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If sec θ - tan θ = m, what is the value of sec θ + tan θ?
If sec θ - tan θ = m, what is the value of sec θ + tan θ?
What is the probability of randomly selecting a prime number from the data set 1, 4, 7, 9, 16, 21, 25 after removing all even numbers?
What is the probability of randomly selecting a prime number from the data set 1, 4, 7, 9, 16, 21, 25 after removing all even numbers?
Given data x1, x2,..., with respective frequencies f₁, f₂,..., what does the expression Σ n (xi - x)² / Σ fi represent?
Given data x1, x2,..., with respective frequencies f₁, f₂,..., what does the expression Σ n (xi - x)² / Σ fi represent?
If the zeroes of the polynomial x² + px + q are twice the zeroes of the polynomial 4x² – 5x – 6, what is the value of p?
If the zeroes of the polynomial x² + px + q are twice the zeroes of the polynomial 4x² – 5x – 6, what is the value of p?
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If the points (3, -5) and (x, -5) are 15 units apart, what are the possible values for x?
If the points (3, -5) and (x, -5) are 15 units apart, what are the possible values for x?
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What is the ratio of the surface areas of a sphere to two hemispheres taken together?
What is the ratio of the surface areas of a sphere to two hemispheres taken together?
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When two dice are rolled, what is the probability of the sum being 2, 3, or 5?
When two dice are rolled, what is the probability of the sum being 2, 3, or 5?
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If the center of a circle is (2, 0) and one end of the diameter is (6, 0), what are the coordinates of the other end?
If the center of a circle is (2, 0) and one end of the diameter is (6, 0), what are the coordinates of the other end?
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What is the probability of drawing the queen of hearts after losing a black card from a pack of 52 playing cards?
What is the probability of drawing the queen of hearts after losing a black card from a pack of 52 playing cards?
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If two tangents are drawn from the ends of a diameter of a circle, what can be concluded about the relationship of these tangents?
If two tangents are drawn from the ends of a diameter of a circle, what can be concluded about the relationship of these tangents?
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What is the sum of 2√2 cos 45° sin 30° and 2√3 cos 30°?
What is the sum of 2√2 cos 45° sin 30° and 2√3 cos 30°?
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What can be derived from the statement that a polynomial touches the x-axis at only one point?
What can be derived from the statement that a polynomial touches the x-axis at only one point?
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In the quadrilateral ABCD where diagonals bisect angles B and D, which conclusion can be drawn?
In the quadrilateral ABCD where diagonals bisect angles B and D, which conclusion can be drawn?
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If a circle is inscribed in quadrilateral ABCD, and given certain length conditions, how can the length DC be determined?
If a circle is inscribed in quadrilateral ABCD, and given certain length conditions, how can the length DC be determined?
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What ratio does the point (8/5, y) divide the line segment joining (1, 2) and (2, 3)?
What ratio does the point (8/5, y) divide the line segment joining (1, 2) and (2, 3)?
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What statement is true regarding the number 5 x 11 x 17 + 3 x 11?
What statement is true regarding the number 5 x 11 x 17 + 3 x 11?
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What is the value of k if the sum of the zeroes of the polynomial $p(x) = 2x² - k√2x + 1$ is $√2$?
What is the value of k if the sum of the zeroes of the polynomial $p(x) = 2x² - k√2x + 1$ is $√2$?
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If the probability of a player winning a game is 0.79, what is the correct probability of his losing the same game?
If the probability of a player winning a game is 0.79, what is the correct probability of his losing the same game?
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For which condition do the roots of the equation $ax² + bx + c = 0$ become real and equal?
For which condition do the roots of the equation $ax² + bx + c = 0$ become real and equal?
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Given an arithmetic progression (AP) with first term $a = 7$, nth term $a = 84$, and sum of first $n$ terms $S = 2093$, what is the value of n?
Given an arithmetic progression (AP) with first term $a = 7$, nth term $a = 84$, and sum of first $n$ terms $S = 2093$, what is the value of n?
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If two positive integers are expressed as $p = 18a²b⁴$ and $q = 20a³b²$, what is the LCM (p, q)?
If two positive integers are expressed as $p = 18a²b⁴$ and $q = 20a³b²$, what is the LCM (p, q)?
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What is the length of median AD in triangle ABC with vertices A(5, -6), B(6, 4), and C(0, 0)?
What is the length of median AD in triangle ABC with vertices A(5, -6), B(6, 4), and C(0, 0)?
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If the first term in an AP is equal to 7 and the sum of the first n terms is equal to 2093, what is a feasible relationship between n and the common difference?
