Paper 2. - Siglap Secondary School

SIGLAP SECONDARY SCHOOL
Go Forth with Wisdom and Courage
2015 EOY Revision Worksheet (Paper 2)
3NA
Name: __________________________ (
) Class: __________ Date: _______________
Standard Form
Question 1
Evaluate and correct
(5.6 × 10 3 ) −2
to 3 significant figures, in standard form.
2.2 × 10 − 4
Question 2
Express 0.00387 in standard form.
Question 3
Write 55 billion in standard form.
[Answer Key]
1. 1.45 × 10 −4
2. 3.87 × 10 −3
3. 5.5 × 1010
4. (a) 6.0 ×1011 bytes
(b) 210500 documents
Question 4
The harddisk space in a laptop is 60 gigabytes.
(a) Write 60 gigabytes using standard form.
(b) The average size of a document is 2.85 megabytes. How many documents can be
stored in the harddisk of the laptop? Give your answer correct to the nearest 100
documents.
Simple Interest / Monthly installment
Question 1
The cash price of a plasma TV was $5500. Mr Lim bought the TV on a hire purchase
scheme by paying an initial deposit of 20% of the cash price. The remaining amount was
charged with simple interest at 4% per annum, paid in 24 equal monthly instalments,
Find
(a) the amount of initial deposit Mr Lim paid.
(b) how much more Mr Lim paid for the TV when paying by the hire purchase scheme
as compared to paying in cash.
(c) the amount of monthly instalments.
Question 2
The cash price of a leather sofa set is S$3600. Karthik bought the sofa set by hire
purchase. He paid a 20% deposit and the rest by monthly instalments over 2 years.
The bank charges a fixed interest rate of 2.25% per annum.
(a) How much is each monthly instalment?
(b) What is the hire purchase price of the leather sofa set?
Page | 1
Question 3
Alvin bought a car at the price of $64 000 from a car dealer. He paid a down payment of
20% and paid the balance in equal monthly installments at an interest rate of 8% per
annum. Calculate the monthly installment he has to pay if his loan period is five years.
[Answer Key]
1. (a) $1100
2. (a) $125.40
3. $1194.6
(b) $352
(c) $198
(b) $3729.60
Algebra (factorisation)
Question 1
Factorize x 2 − 7 x + 12 completely.
Question 2
Factorise v 2 − 49 .
Question 3
Factorise completely:
p² – 4q²
Question 4
Factorise 2 y 2 − 128 .
[Answer Key]
1. ( x − 3)( x − 4)
2. ( y + 7 )( y − 7 )
4. ( p + 2q )( p − 2q )
2 ( y + 8)( y − 8)
5. 6. 7. 8. (n + 3)(2 − m)
(a − b)( x + 2 y)
(2a − 3)(b + c)
(2m + 3n)(4y + 5x)
3. Question 5
Factorise 2n + 6 − mn − 3m completely.
Question 6
Factorise ax − bx + 2ay − 2by completely.
Question 7
Factorise 2ab − 3b + 2ac − 3c completely.
Question 8
Factorise 8my + 12ny + 10mx + 15nx completely.
Algebra (Simultaneous Equation)
Question 1
Solve the simultaneous equations.
2 x − 3 y = 15
3x − 7 y = 27
[Answer Key]
1. x = 4.8, y = −1.8
2.
Question 2
Solve the simultaneous linear equations.
1
x = 1 , y = −3
2
2 x − 3 y = 12
4x + y = 3
Page | 2
Algebra (Quadratic Equation)
Question 1
Solve the equation 4 x 2 − 8 x + 1 = 0 by using quadratic formula, giving your answer
correct to 3 significant figures.
[Answer Key]
Question 2
Solve 2 x 2 − 2 x = 60 .
1. 1.87 or 0.134
2. − 5, 6
3. 0.5 or 2
4. b) AB = 13.9 cm
c) 118cm 2
Question 3
Solve 2 y 2 − 5 y + 2 = 0 .
BC = 16.9 cm
Question 4
The diagram shows a triangle ABC. The length of AB is x cm, BC is (x + 3) cm, AC is
(x + 8) cm and angle B is 90° .
(a) Use Pythagoras’ theorem to show that x 2 − 10 x − 55 = 0 .
(b) Find the lengths of AB and BC. Give your answer rounded to 3 significant figures.
(c) Find the area of triangle ABC. Give your answer rounded to the nearest whole number.
A
C
B
Similarity and congruency
Question 1
The diagram below shows two similar figures, PQRA and
BCDA. PQ = 21 cm,
CD = 18 cm, QR = 27 cm,
∠CBA = 122°, ∠BAD = x°, ∠QRA = 62°, ∠PQR = 58° .
21
Find
(a) the length BC,
27
18
(b) the value of x,
(c) PB
, express your answer as a fraction in its lowest
PA
term.
