2022 QCE Maths Methods Paper 1 Mini Test 2
External Assessment Paper 1 — Technology-free
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.
A binomial random variable arises from the number of successes in \(n\) independent Bernoulli trials.
A context not suitable for modelling using a binomial random variable is recording the number of
- (A) heads when a coin is tossed 12 times.
- (B) left-handed people in a sample of 100 people.
- (C) times a player hits a target from 20 shots where each shot is independent of all other shots.
- (D) red marbles selected when three marbles are drawn without replacement from a bag containing four blue and five red marbles.
The area between the curve \(y = 9 - x^2\) and the x-axis is
- (A) 12 units\(^2\)
- (B) 18 units\(^2\)
- (C) 36 units\(^2\)
- (D) 54 units\(^2\)
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.
Two triangles are said to be similar if their corresponding angles are congruent and the corresponding sides are in proportion, e.g. if \(\triangle UVW\) is similar to \(\triangle XYZ\) then
\(\angle U = \angle X, \angle V = \angle Y\) and \(\angle W = \angle Z\) and \[ \frac{UV}{XY} = \frac{VW}{YZ} = \frac{UW}{XZ} \]
Two parallel walls \(AB\) and \(CD\), where the northern ends are \(A\) and \(C\) respectively, are joined by a fence from \(B\) to \(C\). The wall \(AB\) is 20 metres long, the angle \(\angle ABC = 30^\circ\) and the fence \(BC\) is 10 metres long.
A new fence is being built from \(A\) to a point \(P\) somewhere along \(CD\). The new fence \(AP\) will cross the original fence \(BC\) at \(O\).
Let \(OB = x\) metres, where \(0 < x \le 10\).
Determine the value of \(x\) that minimises the total area enclosed by \(\triangle OBA\) and \(\triangle OCP\). Verify that this total area is a minimum.
END OF PAPER
