Sec 3 WA3 A-Math Practice Paper

Secondary 3 WA3 Practice Paper Name : ________________________ Date :_________________________ ADDITIONAL MATHEMATICS Practice Paper 1 hour and 57 minutes READ THESE INSTRUCTIONS FIRST: Write your name and centre in the spaces at the top of this page. Write in dark blue or black pen. You may use a HB pencil for any diagrams or graphs. Do not use staples, paper clips, glue or correction fluid. Answer all the questions. Give non-exact numerical answers correct to 3 significant figures, or decimal place in the case of angles in degrees, unless a different level of accuracy is specified in the question. The use of an approved scientific calculator is expected, where appropriate. You are reminded of the need for clear presentation in your answers. The number of marks is given in brackets [ ] at the end of each question or part question. The total number of marks for this paper is 78. © Loh John Ray 4049/PRACTICE/WA3/24 [End of paper

© Loh John Ray 4049/PRACTICE/WA3/24 [End of paper

Points are awarded according to the question’s allocated mark boundary. Expect 1 mark per essential working. However, points are deducted when a question fails to be answered correctly and where mistakes lie. For examiner’s use : Question: 1 2 3 4 5 6 7 8 9 10 Total Points: 6 6 10 10 6 9 9 10 7 5 78 Score: Presentation points : Excellent -> 3, Great -> 2, Acceptable -> 1, Poor -> 0 Total Points Deductions Final score © Loh John Ray 4049/PRACTICE/WA3/24 [End of paper

1 Solve the simultaneous equations 𝑥2+𝑦2−4𝑥−6𝑦+9=0 10𝑦 2𝑥= 2𝑥+1(5𝑦) Ans: ____________________ [6] © Loh John Ray 4049/PRACTICE/WA3/24 [End of paper

2 (a) By using the substitution of (where find the exact real value of which 𝑦=𝑥 𝑦 ≥ 0), 𝑥 satisfies the equation 𝑥 +3𝑥=1 2 Ans: ____________________ [4] 2 (b) Hence using this value of , show that 𝑥 1 𝑥2+𝑦2−1=805+23711 Ans: ____________________ [3] © Loh John Ray 4049/PRACTICE/WA3/24 [End of paper

3 In wireless communications, the further a receiver is located from the source, the weaker its reception will become, and thus its lower Signal-to-Noise Ratio (SNR) calculated in units of decibel. In particular, suppose the receiver is located at a reference point metres away from the source and 𝑥0 measures an SNR of . As the receiver’s distance from the source increases to metres, its SNR 𝑆𝑁𝑅0 𝑥 will drop to using the formula 𝑆𝑁𝑅𝑥, 𝑆𝑁𝑅𝑥= 𝑆𝑁𝑅0−10lg(𝑥 𝑥0 )2 where and are obtained via measurements, and are the reference values. 𝑥 𝑆𝑁𝑅𝑥 𝑥0 𝑆𝑁𝑅0 (a) Show that whenever the receiver doubles its distance from the source, the SNR will decrease by about decibels. 6 Ans: ____________________ [3] © Loh John Ray 4049/PRACTICE/WA3/24 [End of paper

(b) A receiver is set at a distance of metres away from the source, and measures an SNR of 20 decibels. If a minimum SNR of decibels is required or reasonable reception quality, how close −5 15 must the receiver move towards the source? Ans: ____________________ [2] (c) Find the exact value of such that 𝑥 log9(4𝑥2+3𝑥+5)−log3(𝑥+1) =1 2 Ans: ____________________ [5] © Loh John Ray 4049/PRACTICE/WA3/24 [End of paper

4 (a) Find the value of given that 𝑛 (3 𝑥−𝑥)5−(8−𝑥3)𝑛= . . . +207𝑥+ . . . Ans: ____________________ [4] © Loh John Ray 4049/PRACTICE/WA3/24 [End of paper

4 (b) Given that the coefficient of is in the expansion of . 𝑥2−120 (3−𝑥)2(2+𝑎𝑥 3)8 Find the possible value(s) of . 𝑎 Ans: ____________________ [6] © Loh John Ray 4049/PRACTICE/WA3/24 [End of paper

5 Express the following as partial fractions 2𝑥2−18𝑥+44−6𝑥3 (𝑥2+4)(2−3𝑥) Ans: ____________________ [6] © Loh John Ray 4049/PRACTICE/WA3/24 [End of paper