Page | 3
Question 2
W
18 cm
X
12cm
D
Z
F
G
6 cm
Y
E
Given that WXYZ is similar to DEFG.
(a) Determine the value of ∠GDE .
(b) Find the length DG.
Question 3
In the figure below ΔPQR is similar to ΔABC . Given that PQ = 18 cm, QR = 12 cm,
AC = 7 cm, BC = 8 cm and ∠PRQ = 72° and ∠RPQ = 54°. Find the values of x , y
and z.
P
A
8
B
18
x
z
7
C
R
12
72°
y
Q
[Answer Key]
1.
(a) 14
(b) 118
(c)
1
3
2. a) 18
b) 4cm
3. z = 72
y = 10.5 cm
x= 12 cm
Page | 4
Mensuration (volume and surface area)
Question 1
A cone has a circular base of radius 3 cm and a height of
6 cm.
Calculate
(a) the slant height, l of the cone.
(b) the total surface area of the cone.
l
6
3
Question 2
The diagram below shows a solid right circular cone. V is the
vertex of the cone, P is a
point on the circumference of the base and O is the center of the
base. The height of the
cone is 12 cm and radius of the base is 9 cm.
(a) Find the length of VP.
(b) Find, in terms of π , the volume of the solid cone.
V
O
9 cm
P
[Answer Key]
1. (a) 6.71 cm
2. (a) 15 cm
(b) 91.5 cm
(b) 324π
Trigonometry
Question 1
In the diagram, PQR is a straight line,
∠QRS = 90°, ∠SQR = 72.5° , PS = 20 cm and
SR = 15 cm.
Find
(a) PR,
(b) x,
(c) QR.
Page | 5
Question 2
In the diagram below, DC = 4 m, CB = 13 m and
∠ACB = 74° .
(a) Show that AB = 45.3 m, correct to 3 significant
figures.
(b) Find AC.
(c) Find angle ADC.
A
74o
D 4m
C
13 m
Question 3
Points P, Q, R, S lie on a horizontal ground. PQ = 280 m, SR = 250 m,
and ∠QPR = 36° , ∠PSR = 47° and
P
∠SPR = 70° .
o
70
Calculate
(a) the length of PR,
(b) the length of QR,
(c) the area of triangle PSR.
36o
B
250
Q
47o
S
[Answer Key]
1. (a) 13.2
2. (b) 47.2 m
3. (a) 222 m
(b) 48.6°
(c) 69.4o
(b) 148 m
285
R
(c) 4.73
(c) 28.2 m2
Coordinate geometry
Question 1
A line passes through the points A(1, 4) and B(4, − 8) , find
(a) the length of the line segment
AB.
[Answer Key]
(b) the gradient of the line AB.
1. (a) 12.4 units
(b) − 4
(c) y = −4 x + 8
(c) the equation of the line AB.
2.
1
5
1
(a) −
(b) y = − x + or 2 y = − x + 5
2
2
2
(c) 6.71 units
Question 2
Given that point A(−1, 3) and point B(5, 0) lie on a straight line. Find
(a) the gradient of the line.
(b) the equation of the line.
(c) the length of the line.
Page | 6
Quadratic Graphs
Question 1
Answer the whole of this question on a single sheet of graph paper.
The table below shows the corresponding values of x and y for the function
y = x 2 − 4x − 5.
x
y
−2
7
−1
0
0
−5
1
p
2
−9
3
−8
4
−5
5
0
6
7
(a) Calculate the value of p.
(b) Draw the graph of y = x 2 − 4 x − 5 for − 2 ≤ x ≤ 6 . Use the scale of 2 cm to 1 unit on
the horizontal x-axis and 1 cm to 1 unit on the vertical y-axis.
(c) Use your graph to find the values of x when y = −1.
(d) By drawing a suitable tangent, find the gradient of the graph when x = 4.
Question 2
Answer the whole of this question on a single sheet of graph paper.
The variables x and y are connected by the equation y = −2 x 2 + 5 x − 2 .
Some corresponding values of x and y are given in the following table.
x
y
−2
− 20
−1
p
0
−2
1
1
2
0
3
q
4
− 14
(a) Calculate p and q.
(b) Using a horizontal scale of 2 cm to represent 1 unit, and a vertical scale of 1 cm to
represent 1 unit, draw the graph y = −2 x 2 + 5x − 2 for − 2 ≤ x ≤ 4 .
(c) From your graph
(i) state the minimum value of − 2 x 2 + 5 x − 2 .
(ii) find the value of y when x = 3.3.
(iii) write down the solutions of the equation − 2 x 2 + 5 x − 2 = 0 .
[Answer Key]
1. (c) − 0.9 or 4.9
2. (a) p = −9, q = −5
(d) 3
(c) (i) 1.2
(ii) − 8
x = 0.5, 2
Page | 7