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Questions and Answers
What value of 'k' makes the equations 2x + 3y = 7 and kx + 9/2y = 12 inconsistent?
What value of 'k' makes the equations 2x + 3y = 7 and kx + 9/2y = 12 inconsistent?
- -3
- rac{3}{2} (correct)
- rac{2}{3}
- 3
For the quadratic polynomial ax^2 + bx + c = 0 to have reciprocal zeroes, which relation must hold?
For the quadratic polynomial ax^2 + bx + c = 0 to have reciprocal zeroes, which relation must hold?
- a = b
- b = c
- a + c = 0
- a = c (correct)
Which expression correctly represents the discriminant of the quadratic equation bx^2 + ax + c = 0?
Which expression correctly represents the discriminant of the quadratic equation bx^2 + ax + c = 0?
- rac{b^2 + 4bc}
- rac{b^2 - 4ac} (correct)
- rac{b^2 + 4ac}
- rac{b^2 - 4bc}
The values of 'a' and 'c' such that the numbers a, 7, b, 23, c are in arithmetic progression are:
The values of 'a' and 'c' such that the numbers a, 7, b, 23, c are in arithmetic progression are:
What is the radius of a circle defined by endpoints of a diameter at (2, 4) and (-3, -1)?
What is the radius of a circle defined by endpoints of a diameter at (2, 4) and (-3, -1)?
What is the area of a sector of angle p in degrees for a circle with radius R?
What is the area of a sector of angle p in degrees for a circle with radius R?
If 4 tan θ = 3, what is the value of rac{4 ext{sin}θ - ext{cos}θ}{4 ext{sin}θ + ext{cos}θ}?
If 4 tan θ = 3, what is the value of rac{4 ext{sin}θ - ext{cos}θ}{4 ext{sin}θ + ext{cos}θ}?
In a right triangle ABC where AB = 5 cm and ∠ACB = 30°, what is the length of side BC?
In a right triangle ABC where AB = 5 cm and ∠ACB = 30°, what is the length of side BC?
Flashcards
What must 'a' be for (a x 5) to end with zero?
What must 'a' be for (a x 5) to end with zero?
A number ending with zero is divisible by 10. A number is divisible by 10 if it is divisible by both 2 and 5. For a product to end in zero, one of the factors must be divisible by 5. Therefore, the value of 'a' must be divisible by 5.
When do two equations have no solution?
When do two equations have no solution?
The pair of equations have no solution if the lines are parallel (same slope, different y-intercepts). The slope of the first equation is -2/3. The slope of the second equation is -2k/9. For the lines to be parallel, the slopes must be equal.
How to find the relationship between coefficients if quadratic roots are reciprocals?
How to find the relationship between coefficients if quadratic roots are reciprocals?
If the zeroes of a quadratic are reciprocals, then the product of the zeroes is 1. The product of the zeroes of the quadratic ax^2 + bx + c = 0 is equal to c/a.
What is the discriminant of a quadratic equation?
What is the discriminant of a quadratic equation?
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How to check if a sequence is arithmetic?
How to check if a sequence is arithmetic?
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How to find the radius of a circle given two endpoints of its diameter?
How to find the radius of a circle given two endpoints of its diameter?
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What kind of triangle is formed by the given vertices?
What kind of triangle is formed by the given vertices?
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How to calculate the area of a circle sector?
How to calculate the area of a circle sector?
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Study Notes
Trigonometry and Geometry Problems
- Problem 1: If p = (a x 5), for p to end with the digit zero, 'a' must be an even number
- Problem 2: If 2x + 3y = 7, kx + 9/2y = 12 have no solution, then k = 3
- Problem 3: If zeroes of ax² + bx + c = 0 are reciprocals, then a = c
- Problem 4: The discriminant of bx² + ax + c = 0 (b ≠0) is √(b² - 4ac)
- Problem 5: If a, 7, b, 23, c are in AP, then a = -1, c = 31
- Problem 6: End points of a diameter are (2, 4) and (-3, -1). The radius is 5√2 / 2 units
- Problem 7: Points (-4, 0), (4, 0), (0, 3) form a right triangle
- Problem 8: Area of a sector (angle p, radius R) is (p x π x R²) / 360
- Problem 9: If 4 tan θ = 3, then (4 sin θ - cos θ) / (4 sin θ + cos θ) = 1/3
- Problem 10: In a right-angled triangle ABC at B, AB = 5 cm, ∠ACB = 30°, BC = 5√3 cm
- Problem 11: If sec A + tan A = x, then sec A = (x² - 1) / x
- Problem 12: APQR ~ AXYZ. XY = 4 cm, YZ = 4.5 cm, ZX = 6.5 cm, PQ = 8 cm. Perimeter of APQR is 25 cm
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