1. Diagram shows the graph of quadratic function f(x) = (x + 3)2 + 2k – 6 , where k is a constant.

a. State the equation of the axis of symmetry of the curve.b. Given that the minimum value of the function is 4, find the value of k.

SPM 2011(3 marks)

2. Diagram shows the graph of a quadratic function y = f(x).State

a. the roots of the equation f(x) = 0b. the equation of the axis of symmetry of the curve.c. State the equation of f(x).

SPM 2010 (3 marks)

3. Diagram shows the graph of quadratic function y = f(x) . The straight line y = –4 is a tangent to

the curve y = f(x).a. Write the equation of the axis of symmetry of the curve.b. Express f(x) in form of (x + b)2 + c, where b and c are constants.

SPM 2006 (3 marks)

y

y = f(x)

10x

5

y = –4

•

f(x)

f(x) = (x + 3)2 + 2k – 6

4

0x

y = f(x)

x

y

–1 0

5

3

HIGHER ORDER THINKING SKILL (HOTS)SPM ADDITIONAL MATHEMATICS PAPER 1

HOTS DRILLING EXERCISE

Topic: Quadratic Functions

SPM/SBP Past-Year Questions

ReviewQuestions

y

–3 (2, –3)

0

4. Diagram shows the graph of a quadratic function f(x) = – (x – k)2 – 2, where k is constants

State

a. the value of kb. the equation of the axis of symmetry.c. the coordinates of the maximum point

SPM 2004 (3 marks)

x

5. Diagram shows the graph of the function y = f(x) has a maximum point (–2, 6) and y-intercept is –5.

Find f(x).SMKJ 2012 / (3 marks)

y

y = f(x)0 x

–5

(–2, 6)

1. Fine the value(s) or range of values of p for which the quadratic function

a. f(x) = x2 + 2px + (2 – p) has only one x-intercept.

b. f(x) = 2x2 – 4x + 3 – p intercept the x axis at two distinct points.

c. f(x) = 4x2 + (4 + p)x + p + 1 touches the x-axis

d. f(x) = px2 + (2p + 4)x + p + 7 is always positive.

2. Show that the graph of quadratic equation f(x) = x2 + (1 + p)x + p intercepts the x-axis at two distinct points for all values of p.

HIGHER ORDER THINKING SKILL (HOTS)SPM ADDITIONAL MATHEMATICS PAPER 1

HOTS DRILLING EXERCISE

Topic: Quadratic Functions

HOTS (KBAT) Questions and Answer

Forecast Question

s

3. Show that the graph of quadratic equation f(x) = 2x2 + p – 2(x – 1) does not

intercept the x-axis if p > .

4. Diagram shows a quadratic curve f(x) = q – (x – p)2 cuts the x-axis at the points (1, 0) and (3, 0)

Finda. the value of p and of qb. the maximum value of f(x)

5. For each of the curve, express its equation in the form of f(x) = a(x + p)2 + q

a. b.

yf(x) = q – (x – p)2

0 x1 3

y

0 x

(0, –2)

(–3, –7)

y

0 x

(0, 4)

(3, 10)

0

6. Diagram shows the graph f(x) = x(x – 6). The graph passes through the origin 0 and crosses x-

axis at point A. B is a lowest point.

a. Find the coordinates of point A and point B.b. If point D(2, p) is a point on the curve, calculate the value of p.

c. If the area of shaded region R is cm2, calculate the area of shaded

region Q.

7. A quadratic curve is symmetrical about the line x = –1 and passes through the point (0, 5) and

(1, 2). Find its equation and sketch the graph.

R

Q

D(2, p)

B

y

xA

8. A book store which sells Biology work books found out that when it sells them at a p ringgit

a book, the revenue (Perolehan) R, in ringgit, they are collecting is

R(p) = 150p – 10p2

Diagram show the graph revenue function R. Find

a. the revenue, in RM, when the book price is RM 5. b. the book price should be established in order to maximise revenue.

Hence, state the maximum revenue.

R(p) = 150p – 10p2

0

R(RM)

p (RM)

9. Diagram shows a side elevation of inner surface of a bowl which can be represented by the

equation y = ax2.

a. Show that .

b. Determine the volume, in cm2, of water needed to fill the bowl to a depth of 20 cm.

(SPM 2014 / 6 marks)

60 cm

30 cm

10. Diagram show a suspension bridge with two tall towers and suspended by huge cable. Its 200 m tall towers are 1000 m apart and the road surface is 50 above the water. The cable is parabolic in shape and touches the road surface at the centre of bridge. By considering the point 0 as the origin on the axes, find

a. the equation of the cable in parabolic shape.b. the height of the cable at a distance of 300 m from the centre.

200 m

1000 m

x50 m

?

300 m

y

0

(500, 150)(–500, 150)

11. Diagram shows a graph of quadratic equation f(x) = (x – 3)2 – 25. State

a. the coordinates of the minimum point of the curve.b. the equation of the axis of symmetry of the curve.c. the range of values of x when f(x) is negative.

3 marks / SPM 2014

f(x)

0 x–2 8