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Melaka Trial 2024 Matematik Kertas 1

1
It is given that the height of a stack of paper is 510 mm and the thickness of a sheet of paper is approximately 1.0 x 10^-1 mm. Estimate the number of sheets of papers in the stack.
2
Simplify : \frac{(r^6s^3)^\frac{1}{3}}{r^4}
3
### Table 1 | j | p | q | |---|---|---| | m | r | 6 | Given that j varies inversely with m and the value of p x r is 24. Calculate the value of q.
4
The distance, d travelled by a bicycle varies directly with the square of the speed, v and inversely with the acceleration, a. Given that d = 1600 m, v = 40 ms^{-1} and a = 0.5 ms^{-2}. Calculate the value of a when d = 4500 m and v = 50 ms^{-1}.
5
Solve : 3x - 2 < -5 - \frac{3}{4}x
6
Given matrix K = \begin{pmatrix} 5 & 0 & 2 \\ 7 & 4 & -3 \end{pmatrix}, matrix L = \begin{pmatrix} 14 & -2 & 1 \\ 13 & 18 & 10 \end{pmatrix} and matrix M = \begin{pmatrix} 10 & -8 & 4 \\ 6 & -11 & 7 \end{pmatrix}. Calculate the value of 2K + L - M.
7
Given B = \begin{pmatrix} 5 & -2 \\ 1 & 6 \end{pmatrix} and BY = \begin{pmatrix} 11 \\ 15 \end{pmatrix}. Which of the following is true? | | Order of matrix Y | Element Y_11. | |---|---|---| | A | 2 x 1 | - 3 | | B | 2 x 2 | 2 | | C | 2 x 2 | - 2 | | D | 2 x 1 | 3 |
8
\begin{pmatrix} 5 & 1 \\ 3 & 4 \end{pmatrix} \begin{pmatrix} -2 \\ 4 \end{pmatrix} =
9
Diagram 1 shows an empty cylinder with the height is 90 cm and the diameter 28 cm. Raziq fills up the cylinder full with water. Calculate the volume of water, in cm^3, needed to fill up three cylinders of the same size. (Guna / Use \pi = \frac{22}{7})
10
In Diagram 2, QR is a flag pole. SPTQ is a straight line. If T is a midpoint of PQ, find cos x.
11
Diagram 3 shows the distance-time graph of a particle. The graph indicates that
12
A box contains 50 mangoes. 15 of them were found to be damaged. What percentage of mangoes are spoiled in the box.
13
Diagram 4 shows JLM is part of a regular polygon. KLM is a straight line. Find the number of sides of the polygon.
14
Find the root for the following quadratic equation 2x^2 – x = 6.
15
Diagram 5 shows the sofa set and dining table set purchased by Puan Intan. Given that the total price of the two sets is RM1 364. Calculate the value of W.
16
Diagram 6 shows three parallel lines, RS, TU and VW. KL and MN is a straight line. Calculate the value of x + y.
17
Diagram 7 shows the prices of two types of food at a restaurant. A customer pays RM30 for 3 sets of burgers and 4 sets of chicken rice. Express y in terms of x.
18
Given that universal set, \xi = {2, 3, 4, 5, 6, 7, 8, 9, 10, 11}, set P = {even numbers} and set Q = {prime numbers}. Which of the following Venn diagrams represents the relationship for the sets?
19
Diagram 8 shows a directed and weighted graph connecting 7 factories. Aizam drives a van to deliver goods from factory R to factory X. Determine the route of Aizam's van, if he wants to take the shortest route to reach factory X.
20
Diagram 9 shows object M is mapped onto position N under a translation. Determine the position of image H under the same translation.
21
In Diagram 10, MN is a straight line. Among points A, B, C and D, which is the object for image P' under a reflection on line MN?
22
The following shows part of an argument. | Premise 1 | : The sum of interior angles of a n-sided polygon is (n − 2) × 180°. | | Premise 2 | : W is a 7-sided polygon. | Determine the sum of interior angles of polygon W.
23
The interquartile range obtained from an ogive is 1.6. A student draws a box plot based on the ogive. Which of the following is the correct box plot drawn by the student?
24
Diagram 11 shows a circle centered at O. LMN is tangent to the circle. Given that \angle LKM = 20.3^{\circ} and KOL is a straight line. Find the value of x.
25
Diagram 12 shows a circle PQRST. Calculate the value of x + y.
26
### Table 2 | Age | Male (RM) Non-smoker | Male (RM) Smoker | Female (RM) Non-smoker | Female (RM) Smoker | |---|---|---|---|---| | 25 | 2.11 | 2.70 | 1.15 | 1.37 | | 26 | 2.12 | 2.70 | 1.16 | 1.37 | | 27 | 2.12 | 2.71 | 1.17 | 1.39 | | 28 | 2.13 | 2.73 | 1.19 | 1.42 | Based on the face value of RM150 000. Calculate the annual premium for a 26 years old woman who does smoke.
27
Encik Rashid has made a personal loan of RM50 000 from a bank. The bank has charged an interest rate of 5% per annum. Calculate the monthly installment if the loan period is 9 years.
28
Express \frac{2x+6}{y-3} \div \frac{2(x+3)^2}{y^2-9} as a single fraction in its simplest form.
29
Diagram 13 shows a sector OPRQ of a circle with centre O and OQS is a semicircle. Calculate the area of the shaded region.
30
Diagram 14 shows a kite. Find the value of x.
31
Diagram 15 shows a trigonometric function that represents the height of the bicycle pedal from the ground, H and with, t. What is the trigonometric function that represents the graph?
32
Given sin x = 0.7071 and 0° <= x <= 360°. Calculate the value of x.
33
### Table 3 | Score | 5 | 6 | 7 | 8 | 9 | 10 | |---|---|---|---|---|---|---| | Frequency | 7 | 11 | 5 | 9 | 10 | 8 | Find the median score.
34
A map is drawn to a scale of 1: 30 000. If the actual length of a river is 4.2 km, calculate the length of the river, in cm, on the map.
35
Determine the equation of a straight line parallel to the straight line 4x + 7y = 28 and passes through point (6, -1).
36
Diagram 16 shows two right-angled triangles SPQ and SQR. Calculate the length of PR.
37
Diagram 17 shows a box plot. State the value of third quartile.
38
Which of the following are passive income? - I Gaji / Salaries - II Dividen / Dividends - III Komisen / Commissions - IV Sewa yang diterima / Rental received - V Elaun / Allowances
39
Encik Mamat owns a piece of land of 0.3 km^2 which is three times the land area that's of Encik Harun. It is given that they have the same quit rent of RM0.25/m^2, calculate the difference of the quit rent paid by them.
40
Which of the range of values of the scale factor, k will produce a congruent of shape of the object and the image? - I k > 1 - II k = 1 - III 0 < k < 1 - IV -1 < k < 0 - V k = -1 - VI k < -1
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