Perlis Trial 2025 Mathematics Kertas 1

Express 111010_2 as a number in base nine.

In a test, Aida obtained 112_8 and 1100_4 marks in Science and Mathematics subjects. Calculate the mean mark obtained by Aida, in base ten.

Table 1 shows the income and expenses for Mawar in August. | Pendapatan Aktif | RM5 000 | | Active income | | | Pendapatan Pasif | RM1 500 | | Passive income | | | Perbelanjaan Tetap | RM2 500 | | Fixed expenses | | | Perbelanjaan Tidak Tetap | RM500 | | Variable expenses | | In September, her monthly bank installment payment of RM500 has ended. However, Mawar's variable expenses increased by 20%. Calculate Mawar's cash flow for September.

Khalish owns an apartment in Pulau Pinang. The rent for the apartment is estimated at RM1 500 per month and he pays RM810 per year for the property assessment tax. Calculate the property assessment tax rate for the apartment.

Faizul bought a third-party motor insurance policy for his car. Which of the following situations is covered by the policy?

Diagram 2 shows the information of Zaimi's car that needs to be insured in Ipoh. Table 2 shows the rate charged for the first RM1 000 of the sum insured for comprehensive policy. | Jumlah yang ingin diinsuranskan | | Sum insured | RM90 000 | | Kapasiti enjin | | Engine capacity | 2400 cc | | NCD | 25% | | Kapasiti enjin (tidak melebihi cc) | Polisi komprehensif | | Engine capacity (not exceeding cc) | Comprehensive policy | | | (RM) | | 2 200 | 339.10 | | 3 050 | 372.60 | Calculate the gross premium of Zaimi's car under the comprehensive policy. The formulae to calculate the basic premium of the comprehensive policy for Peninsular Malaysia = Rate for the first RM1 000 + RM26 for each RM1 000 or part thereof on value exceeding the first RM1 000.

Diagram 3 shows a trapezium PQRS drawn on a Cartesian plane. PQ is parallel to SR and O is the origin. Find the x-intercept of the straight lines PQ.

Determine the coordinates of the minimum point from the graph of the quadratic function f(x) = x^2 - 4x + 3.

Which of the following shaded region satisfies the system of linear inequalities x \le 0, y \le 0 and x + y \ge -2?

Diagram 4 shows a distance-time graph for Azri's journey from his house to grocery store. Calculate the average speed, in m min⁻¹, for the whole journey of Azri.

Diagram 5 shows the speed-time graph Hazen's return journey in cycling training for a certain day. Calculate the average speed, in km h^-1, for the whole journey.

Given that w varies directly as the cube roots of x. Express w in terms of x.

Given that D varies inversely as E and E = 4F-3. Express D in term of F.

Table 3 shows the change of three quantities, R, S and T. Given R varies inversely with the square root of S and cube of T. | R | 5 | x | 6 | |---|---|---|---| | S | 9 | 36 | y | | T | 2 | 1 | 1 | Calculate the value of x and value of y.

Given \begin{pmatrix} x & 6 \\ 1 & -2 \end{pmatrix} + \begin{pmatrix} -6 & 7 \\ 3 & y-1 \end{pmatrix} = \begin{pmatrix} 3 & 13 \\ 4 & 4 \end{pmatrix} Find x and y.

Given that matrix A = \begin{pmatrix} 3 & 5 \\ x & 2+y \end{pmatrix} and matrix B = \begin{pmatrix} 3 & 5 \\ 9 & -2 \end{pmatrix}. Determine the values of x and of y if A = B.

Diagram 6 shows a regular pentagon DEFGH. Calculate the value of x.

Diagram 8 shows two trapeziums drawn on a Cartesian plane. Trapezium L' is the image of the trapezium L under an enlargement transformation. Which of the points, A, B, C and D, is the centre of the enlargement?

In Diagram 10, PQR is the image of STU under the combined transformation MN. Which of the following is correct? | | N | M | |---|---|---| | A | Rotation 90° clockwise at centre (3, -3) | Enlargement at centre (5, -2) with scale factor 2 | | B | Rotation 90° clockwise at centre (3, -3) | Enlargement at centre (2, 1) with scale factor \frac{1}{2} | | C | Rotation 90° anticlockwise at centre (3, -3) | Enlargement at centre (5, -2) with scale factor 2 | | D | Rotation 90° anticlockwise at centre (3, -3) | Enlargement at centre (2, 1) with scale factor \frac{1}{2} |

Diagram 11 shows a unit circle with centre O. Point P and point Q lie on the arc of the circle. Find the value of tan x + sin y.

Diagram 12 shows a graph that represents a trigonometric function. Which of the following trigonometric function that represent the graph?

Which of the following is a converse for implication "If 16 is a multiple of 8, then 16 is a multiple of 4"

Given: Universal set, ξ = J U K U L, Set J = {2, 3, 5, 7} Set K = {2, 3, 6, 10 } Set L = { 1, 3, 5, 7, 9 } List the elements of (J ∩ L)'.

Diagram 14 is a Venn diagram showing the universal set, \xi = {Form 5 students}, set G = {students who play guitar}, set H = {students who play piano}. Given n(\xi) = 38, n(G) = 18, n(H) = 10 and n(G \cap H) = 5, find the number of students who do not play both musical instruments.

Diagram 15 shows an undirected graph. Which of the following represents the correct set of edges and the sum of degrees? | | List of vertices | Sum of degrees | |:---|:---|:---| | A | {(P, Q), (P, S), (P, T), (Q, R), (Q, R), (Q, Q), (R, S), (S, T), (T, T) | 18 | | B | {(P, Q), (P, S), (P, T), (Q, R), (Q, Q), (R, S), (S, T), (T, T), (T, T) | 18 | | C | {(P, Q), (P, S), (P, T), (Q, R), (Q, R), (R, S), (S, T), (T, T) | 16 | | D | {(P, Q), (P, S), (Q, R), (Q, R), (Q, Q), (R, S), (S, T), (T, T) | 16 |

The mean pocket money of 6 students is RM6.40. Adam and Kamalia have joined this group. Adam's pocket money is RM7 and Kamalia's pocket money is RM5. Calculate the new mean of pocket money, in RM, of the students.

Diagram 16 is a set of data showing the masses of six students. Determine the median.

Diagram 17 shows a dot plot of STEM quiz scores of a group of 20 students. Determine the mode of the data.

The Mathematics scores of eight students of 3 Bestari Class students were recorded as 45, 59, 35, 80, 72, 54, 65 and 89. Determine the variance for the data.

Diagram 18 is a Venn diagram that shows the relationship between set E, F, G and H. It is given the universal set, \xi = E \cup F \cup G \cup H. Which of the following is a non-mutually exclusive event?

Diagram 19 shows an ogive of books read by 60 of students in June. Which of the following box plots represents the ogive?