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Spm 2014 add math modul sbp super score [lemah] k2 set 1 dan skema
1. MODUL SUPER SCORE SBP 2014
KERTAS 2
SET 1
NAMA : MARKAH
TARIKH :
Answer all questions.
Jawab semua soalan.
1. Solve the following simultaneous equations 2x + y = 1 and 2x 2 + y 2 + xy = 5.
Give the answers correct to three decimal places. [5 marks]
Selesaikan persamaan serentak 2x + y = 1 dan 2x 2 + y 2 + xy = 5.
Beri jawapan betul kepada tiga tempat perpuluhan. [5 markah]
2. (a) Sketch the graph of y = 1 + 2 cos x for 0 x 2π. [4 marks]
Lakar graf bagi y = 1 + 2 kos x untuk 0 x 2π. [4 markah]
(b) Hence, using the same axes, sketch a suitable straight line to find the number of solutions
for the equation cos x =
1
2
x
for 0 x 2π. State the number of solutions. [3 marks]
Seterusnya, dengan menggunakan paksi yang sama, lakar satu garis lurus yang sesuai untuk
mencari bilangan penyelesaian bagi persamaan cos x =
1
2
x
untuk 0 x 2π.
Nyatakan bilangan penyelesaian ini. [3 markah]
3. The table shows the values of two variables, x and y, obtained from an experiment. Variables x
a b
and y are related by the equation 2
y x x
, where a and b are constants.
2
a
Jadual menunjukkan nilai-nilai bagi dua pembolehubah, x dan y, yang diperoleh daripada satu
a b
eksperimen . Pembolehubah x dan y dihubungkan oleh persamaan 2
y x x
, dengan
2
a
keadaan a dan b ialah pemalar.
x 2 3 4 5 6 8
y 7.4 12 17.6 23.5 31.2 46.4
(a) Plot
y
x
against x, using a scale of 2 cm to 1 unit on both axes. Hence, draw the line of best
fit.
Plot
y
x
melawan x, dengan menggunakan skala 2 cm kepada 1 unit pada kedua-dua paksi.
Seterusnya, lukis garis lurus penyuaian terbaik.
(b) Use the graph in (a) to find the value of
Gunakan graf di (a) untuk mencari nilai
(i) a
(ii) b
(iii) y when x = 2.4
y apabila x = 2.4
[10 marks]
[10 markah]
2. MODUL SUPER SCORE SBP 2014
4.
P Q
T
S R
x
y 4
In the diagram ,
x5
PQ= 5x,
PS = 4y and
SR = x
Dalam rajah,
PQ= 5x,
PS = 4y dan
SR = x
Express in terms of x and y.
Ungkapkan dalam ungkapan x dan y
(a)
PR
(b)
QS
(c)
QR
[4 marks / markah]
5. a) Given that 90% of form four Technical students will pass the SPM examination. If a sample
of 10 students is chosen at random, calculate the probability that all of them pass the SPM
examination. [2 marks]
Diberi bahawa 90% daripada pelajar tingkatan empat teknikal akan lulus peperik-saan SPM.
Jika 10 sampel pelajar dipilih secara rawak, kirakan kebarangkalian bahawa semua pelajar
tersebut lulus SPM. [2 markah]
b) the diameter of limes from a farm has a normal distribution with a mean of 3.2 cm and a
standard deviation of 1.5 cm. calculate the probability that a lime chosen at random from this
farm has a diameter more than 3.9 cm, [5 marks]
Diameter bagi buah limau dari sebuah ladang adalah mengikut taburan normal dengan min
3.2 cm dan sisihan piawai 1.5 cm. hitung kebarangkalian bahawa sebiji limau yang dipilih
secara rawak dari ladang ini mempunyai diameter lebih daripada 3.9 cm, [5 markah]
6. Table shows the prices and the price indices of four ingredients, milk, flour, baking powder and
sugar, used to make a type of cakes. Diagram shows a pie chart which represents the relative
quantity of the ingredients used.
Jadual menunjukkan harga dan indeks harga bagi empat bahan, susu, tepung, tepung penaik dan
gula, diganakan untuk membuat sejenis kek. Rajah menunjukkan carta pai yang mewakili kuantiti
relatif bahan-bahan yang digunakan.
3. MODUL SUPER SCORE SBP 2014
Ingredients
Bahan
Price ( RM ) per kg
in the year
Harga (RM) per kg
pada tahun
Price index for the
year 2005 based on
the year 2004
Indeks harga pada
tahun 2005 berasaskan
tahun 2004.
