hots contoh non rutin pdf

8/12/2019 Hots Contoh Non Rutin PDF

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CONTOH SOALAN HOTS NON RUTIN

SEKOLAH MENENGAH SAINS TELUK INTAN, PERAK

QUESTION 1

Table 1 shows two functions,and .

TABLE 1

A new function, is defined such that

Express in terms of

[2 marks]


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QUESTION 2

Find all the possible values of in the equation

[2 marks]


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QUESTION 3

A quadratic function is defined as

where , and are constants, such that , and .Determine the quadratic function.

[2 marks]


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QUESTION 5

Find the values of and in the following simultaneous equations.

[2 marks]


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QUESTION 6

Table 2 shows four equations of straight lines.

TABLE 2

The straight lines are drawn on a Cartesian coordinate. The pairs of these lines intersect each other

at four distinct points. These points are connected to form a quadrilateral.

Find the area, in unit, of the quadrilateral formed.

[2marks

]


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QUESTION 8

Diagram 1 shows a circle with centre .

DIAGRAM 1

Line is the diameter of the circle with the length of cm. Line is a chord of the circle. It isgiven that the angle is

12

rad.

Find the length, in cm, of the major arc

, in term of .

[2 marks]

cm


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QUESTION 9

The trianglehas all distinct integer sides. The length of sidesand are cm and cmrespectively. It is given that

2

3.

Find the length, in cm, of the sideof triangle.

[2 marks]


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QUESTION 10

A book is first sold with a certain price in the year 2003. In the year 2005, the price of the book

increases by from the year 2003. In the year 2007, the price of the book decreases by from the year 2005. In the year 2009, the price of the book increases by

from the year 2007.

Finally, in the year 2011, the price of the book decreases by from the year 2009.Determine the price index of the book in the year 2011 based on the year 2003.

[2marks

]


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QUESTION 11

A polynomial functionis given by

Using differentiation, find the coordinate of all turning point of the curve.Hence, determine whether the turning points are the maximum or minimum points of the curve.

[5 marks]


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QUESTION 12

Diagram 2 shows a right cone with vertical height of cm and a base diameter of cmrespectively.

DIAGRAM 2

Water is poured into the cone at the rate of cm s. At a certain time, the vertical height andthe surface diameter of the water in the cone reach cm and cm respectively, where and arevariables.

Using differentiation, find the instantaneous rate of change of the vertical height of water in the

cone, in cm s, when the vertical height of the water is cm.

[5 marks]

cm

cm

cm

cm


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JAWAPAN

QUESTION 1

By taking a closer look,

Thus, is actually the inverse function of. Hence,

This is also true for anyand , where is any positive integer. Simplifying , Thus,

QUESTION 2

Rearranging the terms in the equation,

Factorising the term in the equation, Factorising the equation completely,


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Thus,

QUESTION 3

Substituting all values of and, ...(1) ...(2) ...(3)From equation (1),

Substituting in equations (2) and (3), ...(4)

...(5)Subtracting equation (1) from equation (2),

From equation (4),

For ,

Thus,


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QUESTION 4

From the equation,

Since both equations have , thus, From these equations, taking a linear equation and a non-linear equation,

Substituting in another equation,

Substituting

in the equation,

Thus,


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QUESTION 5

Treating both equation as quadratic equations,

Comparing both sides of equations,

Solving both equations,

Thus,

QUESTION 6

Sketching the graph,

Let the quadrilateral be.


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Pointlies on the -axis. So, pointis . For point ,

So, point is .For point ,

So, point is .

For point ,

So, point is .

Using area formula,

Thus, the area of quadrilateralis unit.

QUESTION 7

From the standard deviation,

Since and are the only perfect squares whose sum is , and , thus


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QUESTION 8

Since and are the radii of the circle, forms an isosceles triangle. Thus,

So, for minor arc , Thus, for major arc ,

The radius of the circle is cm.Using formula,

Thus, the length of major arc

is

cm.

QUESTION 9

Since 2

3, there are two possible values for .

Using Cosine Rule for both values of , cm cmSince the value of sideis integer, thus, the length of sideis cm.


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QUESTION 11

Using differentiation,

For any turning point, the gradient is always . Using factorisation,

When

2

1 ,

When , When ,

Thus, the coordinate of the turning points are

2

1

16

5 , and .Using differentiation,


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When 2

1 ,

2

1

2

1

2

1

Thus,

2

1

16

5 is a maximum point.When ,

Thus, is a minimum point.When ,

Thus, is a maximum point.

21

165

and

are maximum points,

while is a minimum point.


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QUESTION 12

From the situation, there are two variables, and involved. However, this question deals about

. Thus, variable

must be eliminated.

Taking a closer look, variables and increases in a constant ratio. From the part of the cone,

Thus, using ratio,

Using formula of cone,

Substituting in the equation,

Thus, the volume of water in the cone is given by

Using differentiation,

cm

cm

cm

cm


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Substituting in the equation,

When ,

Using chain rule,

From chain rule,

Thus, the rate of change of vertical height of water in the cone is cm s.

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