to agreement loan : 6q + 7p = 3. TWO decimal places, unless stated otherwise.

2 2q + p = 5 (5) [13] Purchase price R5 999. Required deposit R600. ALGEBRA [32] Loan term Only 18 months, at 8% NUMBERS & NUMBER PATTERNS [11] simple interest **QUESTION** 1. **QUESTION** 3. Simplify the following expressions fully : Calculate the monthly amount that 2 2 3x + 1 ; 2x ; 3x - 7 .. are the first three terms a person has to budget for in order to (m - 2n)(m - 6mn - n ) (3). of a linear number pattern. pay for the bicycle. (6). x 3 + 1 - 4x 2 - 3x - 1 (5). 4x + 1 If the value of x is three, write down How much interest does one have to EXAM **PAPERS** : **paper** 1. x - x +1. 2. the FIRST THREE terms. (3) pay over the full term of the loan? (1). Factorise the following expressions fully : Determine the formula for Tn , The following information is given : 2. 6x - 7x - 20 (2) the general term of the sequence. (2) 1 ounce = 28,35 g 2 $1 = R8,79. a + a - 2ab - 2b (3) Which term in the sequence is the first to be less than - 31? (3) Calculate the rand value of a 1 kg gold bar, if 1 ounce of gold is worth $978,34.

3 (4) [14]. Determine, without the use of a calculator, between which two consecutive integers The multiples of three form the number pattern : 3 ; 6 ; 9 ; 12 ; .. 51 lies. (2). th Determine the 13 number in this pattern i i i Prove that 0,245 is rational. (4) [19] that is even. (3) [11]. Q1 Copyright The Answer Gr 10 **MATHS** National Exemplar **paper** 1. PROBABILITY [13] In a class of 40 learners the following information **QUESTION** 7. Q is TRUE : 2. **QUESTION** 5 7 learners are left-handed The graph of f ( x) = a x + q is sketched below. 1 What expression BEST represents the shaded 18 learners play soccer Points A(2; 0) and B(- 3; 2,5) lie on the graph of f. Points A and C are x-intercepts of f. area of the following Venn diagrams? 4 learners play soccer and are left-handed All 40 learners are either right-handed or y left-handed A B Let L be the set of all left-handed people and S be the set of all learners who play soccer. f B(- 3; 2,5). How many learners in the class are (1).

4 Right-handed and do NOT play soccer? (1). Draw a Venn diagram to represent the C A(2; 0). O x above information. (4). A. Determine the probability that a learner is : (a) left-handed or plays soccer (3) -2. (1). (b) right-handed and plays soccer (2) [13]. Write down the coordinates of C. (1). State which of the following sets of events is mutually exclusive : FUNCTIONS & GRAPHS [30] Determine the equation of f. (3). **QUESTION** 6 Write down the range of f. (1). A Event 1: The learners in Grade 10 in the swimming team 3 Write down the range of h, where Given : f ( x) = + 1 and g( x) = - 2x - 4. Event 2: The learners in Grade 10 in x h( x) = - f ( x) - 2. (2). the debating team Sketch the graphs of f and g on the same Determine the equation of an exponential set of axes. (4) x B Event 1: The learners in Grade 8 function, g( x) = b + q , with range y > - 4. EXAM **PAPERS** : **paper** 1. Write down the equations of the asymptotes of f. (2) and which passes through the point A.

5 (3) [10]. Event 2: The learners in Grade 12. Write down the domain of f. (2) TOTAL : 100. C Event 1: The learners who take Mathematics in Grade 10 Solve for x if f ( x) = g( x). (5). Event 2: The learners who take We trust that working through these Physical Sciences in Grade 10 (1). Determine the values of x for which exam **PAPERS** and following our detailed - 1 g( x) < 3. (3) answers and comments will help you prepare thoroughly for your final exam. Determine the y-intercept of k if k( x) = 2 g( x) (2). The Answer Series **MATHS** study guides offer Write down the coordinates of the x - and a key to exam success. In particular, y-intercepts of h if h is the graph of g Gr 10 **MATHS** 3 in 1 provides superb foundation in the major topics in Senior **MATHS** . reflected about the y-axis. (2) [20]. Copyright The Answer Q2. Gr 10 **MATHS** National Exemplar **paper** 2. **QUESTION** 2 ANALYTICAL GEOMETRY [18]. NATIONAL EXEMPLAR **paper** 2. Traffic authorities are concerned that heavy vehicles Q.

6 (trucks) are often overloaded. In order to deal with this **QUESTION** 3. Clearly show ALL calculations, diagrams, graphs, etc. which problem, a number of weighbridges have been set up In the diagram below, D(- 3; 3), E(3; - 5) and 2. you have used in determining the answers. along the major routes in South Africa. The gross (total) F(- 1; k) are three points in the Cartesian plane. Answers only will NOT necessarily be vehicle mass is measured at these weigh bridges. awarded full marks. The histogram below shows the data collected at y You may use an approved scientific calculator a weighbridge over a month. (non-programmable and non-graphical), D(- 3; 3). Histogram showing Gross Vehicle Mass unless stated otherwise. 120. If necessary, round off answers to x TWO decimal places, unless stated otherwise. 110. 103. 99. 100. STATISTICS [15] 90 85 E(3; - 5). 80 77. **QUESTION** 1 70 F(-1; k). Frequency 70. A baker keeps a record of the number of scones that he 60.

