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Others Trial 2024 Mathematics Kertas 1 · Set 1

1
Round off 0.04547 to three significant figures and then, add to 0.00732.
2
Simplify \frac{6^{-1}m^{2}}{(36m)^{\frac{3}{2}}} \times (6m^{\frac{1}{2}})^{3}
3
Given that 110010₂ - x₂ = 101₂, find the value x.
4
When one side of a square is doubled and the other side is reduced by 2 units, the area of the resulting rectangle is 126 unit². Find the area in unit², of the square.
5
A set of 12 positive numbers has a variance of 46 and the sum of squares of the positive numbers is 2280. Find the mean of the set numbers.
6
Triangle JKL and triangle XYZ are congruent such that JK = XY, JL = XZ and ∠J = ∠X. Which of the following properties proves the congruency of both triangle?
7
A box contains 5 rambutans and 15 mangosteens. Raykal puts another 3 rambutans and 2 papayas into the box. A fruit is drawn randomly from the box. What is probability that a rambutan is drawn?
8
Find the duration given for a personal loan of RM 23000 at a rate of 5.5% per year for an equal interest if the total interest to be paid is RM 17710.
9
The Diagram 1 shows two straight lines, PQ and RS. Given that the gradient of line PQ is -\frac{5}{3}. Find the coordinates of point K.
10
Which of the following is not the criteria in creating a financial plan?
11
Diagram 2 shows triangle PRS is the image of triangle PQT under an enlargement at the centre of enlargement P. Q and T are midpoints of PR and PS respectively. Given that the base length of the triangle is twice the height of the triangle and the area of the shaded region is 27 cm², find the length in cm of TS.
12
In the Diagram 3, JK = \frac{1}{3} JL and JM = \frac{1}{3} JN. Find the values of sin x° and sin y°.
13
Given that a set of 50 data has Σfx² = 110500 and the mean 25. Calculate standard deviation for the set of data.
14
In Diagram 4, MNPQRSTU is a regular octagon and TUVW is a straight line. Find the value of x.
15
Table 1 shows the spending money of a group of students in a day. | Spending money (RM) | Number of students | |---|---| | 1 – 5 | 5 | | 6 – 10 | 7 | | 11 – 15 | 18 | | 16 – 20 | 6 | Determine the cumulative frequency at class interval 11 – 15.
16
It is given matrix P = \begin{bmatrix} 6 & -3 \\ k & 2 \end{bmatrix}. Calculate the value of k if matrix P does not have inverse matrix.
17
Mr Alex wants to buy a fire insurance for his house. The insurable value of the house is RM 420000. The fire insurance policy has a co-insurance provision to insure 80% of its insurable value and a deductible of RM 2500. His house caught fire and suffered a loss of RM 14000. If Mr Alex insures his house for RM 280000, calculate the compensation paid by the insurance company.
18
Diagram 5 shows tangent PM touches the circle with centre O at N. KLM is a straight line. Calculate the value of x + y.
19
The box plot in Diagram 6 represents a set of data. Given the range and interquartile range are 150 and 80 respectively. Find the value of p.
20
Which of the following is a short-term financial goal?
21
The speed-time graph in Diagram 7 shows the motion of an object for a period of 15 seconds. Which of the following statements correctly describes the motion of the object from 5th second to the 10th second?
22
Diagram 8 shows a graph. Which vertex has the highest number of degrees?
23
The period of a graph of tangent function is 60º. Which of the following is the possible equation of the graph?
24
Three workers have woven 50 pieces of silk cloth. The time required to complete the weaving is 3 hours 30 minutes. Given the time, t, varies inversely as the number of workers, y. Calculate the time, in minutes, required if seven workers weave 50 silk fabrics.
25
Faroq wants to buy x notebook and y pen. The price of a notebook is RM 3.40 and a pen is RM 1.20. Faroq's father gave him RM 30 to buy the items. Determine the linear inequality that satisfies the situation.
26
Which of the following statements is false?
27
Simplify: \frac{m^2n^{-3}}{(mn^3)^{-2}}
28
A map of Kedah state is drawn with a scale of 1 : 20 000. Calculate the actual distance of Sungai Petani if it is 23 cm long on the map.
29
Mrs Marhanis saves RM 19000 in Bank Jaya at an interest rate of 3% per annum and the interest is compounded every 2 months. Calculate the matured value at the end of the second year.
30
The height of 10 students who participated in a hill climbing activity has a mean of 161 cm and the standard deviation is 3. Find the sum of the squares of the height of the group of students.
31
Given a graph has the set of edges E = {(K,K), (K,L), (K, N), (L, N), (L,M), (M,N)}. Determine the number of degrees for vertices K, L and M.
32
Given that sin x = -sin 50° such that 0° <= x <= 360°. Determine the value of x.
33
Which of the following statements represents a point that is always equidistant from another point?
34
Diagram 9 shows the graph of a quadratic function f(x) = px² + qx + r. Find the range of value of p.
35
Diagram 10 shows two pentagons drawn on a Cartesian plane. Pentagon M' is the image of pentagon M under a rotation. Find the centre of the rotation.
36
Find the intersection point of the straight line 2x - 3y = 11 and 3x = 13 + y.
37
The following shows a number sequence. 0.25, 0.1111, 0.0625, ... Make a conclusion by induction for the number sequence.
38
Hazmeer bought a car worth RM 60000 on credit. He has paid RM 6000 as down payment and the monthly instalment for his loan is RM 630. If the interest rate charged by the bank is 4% per annum, how many years needed by Hazmeer to make the repayment to the bank?
39
Diagram 12 shows the histogram of a set of data. What is the distribution shape of data shown by the histogram?
40
Diagram 13 shows a water container X in the shape of a right prism. Its uniform cross section is a trapezium. Karim has a container Y in the shape of a right pyramid filled up with water. The height of the container Y is 20 cm and its base is a square with sides of 15 cm. Karim pours all the water from container Y into container X. Calculate the height, in cm, of the water level in the container X.
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