Form 4 Mathematics Bab 6: Linear Inequalities in Two Variables
Instructions
Answer all questions clearly. Show substitution steps, state exact inequalities, and clearly define boundary conditions.
10 questions · 24 marks total
1. A school sports day committee sells T-shirts (x) and caps (y) to raise funds. The conditions for the sale are as follows: I. The total number of items sold is at least 50. II. The number of T-shirts sold is at most twice the number of caps sold. III. The maximum budget allocated is RM 600, where a T-shirt costs RM 12 and a cap costs RM 6. Write down the system of three linear inequalities representing all the conditions above.
Short Answer · 3m2. Given the boundary line equation 2y = -3x + 12: (a) Find the x-intercept and y-intercept of the boundary line. (b) State the linear inequality if the shaded region lies strictly above this boundary line.
Short Answer · 3m3. State the three linear inequalities that define the shaded triangular region bounded by the y-axis (x = 0), the horizontal line y = 2, and the line x + y = 6 in the first quadrant.
Short Answer · 3m4. A factory produces two types of chairs, standard (x) and deluxe (y). The production is subject to the following constraints: - Machine process time: Each standard chair takes 1 hour and each deluxe chair takes 2 hours. Total available machine time is 40 hours per week. - Assembly time: Each standard chair takes 2 hours and each deluxe chair takes 1 hour. Total available assembly time is 50 hours per week. - Non-zero constraint: Production counts cannot be negative. (a) Write a system of linear inequalities for the constraints. (b) Determine whether producing 15 standard chairs and 10 deluxe chairs per week satisfies all constraints.
Short Answer · 5m5. Fill in the blank: In graphing linear inequalities, a ________ line is used when the inequality symbol contains '<' or '>'.
Fill in the Blank · 1m6. Write a linear inequality for each of the following real-world situations: (a) A delivery truck carries x small packages and y large packages. The maximum payload count is 120 packages. (b) The price of a shirt is RM x and a pair of trousers is RM y. Encik Ahmad spends at least RM 250 buying 3 shirts and 2 pairs of trousers.
Short Answer · 4m7. Which of the following phrases represents the inequality symbol '≥'?
Multiple Choice · 1m8. True or False: The inequality 5x - y² ≤ 10 is a linear inequality in two variables.
True / False · 1m9. True or False: The point (3, 2) is part of the solution region for the inequality 2x - y > 4.
True / False · 1m10. Determine whether the point (-1, 4) satisfies the linear inequality 3x + 2y ≥ 5. Show your calculations.
Short Answer · 2m