Mathematics 4024 · O Level · Sketching curves

Sketching curves — practice question

The variables $x$ and $y$ satisfy the equation $y=3+x-\frac{x^2}{2}$.
(a(i))[1]

Complete the table shown.

(a(ii))[3]

Draw the graph of $y=3+x-\frac{x^2}{2}$ for $-3\le x\le5$ on the scales provided.

(a(iii))[2]

Estimate the gradient of the curve at $(3,1.5)$ by drawing a tangent.

(a(iv)(a))[1]

Find the value of $k$ when the intersection points with the line $y=k$ satisfy $10+2x-x^2=0$.

(a(iv)(b))[2]

By drawing the line $y=k$ on your graph, determine the solutions of $10+2x-x^2=0$.

(b(i))[1]

State the value of $p$ when $y=pa^x$ passes through $(0,4)$ and $(2,36)$.

(b(ii))[1]

Determine the value of $a$.

(b(iii))[1]

The graph goes through the point $(4,q)$. Determine the value of $q$.

Worked solution & mark scheme

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