DSE Maths Core · Past Paper Questions

2018 · Paper 1 Q17 Trigonometry

(a) In Figure 3(a),

ABCD

is a paper card in the shape of a parallelogram. It is given that

AB = 60 \text{ cm}

,

\angle ABD = 20^{\circ}

and

\angle BAD = 120^{\circ}

. Find the length of

AD

.

(b) The paper card in Figure 3(a) is folded along

BD

such that the distance between

A

and

C

is

40 \text{ cm}

(see Figure 3(b)).

(i) Find

\angle ABC

.

(ii) Find the angle between the plane

ABD

and the plane

BCD

. (5 marks)

2018 · Paper 1 Q18 Variations

It is given that

f(x)

partly varies as

x^{2}

and partly varies as

x

. Suppose that

f(2)=60

and

f(3)=99

.

(a) Find

f(x)

. (3 marks)

(b) Let Q be the vertex of the graph of

y = f(x)

and R be the vertex of the graph of

y = 27 - f(x)

.

(i) Using the method of completing the square, find the coordinates of Q.

(ii) Write down the coordinates of R.

(iii) The coordinates of the point

S

are

(56, 0)

. Let

P

be the circumcentre of

\Delta QRS

. Describe the geometric relationship between

P

,

Q

and

R

. Explain your answer. (5 marks)

2018 · Paper 1 Q19 Equations of circles

(a) Find the equation of

C

in terms of

r

. Hence, express

r^{2}

in terms of

k

. (4 marks)

(b)

L

passes through the point

D(18,39)

.

(i) Find

r

.

(ii) It is given that

L

cuts the

y

-axis at the point

E

. Let

F

be a point such that

C

is the inscribed circle of

\Delta DEF

. Is

\Delta DEF

an obtuse-angled triangle? Explain your answer. (8 marks)