AS Maths Test.pdf
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This document contains 11 multi-part math problems involving geometry, trigonometry, and algebra. The problems include finding areas and coefficients in polynomial expansions, solving equations, graphing functions, and expanding binomial expressions. Diagrams are provided to illustrate some of the geometry problems.
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![1 The coefficient of x3 5
A B
C
D
Y X
7 8
in the expansion of 1 − px
6
cm E
D
C
B
A
O
1.8
rad
The diagram shows a major arc AB of a circle with centre O and radius 6 cm.
Points C and D on OAand OB respectively are such that the
line AB is a tangent at E to the arc CED of a smaller circle
alsowith centre O. Angle COD = 1.8 radians.
(i) Find the radius of the arc CED, correct to 3 significant figures. [2]
(ii) Find the area of the shaded region. [4]
0
1 +
x
2
1n
2
10cm
D
C
B
1.2 rad
A O
The diagram shows a metal plate ABCD made from two parts.
The part BCD is a semicircle.
Thepart DAB is a segment of a circle with centre O
and radius 10 cm. Angle BOD is 1.2 radians.
The radius of the semicircle is 5.646 cm, correct to 3 decimal places.
θ θ
θ
+ θ θ θ θ
+
−
≡
−
sin
sin cos
cos
sin cos
1
sin cos
.
2 2
ii Hence solve the equation
sin
sin cos
cos
sin cos
3,
θ
θ θ
θ
+ θ θ
+
−
= for 0 360 .
θ
f : 5 3cos
1
2
x x is defined for π
0 2
x
° °
is −2160.
Find the value of the constant p. [3]
In the diagram, CXD is a semicircle of radius 7 cm with centre A
and diameter CD.
The straight line YABX is perpendicular to CD, and the arc CYD
ispartof a circle with centre B and radius 8 cm. Find
the total area of the region enclosed by the two arcs. [5]
2
[3]
[4]
4 The function → +
θ
3 i Show that
7 0
2
x x for 0 x 360 .
ii Hence find the solution of the equation θ θ
+
4sin − =
1
2
8cos
1
2
7 0
2
for 0 360 .
5 i Solve the equation 4sin + −
8cos =
3).
1 1
x − =
− −
6 Find the value of x satisfying the equation sin ( 1) tan ( [3]
7
8 In the expansion of 3 − 2x
9
(ii) Find the perimeter of the metal plate. [3]
(iii) Find the area of the metal plate. [3]
, the coefficient of x is 7.
Find the value of the constant n andhence find the coefficient of x
π
O
–1
1
2
3
–π 2π
y
y = a + bsin x
x
π
1
2
– –
1
–π
2
– –
3π
2
3
2
– π
The diagram shows part of the graph of = + sin
10
.
i Solve the equation f(x) 7
= , giving your answer correct to 2 decimal places. [3]
° °
θ [2]
° ° [4]
11 a Find the first three terms, in ascending powers of y, in the expansion of (1+ )4
5 2 2
x x , find the coefficient of 5 2 )
2 4
x x .
. [4]
y a b x.
State the values of the constants a and b. [2]
[2]
[3]
y .
b By replacing y with − x in the expansion of (1+ −
4](https://image.slidesharecdn.com/asmathstest-231010035414-3cc60616/85/AS-Maths-Test-pdf-1-320.jpg)
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'Land uses,' which are determined by both human activities and the physical characteristics of the
land.
The utilization of land is impacted by human needs and environmental factors. In countries
like India, rapid population growth and the emphasis on extensive resource exploitation can lead
to significant land degradation, adversely affecting the region's land cover.
Therefore, human intervention has significantly influenced land use patterns over many
centuries, evolving its structure over time and space. In the present era, these changes have
accelerated due to factors such as agriculture and urbanization. Information regarding land use and
cover is essential for various planning and management tasks related to the Earth's surface,
providing crucial environmental data for scientific, resource management, policy purposes, and
diverse human activities.
Accurate understanding of land use and cover is imperative for the development planning
of any area. Consequently, a wide range of professionals, including earth system scientists, land
and water managers, and urban planners, are interested in obtaining data on land use and cover
changes, conversion trends, and other related patterns. The spatial dimensions of land use and
cover support policymakers and scientists in making well-informed decisions, as alterations in
these patterns indicate shifts in economic and social conditions. Monitoring such changes with the
help of Advanced technologies like Remote Sensing and Geographic Information Systems is
crucial for coordinated efforts across different administrative levels. Advanced technologies like
Remote Sensing and Geographic Information Systems
9
Changes in vegetation cover refer to variations in the distribution, composition, and overall
structure of plant communities across different temporal and spatial scales. These changes can
occur natural.
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Syllabus
Chapter-1
Introduction to objective, scope and outcome the subject
Chapter 2
Introduction: Scope and Specialization of Civil Engineering, Role of civil Engineer in Society, Impact of infrastructural development on economy of country.
