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Ireland
(c) Draw the graph of the function \( f(x)=2 x^{2}-x-6 \) in the domain \( -2 \leq x \leq 2 \), where \( x \in \mathbb{R} \), on the co-ordinate grid opposite. Show your working out. ,
Algebra Jan 19, 2025
A function is defined as \( f(x)=2 x^{2}-x-6 \), where \( x \in \mathbb{R} \). (a) Write down the two factors of \( f(x) \). \[ \begin{array}{lll}2 x^{2}-x-6 & \text { T.U.12 } & (2 x+3)(x-2) \\ 2 x^{2}-4 x+3 x-6 & 2 x+3=0 & x=2 \\ 2 x(x-2) 3(x-2) & 2 x=-3\end{array} \begin{array}{l}12 \times 1 \\ 1 \times 12 \\ 2 \times 6 \\ 6 \times 2 \\ 4 \times 3 \\ 3 \times 4\end{array} \]
Algebra Jan 19, 2025
A function is defined as \( f(x)=2 x^{2}-x-6 \), where \( x \in \mathbb{R} \). (a) Write down the two factors of \( f(x) \). (b) Hence, or otherwise, solve for \( f(x)=0 \) (b)
Algebra Jan 19, 2025
\( € 2000 \) is invested for 3 years at \( 4 \% \) per year at compound interest. (a) Work out the amount of the investment after 1 year.
Arithmetic Jan 18, 2025
Question 3 \( € 2000 \) is invested for 3 years at \( 4 \% \) per year at compound interest. (Suggested maximum (a) Work out the amount of the investment after 1 year.
Arithmetic Jan 18, 2025
10. If \( \cos \theta=\frac{1}{\sqrt{2}} \), find 2 values for \( \tan \theta \), if \( 0^{\circ} \leqslant \theta \leqslant 360^{\circ} \)
Trigonometry Jan 18, 2025
\( \frac{3 x-2}{x-5} \leq 5, \quad \) where \( x \in \mathbb{R} \) and \( x \neq 5 \)
Algebra Jan 17, 2025
7 The function \( f \) is defined as \( f(x)=x^{3}+3 x^{2}-9 x-8 \), where \( x \in \mathbb{R} \). (a) Find \( f^{\prime}(x) \). (b) Solve the equation \( f^{\prime}(x)=0 \). (c) Hence, find the turning points of the curve \( y=f(x) \) and state whether each point is a local maximum or a local minimum.
Calculus Jan 17, 2025
The function \( f \) is defined as \( f(x)=x^{3}+3 x^{2}-9 x-8 \), where \( x \in \mathbb{R} \). (a) Find \( f^{\prime}(x) \). (b) Solve the equation \( f^{\prime}(x)=0 \). (c) Hence, find the turning points of the curve \( y=f(x) \) and state whether each point is a local maximum or a local minimum.
Calculus Jan 17, 2025
(11) \( f(x)=x^{3}-3 x^{2}-24 x, x \in \mathbb{R} \) (a) Find the co-ordinates of the local maximum point and the local minimum point on the curve of \( y=f(x) \). (b) Show that this curve intersects the \( x \)-axis at \( x=0 \). (c) Draw a rough sketch of the curve given that it crosses the \( x \)-axis between -4 and -3 and also between 6 and 7 .
Calculus Jan 17, 2025
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