Additional Mathematics Paper1 (if found any mistakes from it, please let me know so that I can update it)
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1. The question paper contains 25 questions.Kertas soalan ini mengandungi 25 soalan.
2. Answer all questions. Jawab semua soalan
3. Write your answers in the space provided Jawapan anda hendaklah ditulis dalam ruangan yang disediakan
4. Show your working. It may help you to get marks. f Tunjukkan langkah-langkah kira anda. Ini boleh membantu anda untuk mendapat markah
5. The diagrams in the questions are provided are not drawn to scale unless stated. Rajah yang mengiringi soalan tidak lukis mengikut skala kecuali dinyatakan.
6. The marks are allocated for each question and sub-part of a questions are shown in brackets. Markah yang diperuntukkan bagi setiap soalan dan ceraian soalan ditunjukkan dalam kurungan.
7. The Uppper Tail Probability Q(z) for the Normal Distribution N(1, 0) Table is provided in page 26. Jadual Kebarangkalian Hujung Atas Q(z) bagi Taburan Normal N(1, 0) disediakan di mukasurat 26.
8. A list of formulae is provided on pages 3 to 5 and graph paper is provided Satu senarai rumus disediakan di halaman 3 ke 5 dan kertas graf juga disediakan
9. You may use a scientific calculator. Anda dibenarkan menggunakan kalkulator saintifik
The following information refers to set P and set Q. Maklumat berikut adalah berkaitan dengan set P dan set Q
The relation between set P and set Q is defined by the set of ordered pairs {(−1, 1), (−3, 9), (1, 1), (2, 4), (4, 16)}. Hubungan antara set P dan set Q ditakrifkan oleh set pasangan bertertib {(−1, 1), (−3, 9), (1, 1), (2, 4), (4, 16)}.
(a) State the codomain of the relation. Nyatakan kodomain bagi hubungan ini.
(b) Using function notation, write the relation between set P and set Q. Dengan menggunkan tatatanda fungsi, tulis satu hubungan antara set P dan set Q.
3. A quadratic equation 3x2 + k = 3(2x – 1) where x ∉ ℝ. Find the range of values of k.Satu persamaan kuadratik 3x2 + p = 3(2x – 1) dimana x ∉ ℝ. Cari julat bagi nilai k.
4. Diagram 1 shows the graph of quadratic function f(x) = −a(x – p)2 + qwith the maximum point at B. The straight line AC is parallel to x axis. Rajah 1 menunjukkan graf bagi suatu fungsi kuadratik f(x) = −a(x – p)2 + qdengan titik maksimum B. Garis lurus AC selari dengan paksi-x.
(a) Find the value of k. Cari nilai k.
(b) Find the equation of the curve in the form of y = ax2 + bx + c.
Cari persamaan bagi lengkung itu dalam bentuk y = ax2 + bx + c.[3 marks]
8. Eric deposits RM 10000 at the start of every year into his bank account. The interest paid by the bank is 3%. Any interest she received is kept in the bank. Find the sum of his savings in the bank at the end of the 10th year (including interest received in the 10th year).Eric deposit RM 10000 pada permulaan setiap tahun ke dalam akaun banknya. Faedah yang dibayar oleh bank adalah 3%. Apa-apa kepentingan beliau menerima disimpan di bank. Cari jumlah simpanan di bank pada akhir tahun ke-10(termasuk faedah yang diterima dalam tahun ke-10).
Diagram 2 shows of a implicit curve x2y = px, where p is a constant. When the graph is reduced to linear form, the straight line graph is obtained as in
Diagram 3. Express y in terms of x
1. Hence, find the values of p, r and t.
Rajah 2 menunjukkan keluk tersirat x2y = px, dimana p adalah pemalar. Apabila graf dikurangkan kepada bentuk linear, graf garis lurus diperoleh seperti dalam Rajah 3. Ekspres y dalam sebutan. Oleh itu, cari nilai-nilai bagi p, r dan t.
11. The straight lines l1, l2 and l3 are defined byGaris lurus l1, l2 dan l3 ditakrifkan sebagai
l1: mx + ny = 1; l2: my = 2x + 3; l3: nx – 4y + 5 = 0
It is given that the straight line l1 is perpendicular to the straight line l2. The straight line l1 is parallel to the straight line l3. Find the value of m and n.Diberi bahawa garis lurus l1 berserenjang dengan garis lurus l2. Garis lurus l1 adalah selari dengan garis lurus l3. Cari nilai m dan n.
15. Given that the series cot x, sec x, tan x, … is an arithmetic progression. Show this series give the equation: cos x(2sin x – sin2 x – 1) = 0. Solve the equation for 0° < x < 360°.Diberi siri kot x, sec x, x tan x, ... adalah suatu janjang aritmetik. Tunjukkan bahawa siri ini memberikan persamaan: kos x(2sin x – sin2 x – 1) = 0. Selesaikan persamaan itu untuk 0° < x < 360°.
16. Diagram 5 shows a wall painted by Eric.Rajah 5 menunjukkan dinding yang dicat oleh Eric.
The line AD and BD has the mid-points at E and G whereas ΔABP is a equilateral. Find the area of shaded region.Garis AD dan BD mempunyai titik tengah di E dan G manakala ΔABP mempunyai sisi yang sama. Cari luas rantau berlorek.
17. A right circular cone of height (a + x), where –a < x < a, is inscribed in a sphere a fixed radius a, so that the vertex and all points of the circumference of the base are on the surface of the sphere. Show that the
volume of the cone is given by .))((3
1 2xaxaV Find the maximum
volume of V as x varies.Satu kon tegak ketinggian (a + x), dimana −a < x < a, adalah tertulis dalam sfera berjejari tetap a, supaya bucu dan semua titik lilitan asas yang berada di permukaan sfera. Tunjukkan bahawa jumlah kon diberikan
19. All letters from the cards below are to be arranged. Calculate ifSemua huruf daripada kad bawah hendak disusunkan. Hitungkan jika
(a) begin with the letter “C”. bermula dengan huruf “C”.
(b) begin and end with consonant. bermula dan berakhir dengan konsonan .
[3 marks][3 markah]
Answer/Jawapan:(a)
(b)
20. 3 digits numbers are to be formed from 7, 8, 9, 10 and 11 without repetition. Given that event A = {3 digit even numbers} and event B = {3 digit odd numbers}. Find 3 digit nombor akan untuk dibentuk daripada 7, 8, 9, 10 dan 11 tanpa pengulangan. Memandangkan peristiwa A = {3 digit nombor genap} dan acara B = {nombor 3 digit ganjil}. Cari
23. A set of positive integers consists of 3, 5, p. The standard deviation for
the set is 3
8.
Satu set integer positif terdiri daripada 3, 5, p. Sisihan piawai bagi set
ialah 3
8.
[4 marks][4 markah]
Answer/Jawapan:
24. Given that 8, 7, a, 7, b, 10, 11 has mean of 7, express b in terms of a.Diberi bahawa 8, 7, a, 7, b, 10, 11 mempunyai min 7, ungkapkan b dalam sebutan a.
Diagram 7 shows the graph of binomial distribution for discrete variable X. Find the probability Rajah 7 menunjukkan graf taburan binomial untuk ubah diskret X. Cari kebarangkalian