If the first term in an AP is equal to 7 and the sum of the first n terms is equal to 2093, what is a feasible relationship between n and the common difference?
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In the context of the roots of the equation $ax^2 + bx + c = 0$, if $a = 0$, which consequence does this lead to?
In the context of the roots of the equation $ax^2 + bx + c = 0$, if $a = 0$, which consequence does this lead to?
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What is the radius of a hollow right circular cylinder if the difference between the outer and inner radii is 1 cm and the volume of the metal used is 176 cm³?
What is the radius of a hollow right circular cylinder if the difference between the outer and inner radii is 1 cm and the volume of the metal used is 176 cm³?
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If an arc of radius 21 cm subtends an angle of 60°, what is the length of the arc?
If an arc of radius 21 cm subtends an angle of 60°, what is the length of the arc?
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In an arithmetic progression (AP) where the sum of the first and eighth terms is 32 and their product is 60, which of the following pairs represents a possible first term and common difference?
In an arithmetic progression (AP) where the sum of the first and eighth terms is 32 and their product is 60, which of the following pairs represents a possible first term and common difference?
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According to the properties of triangles, which statement is correct when a line is drawn parallel to one side?
According to the properties of triangles, which statement is correct when a line is drawn parallel to one side?
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What is the expression derived from the given problem regarding the number of tiles if the side length of each tile is increased by 1 unit?
What is the expression derived from the given problem regarding the number of tiles if the side length of each tile is increased by 1 unit?
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In the context of BINGO, if there are 75 balls, which mathematical concept is primarily demonstrated through the cancellation of numbers on the card?
In the context of BINGO, if there are 75 balls, which mathematical concept is primarily demonstrated through the cancellation of numbers on the card?
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What is the formula to find the area of the minor segment created by a chord when a circle's arc subtends an angle?
What is the formula to find the area of the minor segment created by a chord when a circle's arc subtends an angle?
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What is the angle of elevation from point P to the top of the pole if the heights involved are 6 m and the angle of depression is 45°?
What is the angle of elevation from point P to the top of the pole if the heights involved are 6 m and the angle of depression is 45°?
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Study Notes
Latest Examination Paper, 2024 - Set 4
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General Instructions:
- The paper has 38 compulsory questions.
- Divided into five sections (A, B, C, D, E).
- Section A: 18 multiple choice (MCQs), 2 Assertion-Reason questions.
- Section B: 5 short answer questions (2 marks each).
- Section C: 6 short answer questions (3 marks each).
- Section D: 4 long answer questions (5 marks each).
- Section E: 3 case study questions (4 marks each), internal choice provided.
- Calculators are not allowed.
- Constants are given; π = 22/7 unless otherwise stated.
- Neat diagrams where required
Section A
- Question 1: Finding the value of 'k' in polynomial with given condition.
- Question 2: Calculating the probability of losing a game, given a win probability.
- Question 3: Relation between the roots of a quadratic equation with real, equal roots.
- Question 4: Finding the nth term and sum of terms in an arithmetic progression (AP)
Section B
- Question 21: Solving a system of linear equations.
- Question 22: Probability of drawing a queen of hearts, given a missing card from a standard deck
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Question 23(a): Evaluating trigonometric expressions,
- OR verifying a trigonometric identity
- Question 24: Proving similarity of triangles and properties of quadrilateral.
- Question 25: Proving that a given number is irrational. or establishing the given number is composite
Section C
- Question 26: Finding the ratio in which a point divides a line segment
Section D
- Question 32: Calculating arc length and area of a segment in a circle.
- Question 33: Finding the first term and common difference of an arithmetic progression (AP), and the sum of the first few terms.
- Question 34: Proving a theorem related to triangle and parallel lines.
- Question 35: Calculating height of a tower and distance
Section E
- Question 36: Solving a quadratic equation related to tiling a rectangular floor
- Question 37: Analyzing Bingo game data(including median and probabilities).
- Question 38: Finding the median and mode given the data (or solving a geometry problem related to circle and triangle).
Assertion-Reason Questions (Section A)
- Question 19: Parallel tangents drawn at the ends of a diameter.
- Question 20: Polynomial of degree n cannot be quadratic with only one root.
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Description
This examination paper comprises 38 compulsory questions and is divided into five sections covering a variety of topics. Students will encounter multiple choice questions, short answer questions, long answer questions, and case studies, with no calculators allowed. This paper assesses knowledge in key areas of mathematics and problem-solving skills.
