Form 4 Additional Mathematics Group Presentation
1. Given the function f (x) =
𝑥
2
− 2 and g (x) =3𝑥 + 𝑘, where k is a constant, find
a) 𝑓 −1 (3)
b) the value of k if 𝑓 −1 𝑔(𝑥) = 6𝑥 − 4
c) h(x) such that ℎ𝑓(𝑥) = 9𝑥 − 3
(6 marks)
2. a) Given that α and β are the roots of the quadratic equation 𝑥 2 − 3𝑥 + 4 = 0, form
a quadratic equation that has the roots
𝛼
2
and
𝛽
2
.
b) A quadratic equation is defined by 𝑓 (𝑥) = 𝑝𝑥 2 + 4(𝑝 + 1)𝑥 + 8𝑝 − 7.
i. Find the range of values of p if the graph of f (x) intersects the x-axis at two
distinct points.
ii. If p = 1, by completing the square, find the coordinates of the minimum point
of the graph of f (x). Hence, sketch the graph.
(12 marks)
3. a) Solve the following pairs of simultaneous equation:
2𝑥 + 𝑦 = 5
𝑥 2 − 𝑥𝑦 = 12
b) The following diagram shows an enclosed region PQRST constructed using
a 70 cm long wire.
If the area of the enclosed region is 240 cm2, find the possible values of x and
the corresponding values of y.
(10 marks)
4. a) Simplify 2𝑥+3 + 2𝑥 + 16(2𝑥−1 ) in the form 𝑘 (2𝑥 ), where k is a constant.
b) Rationalise the denominator of the following expression:
3 + √24
2 + √6
c) Given that 𝑚 = 3𝑎 and 𝑛 = 3𝑏 , express log 3 (
𝑚𝑛4
27
) in terms of a and b.
(10 marks)
5. The given diagram shows a few rectangles which touch each other.
Q and P are the midpoints of AD and BC respectively, L and K are the midpoints
of AQ and BP respectively, U and T are the midpoints of AL and BK
respectively and so on. It is given that AB = 6 cm and BC = 16 cm.
a) Show that the areas of rectangles with the sides AD, AQ, AL, AU, …..
form a geometric progression.
b) Hence, calculate the sum to infinity of the areas of the rectangles.
(5 marks)
6. Use a graph to answer this question.
The following table shows the experimental values of two variables, x and y.
x
y
2
7.8
3
13.2
4
20.0
5
27.5
6
36.9
7
46.9
𝑞
The variables are related by the equation 𝑦 = 5𝑘𝑥 2 + 𝑥, where k and q are
𝑘
constants.
a) Using a scale of 2 cm to 1 unit on both axes, plot the graph of
Hence, draw the line of best fit.
b) Using your graph in (a), find
i. the value of k and of q.
ii. the value of y when x = 0.9.
𝑦
𝑥
against x.
7. The diagram below shows the straight line AC which is perpendicular to the
straight line BC at point C.
Given that the equation of the straight line BC is 𝑦 − 3𝑥 + 6 = 0, find
a) the coordinates of points A.
b) the coordinates of points D such that ABCD is a parallelogram.
c) the area of ABCD.
8. The given diagram shows a triangle PQR. Point S lies on PQ such that PS : SQ
⃗⃗⃗⃗⃗ = 6𝑏.
= 1 : 2 and T is the midpoint of RQ. It is given that ⃗⃗⃗⃗⃗
𝑃𝑄 = 9𝑎 and 𝑃𝑅
a) Express ⃗⃗⃗⃗⃗
𝑃𝑇 and ⃗⃗⃗⃗⃗
𝑆𝑅 in term of a and b.
⃗⃗⃗⃗⃗ , where h and k are constants, find
⃗⃗⃗⃗⃗ and ⃗⃗⃗⃗⃗
b) Given that ⃗⃗⃗⃗⃗
𝑃𝑈 = ℎ𝑃𝑇
𝑆𝑈 = 𝑘𝑆𝑅
the value of h and k.
(8 marks)
9. The diagram below shows triangles URS, UST and RSV.
RST is a straight line. Calculate
a) the length of US.
b) the length of UR.
c) the length of RV if the area of triangle RSV id 41.36 cm2 and ∠RSV is an
obtuse angle.
(10 marks)
10. The following table shows the price indices of five items exported by Malaysia
for the year 2005 based on the year 2004.
The following pie chart represent the relative quantity of the items exported.
a) The prices of a barrel of petroleum in the years 2004 and 2005 were
RM 140 and RM 154 respectively. Calculate the value of m.
b) The composite index of the values of exports of those items for the year
2005 based on year 2004 is 122.5. Find the value of k.
c) The composite index of the values of exports of those items increased
by 20% from the year 2005 to the year 2006. Calculate
i. the composite index of the values of exports of those items for the
year 2006 based on the year 2004.
ii. the total value of export of those items in the year 2006 if its
corresponding value in the year 2004 was RM 900 billion.
(10 marks)