2004 2005
Milk
Susu
3.00 3.50 116.7
Flour
Tepung
2.50 2.80 h
Baking powder
Tepung penaik
k 2.90 112.5
Sugar
Gula
2.10 2.47 117.6
Baking powder
Tepung penaik
15%
Milk
Susu
Flour
Tepung
42%
Sugar
Gula
30%
(a) Find the value of h and of k. [3 marks]
Cari nilai h dan k. [3 markah]
(b) Calculate the composite index for the cost of making these cakes in the year 2005 based on
the year 2004. [3 marks]
Hitung indeks gubahan bagi kos membuat kek tersebut pada thun 2005 berasaskan tahun
2004. [3 markah]
(c) The composite index for the cost of making these cakes increases by 50% from the year 2005
to the year 2009.
Indeks gubahan kos membuat kek tersebut meningkat sebanyak 50% dari tahun 2005 ke tahun
2009.
Calculate:
Hitung
(i) the composite index for the cost of making these cakes in the year 2009 based on the year
2004,
indeks gubahan bagi kos membuat kek tersebut pada tahun 2009 berasaskan tahun 2004.
4. MODUL SUPER SCORE SBP 2014
(ii) the price of a box of these cakes in the year 2009 if its corresponding price in the year
2004 is RM25.
harga sekotak kek ini pada tahun 2009 jika harganya yang sepadan pada tahun 2004
ialah RM25.
[4 marks]
[4 markah]
7. Diagram shows a quadrilateral KLMN.
Rajah menunjukkan sebuah sisi empat KLMN.
Given that LK = 7 cm, LM = 10 cm, KN = 6 cm, LNM = 44° and the area of the KLN is 20
cm2 with LKN is acute. Calculate,
Diberi bahawa LK = 7 cm, LM = 10 cm, KN = 6 cm, LNM = 44° dan luas bagi KLN ialah
20 cm2 dengan LKN ialah sudut tirus. Hitung,
(a) LKN,
(b) the length, in cm, of LN,
panjang, dalam cm,bagi LN,
(c) MLN,
(d) the area, in cm2, of the LMN,
luas, dalam cm2, bagi LMN,
(e) a triangle LN’M has the same measurements as those given for triangle LNM, that is
LM = 10 cm and LN’ = LN but which is different in shape to triangle LNM. Sketch the triangle
LN’M.
segi tiga LN’M mempunyai ukuran yang sama seperti segi tiga LNM, iaitu LM = 10 cm dan
LN’ = LN tetapi mempunyai bentuk yang berlainan daripada segi tiga LNM. Lakarkan
segitiga LN’M.
[10 marks]
[10 markah]
44°
K
L
M
N
7 cm
6 cm
10 cm
5. MODUL SUPER SCORE SBP 2014
Jawapan/Answer :
No Answer
1
x = 1.443, – 0.693; y = –1.886, 2.386
2
4
3
1
x
a PR PS
SR
y x
b ) QS 5 x
4
y
c QR QS
SR
x y
4 4
)
4
)
5
a) 0.3487
b) 0.3203
6
a) h = 112, k = RM 2.58
a) 114.37
b) (i) 171.56 (ii) 42.89
7
(a) 72.25° or 72° 15’ (b) 7.7063
(c) 103.63° or 103° 38’ (d) 37.4457
(e) M
N’
L
N
Answer 3:
(a)
x 2 3 4 5 6 8
y
x
3.70 4.00 4.40 4.70 5.20 5.80
Y =
y
, X = x
x
π 2π
x
y
0
y
2
Number of solution = 1
6. MODUL SUPER SCORE SBP 2014
y
y
10.00
9.00
8.00
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
2 ax
b
x
ax
2
2
bx
a
b
a
b
y
5.80 3.70
0 1 2 3 4 5 6 7 8 9
y =
2
+
a
x
=
x
+
ax
x
= ( )
2
x +
a
Y = mX + c
m =
2
, c =
a
x
x
y-intercept, c = 3.00
Gradient, m =
8 2
= 0.35
7. MODUL SUPER SCORE SBP 2014
(b)(i) m =
a
2
0.35 =
a
2
a = 0.7
(b)(ii) c =
b
a
3.00 =
b
0.7
b = 2.1
b(iii) When x = 2.4
y
x
= 3.85
y
4.2
= 3.85
y = 9.24