SULIT 3472 SMKA TUN AHMAD ZAIDI MID YEAR TEST FORM FOUR 2021 ADDITIONAL MATHEMATICS DO NOT OPEN THE QUESTION PAPER UNTIL BEING NOTIFIED Disediakan oleh, NUR SYAFIQAH BINTI OTHMAN Guru Matematik Tambahan SMKA Tun Ahmad Zaidi Disahkan oleh, SALMIAH BINTI SAMSUDIN Ketua Panitia Mate. Tambahan SMKA Tun Ahmad Zaidi Kertas soalan ini mengandungi 19 halaman bercetak Name : ………………..……………….. Class: ………………………..………… 3472 Add Math July 2021 For examiner’s use only Question Total Marks Marks Obtained PAPER 1 1 4 2 6 3 5 4 7 5 5 6 5 7 5 8 5 9 5 10 6 11 5 12 6 PAPER 2 1 7 2 5 3 5 4 7 5 5 6 6 7 5 Total 104 1. This question paper consists of 19 questions. 2. Answer all questions. 3. Give only one answer for each question. 4. Write the answers clearly in the space provided in the question paper for Paper 1 and answer in paper sheet for Paper 2. 5. Show your working. It may help you to get marks. 6. If you wish to change your answer, cross out the work that you have done. Then write down the new answer. 7. The diagram in the questions provided are not drawn to scale unless stated. 8. The marks allocated for each question and sub-part of a question are shown in brackets. 9. You may use a non-programmable scientific calculator. 10. This question paper must be handed in at the end of the examination.
SULIT 3472 The following formulae may be useful in answering the questions. The symbols given are the ones commonly used.
SULIT 3472 PAPER 1 Section A Answer all questions. [64 marks] 1. Diagram 1 shows the relation between set P and set Q. Diagram 1 (a) Based on Diagram 1, State (i) State the type of relation between set P and set Q, (ii) the range of the relation. [2 marks] (b) Given the relation between set R and set S is ‘square root of’ where set R= {1, 4, 9, 16} and set S= {1, 2, 3, 4, 5, 6}. (i) Find the image of 4, (ii) Express the relation in the form of ordered pairs. [2 marks] Answer: (a) (i) (ii) (b) (i) (ii) 2. Two function f and g are defined by ∶ → 4 − 17 and ∶ → 5 2−7 , ≠ 3 1 2 . Solve the equation −1 () = −1 (). [6 marks] Answer:
SULIT 3472 3. (a) Given that function : ↦ + 1 and : ⟼ 2 + 3 + 5, find (). [3 marks] (b) The inverse function is defined by ℎ −1 : ⟼ 2 3− , ≠ 3. Find ℎ(). [2 marks] Answer: (a) (b)
SULIT 3472 4. (a) The following information refers to the function ℎ and ℎ −1 . Find the value of and . [3 marks] (b) Given that function ∶ → 5 + 4 and ∶ → 2 + 3. Find (i) −1 () (ii) −1 (3) [4 marks] Answer: (a) (b) (i) (ii) ℎ ∶ → 2 + ℎ −1 ∶ → 3 + 3 2 Where and are constants.
SULIT 3472 5. (a) Given −3 is one of the roots of the quadratic equation ( − ) 2 = 25, where is a constant. Find the value of . [2 marks] (b) Given α and β are the roots of the quadratic equation 2 2 + 5 − 11 = 0. Form a quaratic equation with roots 1 and 1 . [3 marks] Answer: (a) (b)
SULIT 3472 6. It is given that and − 1 are the roots to the quadratic equation 4 2 − 16 + 7 = 0, where > − 1. (a) Find the value of and . [3 marks] (b) Using the value of and from (a), form the quadratic equation which has roots 2 and 2. [2 marks] Answer: (a) (b)
SULIT 3472 7. Find the values or range of values of k, if the quadratic function (a) () = 2 − 4 + − 3 has only one intercept. [3 marks] (b) () = 3 2 − 4 − 2(2 + 4) intersects the x-axis at two different points. [2 marks] Answer: (a) (b)
SULIT 3472 8. The quadratic function is defined by () = 2 + 6 + , where n is constant. (a) Express () in the form ( − ℎ) 2 + , where ℎ and are constant. [3 marks] (b) Given the minimum value of () is −5, find the value of . [2 marks] Answer: (a) (b)
SULIT 3472 9. Diagram 2 (a) Diagram 2 shows the graph of the function = −( − ) + , where and are constants. The curve intersects the -axis at the points (−1, 0) and (5, 0). Find the value of (i) p, (ii) q, (iii) maximum point. [3 marks] (b) Hence, express the function in general form () = ( − )( − ) [2 marks] Answer: (a) (i) (ii) (iii) (b)
SULIT 3472 10. Solve the following equations. (a) 27 = 9 2− [3 marks] (b) log3 = 3 log3 2 + log3 5 [3 marks] Answer: (a) (b) 11. Based on the following questions. (a) Given 3 + 2(3 ) = 3 , express in terms of . [2 marks] (b) Solve the equation 16(2 3−2 ) = 1 [3 marks] Answer: (a) (b)
SULIT 3472 12. (a) Express 2log3 2 − 3 log3 + 1 2 log3 4 as a single logarithm in its simplest form. [3 marks] (b) Solve the equation log2 ( − 4) + 2 = log2 2. [3 marks] Answer: (a) (b)
SULIT 3472 PAPER 2 Section A Answer all questions. [40 marks] 1. Diagram 1 Diagram 1 shows the function maps set A to set B and the function maps set B to set C. Find (a) in terms of , the function (i) that maps set B to set A, (ii) (). [5 marks] (b) the value of such that () = 4 − 3. [2 marks] Answer: (a) (i) (ii) (b) 3 − 2 6 + 1 A B C
SULIT 3472 2. Diagram 2 Diagram 2 shows a right-angles triangle. Based on the information given in the diagram, (a) form a quadratic equation. [3 marks] (b) find the value of x by solving the quadratic equation. [2 marks] Answer: (a) (b) ( + 1) cm (2 + 1) cm 2 cm
SULIT 3472 3. A tunnel at a certain part of a highway is in the shape of parabola. The height in metres, of the curve of the parabola is given by the function ℎ() = 15 − 0.06 2 , where is the width of the tunnel, in metres. (a) Determine the maximum height, in metres, of tunnel. [2 marks] (b) Find the width, in metres, of the tunnel. [3 marks] Answer: (a) (b)
SULIT 3472 4. Solve the following simultaneous equations. 5 − 2 − 4 = 3 3 + 3 + 2 = −3 −2 + 5 + 3 = 3 [7 marks] Answer:
SULIT 3472 5. There were 360 coupons sold during a school carnival. The coupon prices were RM8, RM10 and RM12 and the total income from the coupon sale was RM 3 500. The combined number of RM8 coupons and RM10 coupons sold was five times the number of RM12 coupons sold. Find the number of coupons of each type sold. [5 marks] Answer:
SULIT 3472 6. Diagram 3 Diagram 3 shows a right-angled triangle PQR. (a) Determine the value of tan . Write your answer in the form of +√2 , where , and are integers. [3 marks] (b) Determine the area of triangle , write your answer in the form of +√2 , where , and are integers. [3 marks] Answer: (a) (b)
SULIT 3472 7. Two experiments were carried out to find the relationship between the variables and . Both experiments showed that the relationship between and is in accordance to 3(9 ) = 27 and log2 = 2 + log2 ( − 2). Find the value of and that satisfy both experiments. [5 marks] Answer: END OF THE QUESTION PAPER