CAIE IGCSE Additional Math 2 Quadratic Functions

Covered syllabus points

2.1. Find maximum and minimum values 2.2. Use vertex values to sketch or find range 2.3. Use discriminant conditions 2.4. Solve quadratic equations 2.5. Solve quadratic inequalities

[Maximum number: 4]

(a)

Show that $2 x^{2}+5 x+3$ can be written in the form $2(x+a)^{2}+b$ , where a and b are constants to be found.

[ 2 ]

$2\left(x+\frac{5}{4}\right)^{2}-\frac{1}{8}$ B1 for $2\left(x+\frac{5}{4}\right)^{2}$

B1 for $-\frac{1}{8}$

(b)

Hence write down the coordinates of the stationary point on the curve $y=2 x^{2}+5 x+3$ .

[ 2 ]

$\left(-\frac{5}{4},-\frac{1}{8}\right)$ 2 B1FT on their - a

B1FT on their b

B0 if calculus used as question says ‘Hence’

[Maximum number: 5]

1 A curve has equation $y=x^{2}+2 x-3$ .

(a)

Use the method of completing the square to find the coordinates of the stationary point on the

curve.

[ 3 ]

$(x+1)^{2}-4$ oe
(-1, -4)
B2 $y=(x+1)^{2}-4$ oe
or
B1 $y=(x+1)^{2}+k$ , where k is a constant

(b)

On the axes,sketch the curve,stating the intercepts with the coordinate axes.

Figure for Question (b) — CAIE IGCSE Additional Math

[ 2 ]

[Maximum number: 5]

2 In this question,k is a constant.

It is given that $2 x^{2}+(3 k-2) x+k=0$ has roots that are real and distinct.

Find the set of possible values of k .

$(3 k-2)^{2}-4(2)(k)\left[{ }^{*} 0\right]$
Uses $b^{2}-4 a c$
* could be any inequality sign or = $9 k^{2}-20 k+4\left[{ }^{*} 0\right]$
Correctly simplifies to 3-term quadratic
(9 k-2)(k-2)
FT Factorises or solves their 3-term
quadratic
Critical values $\frac{2}{9}, 2$ $k<\frac{2}{9}$ k>2
Mark final answer

[Maximum number: 2]

1 A curve has equation $y=x^{2}+2 x-3$ .

On the axes,sketch the curve,stating the intercepts with the coordinate axes.

Figure for Question 4 — CAIE IGCSE Additional Math

[Maximum number: 2]

The number of permutations of n items taken 4 at a time is equal to $\frac{1}{6} \times$ the number of permutations of 2 n items taken 3 at a time.

Hence find the value of n.

[Maximum number: 3]

Solve the following inequalities.

$x^2-x-6 \geqslant 0$

(x-3)(x+2)x * 3, x * -2* can be any inequality sign or =.
$x \geqslant 3,\ x \leqslant -2$
Do not allow "and" between inequalities.
Do not accept $-2 \geqslant x \geqslant 3$ .

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CAIE IGCSE Additional Math 2 Quadratic Functions Topic Practice

Covered syllabus points

Question 1

Question (a)

Question (b)

Question 2

Question (a)

Question (b)

Question 3

Question 4

Question 5

Question 6