Chapter 3
Surveying: Object Principles & Types of Surveying; Site Plans, Plans & Maps; Scales & Unit of different Measurements.
Linear Measurements: Instruments used. Linear Measurement by Tape, Ranging out Survey Lines and overcoming Obstructions; Measurements on sloping ground; Tape corrections, conventional symbols. Angular Measurements: Instruments used; Introduction to Compass Surveying, Bearings and Longitude & Latitude of a Line, Introduction to total station.
Levelling: Instrument used Object of levelling, Methods of levelling in brief, and Contour maps.
Chapter 4
Buildings: Selection of site for Buildings, Layout of Building Plan, Types of buildings, Plinth area, carpet area, floor space index, Introduction to building byelaws, concept of sun light & ventilation. Components of Buildings & their functions, Basic concept of R.C.C., Introduction to types of foundation
Chapter 5
Transportation: Introduction to Transportation Engineering; Traffic and Road Safety: Types and Characteristics of Various Modes of Transportation; Various Road Traffic Signs, Causes of Accidents and Road Safety Measures.
Chapter 6
Environmental Engineering: Environmental Pollution, Environmental Acts and Regulations, Functional Concepts of Ecology, Basics of Species, Biodiversity, Ecosystem, Hydrological Cycle; Chemical Cycles: Carbon, Nitrogen & Phosphorus; Energy Flow in Ecosystems.
Water Pollution: Water Quality standards, Introduction to Treatment & Disposal of Waste Water. Reuse and Saving of Water, Rain Water Harvesting. Solid Waste Management: Classification of Solid Waste, Collection, Transportation and Disposal of Solid. Recycling of Solid Waste: Energy Recovery, Sanitary Landfill, On-Site Sanitation. Air & Noise Pollution: Primary and Secondary air pollutants, Harmful effects of Air Pollution, Control of Air Pollution. . Noise Pollution Harmful Effects of noise pollution, control of noise pollution, Global warming & Climate Change, Ozone depletion, Greenhouse effect
Text Books:
1. Palancharmy, Basic Civil Engineering, McGraw Hill publishers.
2. Satheesh Gopi, Basic Civil Engineering, Pearson Publishers.
3. Ketki Rangwala Dalal, Essentials of Civil Engineering, Charotar Publishing House.
4. BCP, Surveying volume 1
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- 1. 1 The coefficient of x3 5 A B C D Y X 7 8 in the expansion of 1 − px 6 cm E D C B A O 1.8 rad The diagram shows a major arc AB of a circle with centre O and radius 6 cm. Points C and D on OAand OB respectively are such that the line AB is a tangent at E to the arc CED of a smaller circle alsowith centre O. Angle COD = 1.8 radians. (i) Find the radius of the arc CED, correct to 3 significant figures. [2] (ii) Find the area of the shaded region. [4] 0 1 + x 2 1n 2 10cm D C B 1.2 rad A O The diagram shows a metal plate ABCD made from two parts. The part BCD is a semicircle. Thepart DAB is a segment of a circle with centre O and radius 10 cm. Angle BOD is 1.2 radians. The radius of the semicircle is 5.646 cm, correct to 3 decimal places. θ θ θ + θ θ θ θ + − ≡ − sin sin cos cos sin cos 1 sin cos . 2 2 ii Hence solve the equation sin sin cos cos sin cos 3, θ θ θ θ + θ θ + − = for 0 360 . θ f : 5 3cos 1 2 x x is defined for π 0 2 x ° ° is −2160. Find the value of the constant p. [3] In the diagram, CXD is a semicircle of radius 7 cm with centre A and diameter CD. The straight line YABX is perpendicular to CD, and the arc CYD ispartof a circle with centre B and radius 8 cm. Find the total area of the region enclosed by the two arcs. [5] 2 [3] [4] 4 The function → + θ 3 i Show that 7 0 2 x x for 0 x 360 . ii Hence find the solution of the equation θ θ + 4sin − = 1 2 8cos 1 2 7 0 2 for 0 360 . 5 i Solve the equation 4sin + − 8cos = 3). 1 1 x − = − − 6 Find the value of x satisfying the equation sin ( 1) tan ( [3] 7 8 In the expansion of 3 − 2x 9 (ii) Find the perimeter of the metal plate. [3] (iii) Find the area of the metal plate. [3] , the coefficient of x is 7. Find the value of the constant n andhence find the coefficient of x π O –1 1 2 3 –π 2π y y = a + bsin x x π 1 2 – – 1 –π 2 – – 3π 2 3 2 – π The diagram shows part of the graph of = + sin 10 . i Solve the equation f(x) 7 = , giving your answer correct to 2 decimal places. [3] ° ° θ [2] ° ° [4] 11 a Find the first three terms, in ascending powers of y, in the expansion of (1+ )4 5 2 2 x x , find the coefficient of 5 2 ) 2 4 x x . . [4] y a b x. State the values of the constants a and b. [2] [2] [3] y . b By replacing y with − x in the expansion of (1+ − 4