$Given that {(4-\sqrt{5})}^2=a-\sqrt{b}, find the values of a and b are rational$

$$\begin{gathered} The n^{th }term of the sequence 5,10,16,........is given by 2^{x+1}+4n \\ Find the 9^{th} term of the sequence. \end{gathered}$$

Find $\int \frac{6}{3\mathcal{x}+1}d\mathcal{x}$

Use Simpson’s Rule, with 5 function values, to find an approximation to ${\int }_0^4\mathcal{x}{e}^{\mathcal{x}}d\mathcal{x}$ to 2decimal places

$The diagram below shows the graph of a function y=f\left(x\right)$

$$\begin{gathered} \left(i\right) For which values of x is the derivative, f^{\text{'}}\left(x\right) negative \\ \left(ii\right) Sketch the graph y=f^{\text{'}}\left(x\right) \end{gathered}$$

$$\begin{gathered} Which one of the following is equivalent to 3.507\times {10}^{-3}? \\ A.3507\times 1000 \\ B.35.07\times 100 \\ C. 0.3507÷100 \\ D.3507÷100 \end{gathered}$$

$$\begin{gathered} The gradient of a function is given by y\text{'} =\frac{4x}{x^2+1} \\ The curve passes through (0, 2). What is the equation of the function? \end{gathered}$$

$$\begin{gathered} What is the angle of inclination to the nearest minute, of \\ the line 3\mathcal{x}+2\mathcal{y}=7 with the positive direction of \\ the \mathcal{x} axis? \\ A. 33°41\text{'} \\ B. 56°19\text{'} \\ C. 123°41\text{'} \\ D. 146°19\text{'} \end{gathered}$$

Integrate $7𝑥-\frac{2}{{𝑥}^2}$

$$\begin{gathered} A curve has a gradient function with equation \frac{dy}{dx}=(x-1)(x+2) . \\ \left(i\right) If the curve passes through the point (1, \frac{5}{6} ), what is the equation of the curve? \\ \left(ii\right) Find the coordinates of the stationary points and determine their nature. \\ \left(iii\right) Find any points of inflexion. \\ \left(iv\right) Graph the function showing all the main features. \end{gathered}$$