Additional Mathematics 4037/11 — May/June 2023

Cambridge O-Level · Calculator · worked solutions for every part, with the mark scheme

questions

marks

120

minutes

Topics Calculus · Trigonometry · Quadratic functions · Equations, inequalities and graphs · Factors of polynomials · Simultaneous equations · +6 more

Q1Quadratic functionsEquations, inequalities and graphsFree sample

(a)

Write $5x^2 - 14x + 8$ in the form $a(x + b)^2 + c$ , where $a$ , $b$ and $c$ are constants to be found.

(b)

Hence write down the coordinates of the stationary point on the curve $y = 5x^2 - 14x + 8$ .

(c)

On the axes below, sketch the graph of $y = |5x^2 - 14x + 8|$ , stating the coordinates of the points where the graph meets the coordinate axes.

Fig. 1

(d)

Write down the range of values of $k$ for which the equation $|5x^2 - 14x + 8| = k$ has 4 distinct roots.

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