๐๐๐ Trinity House Glenvista Grade 10 Mathematics revision Assignment Date: 6 August 2021 Examiner: Dr. N A Bhebhe Moderators: Ms. M Rabothata Mr. Deepchund Name………………………………… Teacher………………………. Class………… PLEASE READ THE FOLLOWING INSTRUCTIONS CAREFULLY 1. This assignment consists of 20 pages and additional graph paper. Please check that your question paper is complete. 2. Read the questions carefully. 3. Answer all the questions. 4. You may use an approved non-programmable and non-graphical calculator unless otherwise stated. 5. Clearly show ALL calculations, diagrams, graphs, etc. that you have used in determining your answers. 6. Answers only will NOT necessarily be awarded full marks. 7. Diagrams are not necessarily drawn to scale. 8. If necessary, round off answers to ONE decimal place, unless otherwise stated. 9. It is in your own interest to write legibly and to present your work neatly. 10. Blank pages are included at the end of the paper. If you run out of space for a question, use these pages. Clearly indicate the question number of your answer should you use this extra space. FOR OFFICE USE ONLY: MARKER TO ENTER MARKS Q1 Q2 Q3 Q4 Q5 Q6 Q7 TOTAL 19 14 24 26 23 16 28 150 1 SECTION A QUESTION 1 Find the product and simplify the following: (a) (๐ฅ + 2)(๐ฅ 2 − ๐ฅ + 3) (b) 5 3 − ๐ฅ+3 2−๐ฅ (2) (3) (c) 2๐ฅ+1 + 2๐ฅ Recall that: 7๐+๐ = 7๐ . 7๐ (2) 2 (d) 3๐ก −3๐ก−2 (3) 2.3๐ก −3๐ก (e) (2) 102๐ฅ+3 .41−๐ฅ (4) 252+๐ฅ (c) 3 (3) 2 21 + ๐+3 − ๐2 −๐−12 ๐−4 (5) (2) [8] [19] 3 QUESTION 2 Factorise the following expressions fully: (a) 5๐ฅ 2 − 125 (b) −7๐ฅ 3 − 42๐ฅ 2 − 63๐ฅ 7๐ฅ (2) (3) (c) 3๐ฅ 2 + 3๐๐ฅ − 2๐๐ฅ − 2๐๐ (3) 4 (d) 3๐ฅ 2 + 9๐ฅ ๐ฅ 4 − 81 (−6๐ฅ 4 − 54๐ฅ 2 ) × 2 ÷ ๐ฅ−3 ๐ฅ + 6๐ฅ + 9 2 (6) [14] QUESTION 3 Solve for x in the following: (a) 1 5๐ฅ = 125 (b) (2) ๐๐ฅ + ๐๐ฅ = ๐ (2) 5 (c) 15๐ฅ 2 − 8 = 14๐ฅ (3) (d) 3๐ฅ + 2 1 + = −5 3 ๐ฅ (5) (f) ๐ฅ 2 −(๐ฅ + 2) + = ๐ฅ 2 − 1 1 − ๐ฅ (๐ฅ − 1)(๐ฅ + 1) 6 (6) (g) Solve the inequality, then draw a number line and write your answer in interval notation. ๐ฅ 2 − 2๐ฅ − 3 ≤ 0. (4) (h) Solve the simultaneous equation: 4๐ฅ 2 − ๐ฆ 2 = 171 ๐๐๐ 2๐ฅ − ๐ฆ = 9 (4) (6) [26] QUESTION 4 Given the following Linear pattern: 8; 3; -2;… (a) Write down the next two terms (T4 and T5) (2) (b) Determine the nth term (general formula) (2) 7 (c) Calculate T32, the thirty second term of the pattern (2) (d) Is -490 a term in the pattern? (3) Given the Quadratic Sequence (Pattern), 0; 5; 12;… , has a general formula (term): ๐๐ = ๐2 + 2๐ + ๐ (e) Show that ๐ = −3 (2) (f) Calculate the 10th term (T10) (2) [13] 8 SECTION B QUESTION 5 ΔQPR and ΔSQR are Right-angled triangles, as shown in the diagram below: ๐๐ = 26, ๐๐ = 24, ๐๐ = 8, ๐๐ = 6, ๐๐ = 10 ๐๐๐ ๐๐ ฬ๐ = ๐ Refer to the diagram and, answer without using a calculator; write down the value of: (a) tan ๐ฬ (1) (b) sin(๐๐ฬ๐ ) (1) 9 (c) cos ๐ (1) (d) sec ๐๐ ฬ๐ (1) (e) Determine the value of cot ๐ csc ๐๐ ฬ ๐ (3) Given 17 cos ๐ฝ + 15 = 0 , 0ห < ๐ฝ < 270ห (f) Draw a sketch of the equation (2) 10 (g) What are your values for the opposite, adjacent and hypotenuse? (3) Without the use of a calculator and using the previous questions (f) and (g) determine: (h) sec ๐ฝ (i) (cos 30)2 . tan ๐ฝ (1) (2) Without the use of a calculator, simplify the following: (j) (k) sin(30) (4) cos(45).cot2 (60) tan2 60 + 4 cos 60 (4) 11 [23] QUESTION 6 The graph of ๐(๐ฅ) = ๐ sin ๐, for ๐ฅ ∈ [0ห, 360ห] and the graph ๐(๐ฅ) = cos ๐ฅ + 1, ๐๐ ๐๐๐ฃ๐๐ below: (a) (b) Sketch the graph of g(x) on the same axis as f(x). What is the value of a in f(x)? (2) (1) (c) The period of f(x) (1) (d) The range of g(x) (1) 12 (e) For which values of x for ๐ฅ ∈ [0ห, 360ห], will ๐(๐ฅ). ๐(๐ฅ) > 0 (2) (f) Find p(x), if ๐(๐ฅ) = −๐(๐ฅ) + 2 (2) (g) Draw the function h(๐ฅ)= tan ๐ฅ for ๐ฅ ∈ [ 0°, 360°] and ๐ฆ ∈ โ. Clearly show all intercepts with the axes and the coordinates of any turning points (3) What are the asymptotes of h(x)? 13 (2) (h) Write down the equation of s(x), if ๐ (๐ฅ) = 2โ(๐ฅ) (2) [16] QUESTION 7 (a) ๐ The sketch below shows the graphs of๐(๐ฅ) = − 1 and ๐ฅ ๐(๐ฅ) = −๐ฅ − 1 The graphs of f and g intersect at P and Q. (1) What are the asymptotes of f ? and indicate them on the graph. (3) (2) The point (-4;0) lies on f. Calculate the value of k. (2) 14 (3) Calculate the coordinates of P and Q. (4) (b) The function ๐ก(๐ฅ) = ๐ ๐ฅ + ๐ is described by the following properties: • 0<๐<1 • X-intercept at (-2,0) • The horizontal asymptote is ๐ฆ = −4 (1)What is the range of t? (1) (1) Determine the equation of t (3) (c) Sketch the graph t(x) on the axis below, with ๐ง(๐ฅ) = ๐๐ฅ 2 + ๐ 15 Show all asymptotes and intercepts with the x-axis clearly. (3) (1) Calculate the coordinates of A (2) (2) Calculate the values of a and q in z(x) (4) (3) The intercepts of t(x) and z(x) (4) 16 (4) For which values of ๐ฅ ๐๐ ๐(๐ฅ) > 0 ? (1) (5) For which values of ๐ฅ, ๐๐ ๐ ๐๐๐๐๐๐๐ ๐๐๐ ? (1) [28] 17 EXTRA WORKING SPACE 18 19 20