Use symbols to test the validity of the argument “If I like logic, I will study arguments. I will study arguments if and only if I have a logical mind. I do not like logic; Therefore, I will not study arguments.”

1. Represent the statements symbolically. (0 mk)
2. Use symbols to test the validity of the argument “If I like logic, I will study arguments. I will study arguments if and only if I have a logical mind. I do not like logic; Therefore, I will not study arguments.” (0 mk)
3. Construct a truth table to test the validity of the argument. (0 mk)
4. State whether the argument is valid or invalid and justify your conclusion. (0 mk)

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List the procedures for computing the determinant of a matrix using a non-programmable calculator.

1. Describe the step-by-step process. (0 mk)

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State five specific objectives for the sub-topic “Elimination Method” in teaching simultaneous equations.

1. List five learning objectives for students. (0 mk)

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Calculate the volume of a frustum given that the full cone has a radius of 18 cm and height 20 cm, while the upper radius of the frustum is 12 cm.

1. Calculate the volume. (0 mk)

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Use the standard results for $\int \sin^2 x dx$ and $\int \cos^2 x dx$ to show that; $\int \cos(2x) dx = \frac{1}{2} \sin(2x) + C$ and then evaluate $\int_0^{\pi/4} \cos(2x) dx$

1. Use the standard results for $\int\cos^2 x dx$ and $\int\sin^2 x dx$ to show that; $$\int (a\cos^2 x + b\sin^2 x) dx = \frac{a+b}{2}x + \frac{a-b}{2}\sin(2x) + C$$ and then evaluate $\int_0^{\pi/2} (3\cos^2 x + 2\sin^2 x) dx$. (0 mk)
2. Show that $\int \cos(2x) dx = \frac{1}{2} \sin(2x) + C$. (0 mk)
3. Evaluate $\int_0^{\pi/4} \cos(2x) dx$. (0 mk)

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Differentiate between assessment and evaluation.

1. Provide a clear distinction between the two terms. (0 mk)

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Given vectors A = i – 2j + nk and B = 2i + j – 4k, find the value of n if the area of the parallelogram formed by A and B is 5√6.

1. Calculate the value of n. (0 mk)

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Given the motion equation x = 4t + ln(1–t): (a) Find the velocity and acceleration at t = 1.5 seconds. (b) Determine the time when the body is at rest.

1. Find the velocity and acceleration at t = 1.5 seconds. (0 mk)
2. Determine the time when the body is at rest. (0 mk)

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You are given the graphical representation of a certain linear programming problem shown below; (a) Identify corner points of a feasible region. (b) Write the constraints. (c) Find the maximum and minimum values of the objective function f(x, y) = 12000x + 15000y.

1. Identify the corner points of the feasible region. (0 mk)
2. Write the constraints. (0 mk)
3. Find the maximum and minimum values of the objective function f(x, y) = 12000x + 15000y. (0 mk)

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Mention four essential aspects in the preparation of a table of specifications.

1. List four key elements in creating a table of specifications. (0 mk)

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Determine the condition such that the equation acosh(x) + b sinh(x) = c has equal roots.

1. Derive the condition for equal roots. (0 mk)

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“A curve passes through point P, where x = 0 and y = 1. If the gradient at any point is $dy/dx = 3x^2 - 2x + 1$. Find (a) The equation of the curve. (b) The area enclosed by the curve, x-axis with the ordinates x = 1 and x = 3.

1. Find the equation of the curve. (0 mk)
2. Find the area enclosed by the curve, x-axis with the ordinates x = 1 and x = 3. (0 mk)

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State five merits of improvising teaching and learning resources.

1. List five benefits of creating teaching materials locally. (0 mk)

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“In spite of having the relevant textbook for lesson preparation, a Mathematics teacher is still required to have a syllabus” Justify this by giving four points.

1. Provide four reasons why a syllabus is essential for a Mathematics teacher, even with a textbook. (0 mk)

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