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Singapore
A data set consist of the following 6 values: The range is 6 . The median is 5 . The lower quartile is 4 . The interquartile range is 3 . Given that \( x<y<z \), find the values of \( x, y \) and \( z \).
Statistics Jan 22, 2025
\( 4 ( x ^ { 2 } - 2 x ) + ( y ^ { 2 } + 4 y ) = 8 \)
Algebra Jan 22, 2025
It is given that \[ f(x)=\left\{\begin{array}{ll}7-x^{2} & \text { for } 0<x \leq 2 \\ 2 x-1 & \text { for } 2<x \leq 4\end{array}\right. \] and that \( f(x)=f(x+4) \) for all real values of \( x \). (i) Evaluate \( f(27)+f(45) \).
Pre Calculus Jan 22, 2025
3 (9.) Express \( -x^{2}+4 x+1 \) in the form \( -(x-p)^{2}+q \). \[ \begin{array}{l} =-(x-p)^{2}+q \\ =-\left[(x-2)^{2}-2^{2}-4 x-1\right] \\ =-\left[(x-2)^{2}-5\right. \\ =-(x-2)^{2}+5 \end{array} \] Name 1 Answer \( \qquad \) [2] 0) Hence solve the equation \( -x^{2}+4 x+1=0 \), giving your answers correct to two decimal places.
Algebra Jan 21, 2025
8 (i) Given that \( \frac{2 x-1}{(x-1)^{2}}=\frac{A}{x-1}+\frac{B}{(x-1)^{2}} \) find the value of \( A \) and of \( B \). (ii) Hence find the derivative of \( \frac{2 x-1}{(x-1)^{2}} \).
Calculus Jan 21, 2025
12 Explain why the graph of \( y=2 x^{2}+4 x-k+1 \) has no \( x \)-intercep when \( k=-5 \).
Algebra Jan 21, 2025
(c) (i) Express \( 6-8 x+x^{2} \) in the form \( a+(b+x)^{2} \)
Algebra Jan 21, 2025
7 (i) Show that \( \frac{x}{x+1}=1-\frac{1}{x+1} \) (ii) Hence find \( \frac{\mathrm{d}}{\mathrm{d} x}\left(\frac{x}{x+1}\right) \)
Calculus Jan 21, 2025
Hence solve the equation \( -x^{2}+4 x+1=0 \), giving your answers correct to two decimal places.
Algebra Jan 21, 2025
6 Find the derivative of (a) \( y=(x+2)^{2} \sqrt{x+2} \) (b) \( y=\frac{\left(2-3 x^{2}\right)^{2}}{\sqrt{2-3 x^{2}}} \)
Calculus Jan 21, 2025
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