Sub. code 2022
NEB — GRADE X
CDC
Model Question
Optional Mathematics Question Paper CDC (Model Question)
The candidates are required to give their answers in their own words as far as practicable. The figures in the margin indicate full marks.
Pass Marks : 32
सबै प्रश्नको उत्तर दिनुहोस् । (Attempt All Questions)
This model question question paper is for Class 10 Optional Mathematics, CDC (subject code 2022), carrying full marks of 75 with a pass mark of 32, to be completed within 3 Hours. Answers with step-by-step solutions are available for every question below.
Group A
Objective Questions.
When solving graphically, the real roots correspond to ..................
The vertex of the parabola.
The y-intercept where the parabola crosses the Y-axis.
The x-intercepts where the parabola crosses the X-axis.
The axis of symmetry.
If function , which of the following is true?
Which of the following is the value of ?
Which of the following expressions correctly expresses ?
What kind of change occurs in the angle of elevation when an observer, while looking at the top of a tall tree standing on a plane surface, moves closer to that tree? Why?
As the distance between the observer and the tree decreases, the measure of the angle of elevation decreases.
As long as the height of the tree remains unchanged, the measure of the angle of elevation remains the same.
As long as the height of the tree remains constant and the distance between the base of the tree and the observer decreases, the measure of the angle of elevation increases.
When the height of the tree remains unchanged, the measure of the angle of elevation decreases.
The equation represents a circle. What is the diameter of the circle?
7
14
49
98
Two lines are perpendicular to each other. If one line has slope m, the slope of the other must be ..........
Two reflections are performed successively in the lines: and . Which point is invariant under the combined transformation?
Every point on
Every point on
Only the origin
Such a point does not exist
In if , then how much is the scalar product of two vectors that forms the sides of a right angle?
A function has equal left-hand and right-hand limits at , but is not defined. How should this function be described at $x=a$?
Continuous, because the left hand and right-hand limits are equal.
Continuous, because limits are more important than function values.
Discontinuous, because the function has no limit at .
Discontinuous, because continuity requires the functional value, the left-hand limit and the right-hand limit should be equal.
The Coefficient of Variation (CV) is used to compare two datasets. What does a higher CV indicate?
More consistent data
Greater variability
Lower mean
Higher median
Group B
The function and a polynomial are given.
Write the condition for to be a factor of .
Use rational root theorem to determine the possible roots of the polynomial .
Given a function and .
Find the composite function .
Convert into the vertex form .
Describe the combined transformation involved to transform the function into .
Matrices and are given.
Find .
Find .
The constraints are , , and . Show the feasible region on graph.
Given the identity .
How can you convert the given identity in the form of ?
If , show that:
.
From the top of a cliff of height 100 m, two points lying on the same straight line on the ground are observed. The angles of depression to these two points are 60° and 45°, respectively.
Draw a labelled diagram showing the height of cliff, the two points on the ground and angles of depression.
Find the distance between the two points on the ground.
Given a conditional identity:
Write in terms of sum or difference.
Verify the above identity if .
State any one possible reason why the identity cannot be verified for , and .
A straight line passes through the points A(1, 2) and B(5, 6).
Write the matrix that transforms the point into the point .
The line makes an acute angle with the line . Find the value of .
is an equation of a circle.
Write the equation of circle with centre and radius .
Find the centre and radius of the circle from the given equation.
Use two-point formula to find the equation of radius, where point lies on the circumference of the circle.
Points and are joined by a straight line.
A combined transformation is applied, where is reflection in the Y-axis and is the translation by vector . Find the images of the points and under this transformation.
Plot object and final image in the same graph paper.
The coordinates of vertices of triangle ABC are given in the figure alongside. D and E are midpoints of AB and AC, respectively.
Write the position vector of D in terms of position vectors of A and B.
Find the position vector of D in terms of and .
Prove by vector method:
The box plots below have shown the information about the battery life of Battery X and Battery Y.
Which battery has higher battery life in terms of median?
The coefficient of quartile deviation of battery Y is 0.098. Calculate the coefficient of quartile deviation of battery X.
A telecommunication company needs to choose between Battery X and Battery Y to power a remote signal tower. Based on the available information, which battery would you suggest to the company and why?
A function p(x) is defined as follows.
Define the continuity of a function.
Find the limit of the function p(x) when x approaches to 3.
Find p(3).
Find whether the function p(x) is continuous or discontinuous at x = 3. Justify your conclusion.
Group C
Cross Content Area
There is a triangle OAB with vertices , and , and a transformation matrix .
Find the coordinates of the image triangle O'A'B' under the transformation of triangle OAB by matrix M.
Find the slope of altitude of triangle OAB drawn from vertex O to AB.
Is M a singular matrix? If not, how do you make it singular?
Dolma claims that the transformation will always be same whether we use matrix M or . Do you agree with Dolma's statement? Justify with an example.
Shreya cuts a wooden cone in a way that it forms a conic section. She draws the outline of the edge of the conic section of the cone on a paper.
Name the shape that would be formed on the paper by the plane surface when the cone is cut in such a way that the cutting surface is inclined greater than semi vertical angle and less than 90°.
Shreya formed a semicircle ABC and found that the chords from any point B on the circumference of the semicircle to the end of diameter A and C always meet at right angle. Use the vector method to prove her statement.
Explain with reason, whether Shreya's claim would still hold if the point B lies inside the semicircle instead on the arc or not.
If , and units, calculate the value of x.
A hiker is climbing the hill. The height of the hill (h) and the horizontal distance (x) are given in meters by the function: . The slope of a hill is measured by .
Prove that:
The angle of the hill is such that . Hence, find the value of slope .
Using the inverse function , find the horizontal distance covered, if the hiker is at a height of 150 meters.
Bina claims, "If the angle made by a line with the positive direction of the X-axis doubles, then, the slope (inclination) of that line also doubles." Using and specific value of , verify her claim.
Department of Road wants to place a bus stop at position kilometers along a straight road. The table below shows how many residents live in each section of the road.
Length of section of the road (in meter) | Mid value (m) | Population (f) |
|---|---|---|
0–200 | 100 | 20 |
200–400 | 300 | 30 |
400–600 | 500 | 40 |
600–800 | 700 | 10 |
Department of Road measures how good a position is by calculating the total squared walking distance because a smaller value of gives a better position. It is found that the total squared walking distance can be represented by the function
.
Calculate the coefficient of variation of the residence distribution along the road.
Is the function a continuous function for all values of ?
Any calculated . With this value, will the function be continuous at 3.8?
Paper Overview & Analysis
CDC
Year
Model Question
Type
75
Full Marks
32
Pass Marks
3 Hours
Duration
58
Question Items
Question Type Breakdown
Group Breakdown