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Kenya
2 What is the value of \( 24(72-69)+6 \times 4 \)
Arithmetic Jan 20, 2025
1. What is the value of \( \frac{2}{3}+\frac{1}{2} \) of \( \left(\frac{1}{2}-\frac{1}{5}\right) \div \frac{3}{5} \times \frac{2}{5} \)
Arithmetic Jan 20, 2025
2 What's the next number in th sequence. a) \( 4,7,10,13,16 \),
Arithmetic Jan 20, 2025
(b) Find an equation of a line tangent to the curve \( x^{2}+x y-y^{3}=7 \) at the point \( (3,2) \). 6 (4iven \( H(3)=1, F(3)=5, H^{\prime}(3)=3, F^{\prime}(3)=4 \). Find:
Calculus Jan 20, 2025
\( 2 \cosh ^ { 2 } x + \sinh x = 3 . \)
Pre Calculus Jan 20, 2025
\( 2 \cosh ^ { 2 } x + \sinh x = 3 . \)
Pre Calculus Jan 20, 2025
QUESTION TWO (15 MARKS) (a) Consider a rock that is launched from the ground at a speed of \( 96 \mathrm{ft} / \mathrm{sec} \). Neglecting air resistance, a well known formula from physics states that the position of the rock after \( t \) seconds is given by the function \( S(t)=-16 t^{2}+96 t \). The position is measured in feet with \( S=0 \) corresponding to the ground. Find the average velocity of the rock between each pair of intervals given as i) \( t=1 \mathrm{sec} \) and \( t=3 \mathrm{sec} \), ii) \( t=1 \mathrm{sec} \) and \( t=1.00001 \mathrm{sec} \), iii) Make a conjecture regarding your observation in (i) and (ii), (1 mark) iv) By clearly showing your working evaluate \( \lim _{t \rightarrow 1} \frac{S(t)-S(1)}{t-1} \). 1 mark) (2 marks)
Calculus Jan 20, 2025
QUESTION ONE ( 16 MARKS) (a) Compute the derivative of \( y=\frac{1}{x} \) using the first principle (or by definition).
Calculus Jan 20, 2025
QUESTION ONE ( 16 MARKS) (a) Compute the derivative of \( y=\frac{1}{x} \) using the first principle (or by definition).
Calculus Jan 20, 2025
(b) Determine an equation of the line tangent to the graph of \( f \) at \( (a, f(a)) \) for the given value of \( a \). i) \( f(x)=\sqrt{3 x+1} ; \quad a=8 \) ii) \( f(x)=\frac{2}{3 x+1} ; \quad a=-1 \)
Calculus Jan 20, 2025
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