Melaka Trial 2025 Add Maths Paper 2, Question 6Vectors

Solved on video in English · Form 4, Vectors · 6:12 video

The question

(a)(i)

In Diagram 3, ABCD is a quadrilateral. AED, CFE and BFD are straight lines. It is given that AB = 20x, AE = 4y, BC = 5x + 4y, BD = −20x + 16y and BD = 4BF, where x and y are vectors.

(a) Express in terms of x and/or y: (i) CD

(a)(ii)

In Diagram 3, ABCD is a quadrilateral with AED, CFE and BFD straight lines; AB = 20x, AE = 4y, BC = 5x + 4y, BD = −20x + 16y and BD = 4BF (x and y are vectors).

(a)(ii) Express CF in terms of x and/or y.

(b)

In Diagram 3 (ABCD a quadrilateral; AED, CFE, BFD straight lines; AB = 20x, AE = 4y, BC = 5x + 4y, BD = −20x + 16y, BD = 4BF, x and y vectors):

(b) Given that CF = kCE, where k is a constant, find the value of k.

(c)

In Diagram 3 (ABCD a quadrilateral; AED, CFE, BFD straight lines; AB = 20x, AE = 4y, BC = 5x + 4y, BD = −20x + 16y, BD = 4BF, x and y vectors):

(c) If |x| = 1, |y| = 3 and ∠DAB = 90°, find |BC|.

Melaka Trial 2025 Add Maths Paper 2, Question 6: the question as drawn in Eduly's video6:12

Part (a)(i)

Step 1

Use the triangle law: CD = CB + BD.

Why this step

CD isn't given, but BC and BD are. Hop C → B → D so both pieces are known, then add the vectors head to tail.

3 more steps, each with the reason for it, in the full solution

Final answer

CD = −25x + 12y

Where students lose marks

Watch out: CD = CB + BD needs CB, not BC. Reverse BC first, so CB = −5x − 4y.

Part (a)(ii)

4 more steps, each with the reason for it, in the full solution

Final answer

CF = −10x

Where students lose marks

Watch out: BD = 4BF means BF = ¼BD, not 4BD. Also check the sign of CB, or the y-terms won't cancel.

Part (b)

4 more steps, each with the reason for it, in the full solution

Final answer

k = 2/5

Where students lose marks

Watch out: BA = −AB = −20x. A wrong sign here gives the wrong CE, so k comes out wrong too.

Part (c)

4 more steps, each with the reason for it, in the full solution

Final answer

|BC| = 13

Where students lose marks

Watch out: ∠DAB = 90° makes x ⊥ y, so use Pythagoras: |BC|² = (5|x|)² + (4|y|)², not 5|x| + 4|y|.

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