Mathematics 9709 · AS & A Level · Functions

Functions — practice question

The function $f : x \mapsto p\sin^2 2x + q$ is defined on $0 \leq x \leq \pi$, with $p$ and $q$ being positive constants. The diagram displays the graph of $y = f(x)$.
(i)[2]

State the range of $f$, in terms of $p$ and $q$.

(ii(a))[1]

State how many solutions the equation $f(x) = p + q$ has.

(ii(b))[1]

State how many solutions the equation $f(x) = q$ has.

(ii(c))[1]

State how many solutions the equation $f(x) = \tfrac{1}{2}p + q$ has.

(iii)[5]

For $p = 3$ and $q = 2$, solve the equation $f(x) = 4$, showing all the working needed.

Worked solution & mark scheme

This 10-mark question has a full step-by-step worked solution and mark scheme. One marking point: Correct range inequality $q\le f(x)\le p+q$

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