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TMUA 2023 · Paper 1

20 questions · 75 min

Question 151 mark

The difference between the maximum and minimum values of $f(x)=a\cos x$ , where $a>0$ and $x$ is real, is $3$ . Find the sum of the possible values of $a$ .

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Current level · 5TMUA 2023 · Paper 1 · Q15

The difference between the maximum and minimum values of $f(x)=a\cos x$ , where $a>0$ and $x$ is real, is $3$ . Find the sum of the possible values of $a$ .

0

\frac{3}{2}

\frac{5}{2}

3

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TMUA 2023 · Paper 1 · Question 2

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The graphs of $y=x^2+5x+6$ and $y=mx-3$ do not meet. What is the complete range of possible values of $m$ ?

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TMUA 2023 · Paper 1 · Question 2

Your answer

-11<m<11

You centred the interval on 0. The discriminant centres it on 5.

Step-by-step solution

1Set the equations equal

$x^2+(5-m)x+9=0$

2Require no real roots

$(5-m)^2-36<0$

3Solve the inequality

$|5-m|<6$ , so $-1<m<11$

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Attached to Question 2

Current question

Why does no intersection give $-1<m<11$ ?

Set the equations equal. Their intersections satisfy $x^2+(5-m)x+9=0$ . No intersection means no real roots, so the discriminant must be negative: $(5-m)^2-36<0$ .

Therefore $|5-m|<6$ . The endpoints are $5-6$ and $5+6$ , which gives $-1<m<11$ .

Give me a hintWhy is C wrong?Explain the discriminant

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