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Questions and Answers
What is the HCF of 12, 16, and 20?
What is the HCF of 12, 16, and 20?
What is the degree of the polynomial $ax^2 + bx + c$ where $a
eq 0$?
What is the degree of the polynomial $ax^2 + bx + c$ where $a eq 0$?
Which condition ensures that the system of equations has a unique solution?
Which condition ensures that the system of equations has a unique solution?
When does a quadratic equation have two equal real roots?
When does a quadratic equation have two equal real roots?
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What is the 11th term of the arithmetic progression defined by $−3, 2, 2, ...$?
What is the 11th term of the arithmetic progression defined by $−3, 2, 2, ...$?
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What is the distance between points $P(-7, 7)$ and $Q(-2, -3)$?
What is the distance between points $P(-7, 7)$ and $Q(-2, -3)$?
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In the equation $ax + b = 0$, what defines the existence of a unique solution?
In the equation $ax + b = 0$, what defines the existence of a unique solution?
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What represents the discriminant in a quadratic equation $ax^2 + bx + c = 0$?
What represents the discriminant in a quadratic equation $ax^2 + bx + c = 0$?
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What is the highest common factor (HCF) of the numbers 12, 16, and 20?
What is the highest common factor (HCF) of the numbers 12, 16, and 20?
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What is the value of the determinant in the given linear equations if $a_1 = a_2$, $b_1 = b_2$, and $c_1 \neq c_2$?
What is the value of the determinant in the given linear equations if $a_1 = a_2$, $b_1 = b_2$, and $c_1 \neq c_2$?
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What condition indicates that the quadratic equation $ax^2 + bx + c = 0$ has two distinct real roots?
What condition indicates that the quadratic equation $ax^2 + bx + c = 0$ has two distinct real roots?
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If the roots of a quadratic equation are equal, what can be said about the value of $b^2 - 4ac$?
If the roots of a quadratic equation are equal, what can be said about the value of $b^2 - 4ac$?
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In a linear system represented by equations $a_1 x + b_1 y + c_1 = 0$ and $a_2 x + b_2 y + c_2 = 0$, when are the two lines parallel?
In a linear system represented by equations $a_1 x + b_1 y + c_1 = 0$ and $a_2 x + b_2 y + c_2 = 0$, when are the two lines parallel?
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Which of the following values of $a$, $b$, and $c$ will lead to no real roots for the quadratic equation $ax^2 + bx + c = 0$?
Which of the following values of $a$, $b$, and $c$ will lead to no real roots for the quadratic equation $ax^2 + bx + c = 0$?
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Which form of the quadratic equation shows the relationship between the coefficients for a clearly defined vertex?
Which form of the quadratic equation shows the relationship between the coefficients for a clearly defined vertex?
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Which of the following statements is true regarding the equation $(x - 2)^2 + 1 = 2x - 3$?
Which of the following statements is true regarding the equation $(x - 2)^2 + 1 = 2x - 3$?
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What does the value of $c$ in the equation $ax^2 + bx + c = 0$ represent in a graph?
What does the value of $c$ in the equation $ax^2 + bx + c = 0$ represent in a graph?
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What is the common difference in the arithmetic progression represented by the series $P. 32, 12, -1, 2, -3$?
What is the common difference in the arithmetic progression represented by the series $P. 32, 12, -1, 2, -3$?
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What is the primary strategy for determining the nature of the roots of a quadratic equation?
What is the primary strategy for determining the nature of the roots of a quadratic equation?
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For an event $E$, what does $P(E̅) = 1 - P(E)$ represent?
For an event $E$, what does $P(E̅) = 1 - P(E)$ represent?
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What is the median in relation to the mean and mode according to the empirical relationship?
What is the median in relation to the mean and mode according to the empirical relationship?
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What is the formula for the distance between the points $P(x_1, y_1)$ and $Q(x_2, y_2)$?
What is the formula for the distance between the points $P(x_1, y_1)$ and $Q(x_2, y_2)$?
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What can be said about the common properties of all isosceles triangles?
What can be said about the common properties of all isosceles triangles?
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How many distinct tangents can a single circle have?
How many distinct tangents can a single circle have?
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What is the discriminant 𝐷 for a quadratic equation of the form $ax^2 + bx + c = 0$ with $a \neq 0$?
What is the discriminant 𝐷 for a quadratic equation of the form $ax^2 + bx + c = 0$ with $a \neq 0$?
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What is the angle-angle (AA) similarity criterion?
What is the angle-angle (AA) similarity criterion?
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The sum of the first $n$ terms of an Arithmetic Progression (A.P.), denoted as $S$, can be calculated using which formula?
The sum of the first $n$ terms of an Arithmetic Progression (A.P.), denoted as $S$, can be calculated using which formula?
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Which of the following statements is true about circles?
Which of the following statements is true about circles?
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What is the term used to describe the common point of a tangent and the circle it touches?
What is the term used to describe the common point of a tangent and the circle it touches?
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The sum of the probabilities of all the elementary events of an experiment is always:
The sum of the probabilities of all the elementary events of an experiment is always:
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Which statement accurately describes the tangent at any point of a circle?
Which statement accurately describes the tangent at any point of a circle?
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What is the formula for the curved surface area of a cylinder?
What is the formula for the curved surface area of a cylinder?
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The area of a sector of a circle is calculated using which formula?
The area of a sector of a circle is calculated using which formula?
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What is the curved surface area formula for a hemisphere?
What is the curved surface area formula for a hemisphere?
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What is the value of $\sin 0°$?
What is the value of $\sin 0°$?
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In an arithmetic progression with the first term $a = 5$, common difference $d = 3$, and last term $an = 50$, what is the value of $n$?
