2022 QCE Maths Methods Paper 2 Mini Test 3
External Assessment Paper 2 — Technology-active
Number of marks: 9
Perusal time: 1 minute
Writing time: 15 minutes
Section 1
Instructions
• This section has 10 questions and is worth 10 marks.
• Use a 2B pencil to fill in the A, B, C or D answer bubble completely.
• Choose the best answer for Questions 1 10.
• If you change your mind or make a mistake, use an eraser to remove your response and fill in the new answer bubble completely.
The continuous random variable \(X\) has the probability density function
\[ f(x) = \begin{cases} \frac{\cos(x)}{2}, & -\frac{\pi}{2} \le x \le \frac{\pi}{2} \\ 0, & \text{otherwise} \end{cases} \]The standard deviation of \(X\) is
- (A) 0.467
- (B) 0.684
- (C) 1.211
- (D) 1.467
A stall at the school fete sells cups of lemonade. Assuming the amount of lemonade in a cup is normally distributed with a mean of 60 mL and a standard deviation of 3 mL, 80% of the cups contain more than
- (A) 52.4 mL
- (B) 57.5 mL
- (C) 61.6 mL
- (D) 62.5 mL
Section 2
Instructions
• Write using black or blue pen.
• Questions worth more than one mark require mathematical reasoning and/or working to be shown to support answers.
• If you need more space for a response, use the additional pages at the back of this book.
– On the additional pages, write the question number you are responding to.
– Cancel any incorrect response by ruling a single diagonal line through your work.
– Write the page number of your alternative/additional response, i.e. See page …
– If you do not do this, your original response will be marked.
• This section has nine questions and is worth 45 marks.
A hiker begins her journey at a youth hostel (\(H\)) and walks for 8 km on a bearing of 052°T to her lunch stop (\(L\)). She then walks on a bearing of 210°T for 5.2 km until she reaches a campsite (\(C\)).
Determine the direction she would need to walk in a straight line to return directly to the youth hostel.
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