7 Sells each day. The data for 19 days is shown below. 50. 31 36 62 74 65 63 60 34 46 56 40. Calculate the length of DE. (2). 37 46 40 52 48 39 43 31 66 30. 19. 20 Calculate the gradient of DE. (2). Determine the mean of the given data. (2) 10. Rearrange the data in ascending order and = 90 . Determine the value of k if DEF (4). 0. then determine the median. (2) 500 2500 4500 6500 8500 10500 12500 14500. Mass of Vehicles (in kg) If k = - 8, determine the coordinates of M, Determine the lower and upper quartiles for the data. (2) the midpoint of DF. (2). EXAM **PAPERS** : **paper** 2. Write down the modal class of the data. (1). Draw a box and whisker diagram to represent the data. (2) [8] Determine the coordinates of a point G. Estimate the mean gross vehicle mass for such that the quadrilateral DEFG is the month. (5) a rectangle. (4). We trust that working through these Which of the measures of central tendency, exam **PAPERS** and following our detailed the modal class or the estimated mean, will answers and comments will help you prepare C is the point (1; - 2).

8 The point D lies in the be most appropriate to describe the data set? thoroughly for your final exam. Explain your choice. (1) [7] second quadrant and has coordinates ( x ; 5). The Answer Series **MATHS** study guides offer a key to exam success. In particular, If the length of CD is 53 units, calculate Gr 10 **MATHS** 3 in 1 provides superb foundation the value of x. (4) [18]. in the major topics in Senior **MATHS** . Q3 Copyright The Answer Gr 10 **MATHS** National Exemplar **paper** 2. TRIGONOMETRY [36] **QUESTION** 5 **QUESTION** 6. Q. **QUESTION** 4 Solve for x, correct to ONE decimal place, Consider the function y = 2 tan x. 2 In the diagram below, ABC is right-angled at B. in each of the following equations where 0 x < 90 . Make a neat sketch of y = 2 tan x for 0 x 360 on the axes provided below. A 5 cos x = 3 (2) Clearly indicate on your sketch the intercepts with the axes and the asymptotes. tan 2 x = 1,19 (3). y 4 sec x - 3 = 5 (4). B C 6- An aeroplane at J is flying directly over a 5- Complete the following statements : point D on the ground at a height of 5 kilometres.

9 4- AB. It is heading to land at point K. The angle of sin C = (1) depression from J to K is 8 . S is a point .. 3- along the route from D to K. AB 2- .. A = (1). BC. J 1- Without using a calculator, determine the 8 . 0 x sin 60 . tan 30 90 180 270 360 . value of : (4) -1 - sec 45 . -2 - In the diagram, P(- 5; 12) is a point in the = . -3 - Cartesian plane and ROP. -4 - D S K. y -5 - P(- 5; 12) . Write down the size of JKD (1). EXAM **PAPERS** : **paper** 2. -6 - Calculate the distance DK, correct to (4). the nearest metre. (3). O x If the graph of y = 2 tan x is reflected R If the distance SK is 8 kilometres, about the x-axis, write down the calculate the distance DS. (1) equation of the new graph obtained by this reflection. (1). Calculate the angle of elevation Determine the value of : from point S to J, correct to ONE decimal place. (2) [16]. cos (3). 2. cosec + 1 (3) [12]. Copyright The Answer Q4. Gr 10 **MATHS** National Exemplar **paper** 2. The diagram below shows the graph of If the height of the walls of the tent is **QUESTION** 9.

10 G(x) = a sin x for 0 x 360 . 2,1 metres, calculate the total amount Q. of canvas required to make the tent if In the diagram, BCDE and AODE are parallelograms. y 2. 4- the floor is excluded. (2). A. 3- g A metal ball has a radius of 8 millimetres. 2- 1- Calculate the volume The volume of a sphere = 4 r 0 x of metal used to make 3. B E. 90 180 270 360 this ball, correct to 3. -1 - TWO decimal places. (2). -2 - F. -3 - If the radius of the ball is doubled, -4 - write down the ratio of O. Determine the value of a. (1) the new volume : the original volume. (2). If the graph of g is translated 2 units You would like this ball to be silver plated C D. upwards to obtain a new graph h, to a thickness of 1 millimetre. write down the range of h. (2) [8] What is the volume of silver required? Prove that OF || AB. (4). Give your answer correct to MEASUREMENT [12] TWO decimal places. (2) [12] Prove that ABOE is a parallelogram. (4). **QUESTION** 7 Prove that ABO EOD.