In an arithmetic progression with the first term $a = 5$, common difference $d = 3$, and last term $an = 50$, what is the value of $n$?
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If in triangle $ABC$, $DE || BC$ then what can be concluded about the segments created?
If in triangle $ABC$, $DE || BC$ then what can be concluded about the segments created?
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What are the coordinates of the point that divides the line segment joining $(−1,7)$ and $(4,−3)$ in the ratio 2:3?
What are the coordinates of the point that divides the line segment joining $(−1,7)$ and $(4,−3)$ in the ratio 2:3?
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If the points $A(6, 1)$, $B(8, 2)$, $C(9, 4)$, and $D(p, 3)$ form a parallelogram, what is the value of $p$?
If the points $A(6, 1)$, $B(8, 2)$, $C(9, 4)$, and $D(p, 3)$ form a parallelogram, what is the value of $p$?
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If $sin A = 4$, what can be concluded about the value of $cos A$?
If $sin A = 4$, what can be concluded about the value of $cos A$?
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Evaluate $sin 60° cos 30° + sin 30° cos 60°.
Evaluate $sin 60° cos 30° + sin 30° cos 60°.
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What is the radius of a circle if the length of the tangent from point A, which is 5 cm away from the center, is 4 cm?
What is the radius of a circle if the length of the tangent from point A, which is 5 cm away from the center, is 4 cm?
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What is the probability that Savita and Hamida will have the same birthday?
What is the probability that Savita and Hamida will have the same birthday?
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What is the probability of 'not E' if the probability of 'E' is 0.05?
What is the probability of 'not E' if the probability of 'E' is 0.05?
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In a bag containing 3 red balls and 5 black balls, what is the probability of drawing a red ball?
In a bag containing 3 red balls and 5 black balls, what is the probability of drawing a red ball?
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If a card is drawn from a well-shuffled deck of 52 cards, what is the probability that it will not be an ace?
If a card is drawn from a well-shuffled deck of 52 cards, what is the probability that it will not be an ace?
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What is the height of the tower if the angle of elevation from a point 30 m away is 30°?
What is the height of the tower if the angle of elevation from a point 30 m away is 30°?
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What can be concluded if $3 + \sqrt{5}$ is proven to be irrational?
What can be concluded if $3 + \sqrt{5}$ is proven to be irrational?
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If an observer 1.5 m tall is 28.5 m away from a chimney and sees the top at an angle of elevation of 45°, what is the height of the chimney?
If an observer 1.5 m tall is 28.5 m away from a chimney and sees the top at an angle of elevation of 45°, what is the height of the chimney?
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What is the area of a sector of a circle with a radius of 6 cm and an angle of 60°?
What is the area of a sector of a circle with a radius of 6 cm and an angle of 60°?
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What will be the last digit of $6n$ for any natural number n?
What will be the last digit of $6n$ for any natural number n?
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Study Notes
Exam Information
- Examination: High School Examination
- Subject: Mathematics
- Time: 3 hours
- Total Questions: 23
- Total Printed Pages: 8
- Maximum Marks: 75
Instructions
- All questions are compulsory
- Sub-questions 1-5: 1 mark each
- Questions 6-17: 2 marks each
- Questions 18-20: 3 marks each
- Questions 21-23: 4 marks each
Question 1 Multiple Choice
- HCF of (12, 16, 20): 4
- Degree of a linear polynomial: 1
- Condition for unique solution of linear equations: a₁/a₂ ≠ b₁/b₂ ≠ c₁/c₂
- Condition for equal real roots of a quadratic equation: b² - 4ac = 0
- 11th term of A.P. -3, 1/2, 2 ... : 22
- Distance between P(-7, 7) and Q(-2, -3): 5√5
Question 2 Fill in the blanks
- Discriminant of ax² + bx + c = 0: b² - 4ac
- Sum of first n terms of an A.P.: n/2(2a + (n-1)d)
- All circles are: Concentric
- Common point of tangent and circle: Point of tangency
- Sum of probabilities of all elementary events: 1
- Tangent at any point of a circle: Perpendicular to the radius through the point of contact
Question 3 Matching
- Curved surface area of hemisphere: 2πr²
- Curved surface area of cylinder: 2πrh
- Area of a sector of a circle: (θ/360)πr²
- Cot A: 1/Tan A
- Cosec² A: 1/Sin² A
- Sin 0°: 0
Question 4 True/False
- (x – 2)² + 1 = 2x – 3 is not a quadratic equation: False
- Common difference of A.P. 1/2, -3/2, -1/2, -1/2: is -1
- All isosceles triangles are similar: False
- Midpoint of A(3, -1) and B(6, 4): (4.5, 1.5)
- P(E) = 1 - P(E) : True
- 3 Median = Mode + 2 Mean: True
Question 5 Short Answer
- AA similarity criterion: If two angles of one triangle are congruent to two angles of another triangle, then the triangles are similar.
- Distance between P(x₁, y₁) and Q(x₂, y₂): √((x₂ - x₁)² + (y₂ - y₁)²))
- Line of sight: A straight line from the eye to the object viewed
- Arc length of a sector of a circle: (θ/360)2πr
- Number of tangents of a circle: Infinite
Question 6 - Question 17 (Detailed answers are not included here, but the questions are mathematical calculations or statements.)
Question 18 - Question 23 (Detailed answers are not included here, but the questions are mathematical calculations, proofs, or problem-solving.)
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Description
Test your knowledge with this High School Mathematics exam quiz featuring a variety of question types, including multiple choice and fill in the blanks. Covering key concepts such as HCF, quadratic equations, and arithmetic progressions, this quiz is designed to challenge your understanding of essential mathematical principles.
