Maths Exam Prep 2026-27
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Maths Exam Prep 2026-27
Sample questions with model answers
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Obtain the simple logical expression of the following. Draw the corresponding switching circuit: $\neg (p \wedge q) \vee (\neg p \wedge q) \vee (p \wedge \neg q)$.
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Expression simplifies to $\neg p \vee \neg q$.
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The volume of a sphere increase at the rate of $20 \text{ cm}^3/\text{sec}$. Find the rate of change of its surface area when its radius is 5 cm.
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Rate of change of surface area is $40\pi$ cm$^2$/sec.
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Prove that, The acute angle $\theta$ between the lines represented by $ax^2 + 2hxy + by^2 = 0$ is given by $\tan \theta = |\frac{2\sqrt{h^2 - ab}}{a + b}|$, and Find the acute angle between lines represented by: $x^2 + xy = 0$.
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Angle $\theta = 45^\circ$.
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Find the value of $x$ for which the function $f(x) = x^3 - 12x^2 - 144x + 13$ (a) increasing (b) decreasing.
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Increasing for $x < 4$ and decreasing for $x > 4$.
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