### SECTION: A (8 MARKS)
Question 1: Define rational number:
Answer:
A rational number is any number that can be expressed as the quotient or fraction [tex]\( \frac{p}{q} \)[/tex] of two integers, where [tex]\( p \)[/tex] is the numerator and [tex]\( q \)[/tex] (the denominator) is a non-zero integer.
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Question 2: Every natural number is a whole number (State true or false)
Answer:
True. Every natural number is indeed a whole number.
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Question 3: Write the coefficients of [tex]\( x^2 \)[/tex] in [tex]\( 2x + x^2 + x \)[/tex].
Answer:
The coefficient of [tex]\( x^2 \)[/tex] in the polynomial [tex]\( 2x + x^2 + x \)[/tex] is 1.
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Question 4: Write the degree of the polynomial [tex]\( 5x^2 + 4x^2 + 7x \)[/tex].
Answer:
To determine the degree of the polynomial [tex]\( 5x^2 + 4x^2 + 7x \)[/tex], first combine the like terms:
[tex]\[ 5x^2 + 4x^2 = 9x^2 \][/tex]
so the polynomial simplifies to:
[tex]\[ 9x^2 + 7x \][/tex]
The highest power of [tex]\( x \)[/tex] is 2, so the degree of the polynomial is 2.
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Question 5: What is the name of horizontal and the vertical lines drawn to determine the position of any point in the Cartesian plane?
Answer:
The horizontal line is called the x-axis, and the vertical line is called the y-axis.
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Question 6: Write the name of the point where these two lines intersect.
Answer:
The point where the x-axis and y-axis intersect is called the origin.
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Question 7: Find the surface area of a sphere of radius 10.5 cm.
Answer:
The formula for the surface area of a sphere is given by:
[tex]\[ A = 4\pi r^2 \][/tex]
Given the radius [tex]\( r = 10.5 \)[/tex] cm,
[tex]\[ A \approx 4 \pi (10.5)^2 \approx 1385.4423602330987 \text{ cm}^2 \][/tex]
So, the surface area of the sphere is approximately [tex]\( 1385.442 \)[/tex] cm[tex]\(^2\)[/tex].
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Question 8: Find the volume of a right circular cone with radius 6 cm and height 7 cm.
Answer:
The formula for the volume of a right circular cone is given by:
[tex]\[ V = \frac{1}{3} \pi r^2 h \][/tex]
Given the radius [tex]\( r = 6 \)[/tex] cm and height [tex]\( h = 7 \)[/tex] cm,
[tex]\[ V \approx \frac{1}{3} \pi (6)^2 (7) \approx 263.89378290154264 \text{ cm}^3 \][/tex]
So, the volume of the right circular cone is approximately [tex]\( 263.894 \)[/tex] cm[tex]\(^3\)[/tex].
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### SECTION: B (20 MARKS)
Question No. 9 to 17 carry 2 marks each.
(Questions in this section are to be asked by the user if they need solutions for them.)
