Board Boosters
The questions your board exam loves to ask
800 most-asked Class 11 & 12 (+1 / +2) questions across Physics, Chemistry, Maths and Biology — each with a model answer and the exact marking-scheme points examiners reward. Revise smart, walk in calm.
MathsClass 112 markseasy
Introduction to Three Dimensional Geometry
Find the midpoint of the line segment joining the points (2, 3, 4) and (6, 7, 8).
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The midpoint of the segment joining (x1,y1,z1) and (x2,y2,z2) is ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2). = ((2+6)/2, (3+7)/2, (4+8)/2) = (4, 5, 6).
M = ((x1+x2)/2, (y1+y2)/2, (z1+z2)/2)
Marking-scheme points
- ✓Midpoint = average of endpoints
- ✓= ((2+6)/2, (3+7)/2, (4+8)/2)
- ✓= (4, 5, 6)
MathsClass 112 markseasy
Limits and Derivatives
Evaluate the limit: lim as x approaches 2 of (x^2 - 4)/(x - 2).
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Direct substitution gives 0/0, so factorise the numerator: x^2 - 4 = (x - 2)(x + 2). Then (x^2 - 4)/(x - 2) = x + 2 for x not equal to 2. Taking the limit as x approaches 2 gives 2 + 2 = 4.
a^2 - b^2 = (a - b)(a + b)
Marking-scheme points
- ✓0/0 form -> factorise
- ✓(x^2 - 4)/(x - 2) = x + 2
- ✓Limit = 4
MathsClass 112 markseasy
Limits and Derivatives
State and use the standard limit to evaluate lim as x approaches 0 of (sin x)/x.
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The standard limit is lim as x approaches 0 of (sin x)/x = 1 (with x in radians). This is a fundamental result used throughout limits and derivatives of trigonometric functions.
lim x->0 (sin x)/x = 1
Marking-scheme points
- ✓Standard result (x in radians)
- ✓lim x->0 (sin x)/x = 1
- ✓Used for trigonometric derivatives
MathsClass 113 marksmedium
Limits and Derivatives
Evaluate lim as x approaches 0 of (sin 3x)/(sin 5x).
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Limits and Derivatives
Evaluate lim as x approaches 3 of (x^2 - 9)/(x^2 - x - 6).
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Limits and Derivatives
Evaluate lim as x approaches 0 of (sqrt(1 + x) - 1)/x.
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Limits and Derivatives
Find the derivative of f(x) = x^2 from first principles.
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Limits and Derivatives
Differentiate y = x^3 + 3x^2 - 5x + 2 with respect to x.
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Limits and Derivatives
Differentiate y = (x^2 + 1)(x - 3) using the product rule.
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Limits and Derivatives
Differentiate y = (x + 1)/(x - 1) using the quotient rule.
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Limits and Derivatives
Find the derivative of y = sin x cos x.
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Limits and Derivatives
Find the derivative of sin x from first principles.
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Statistics
Find the mean of the first 10 natural numbers.
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Statistics
Find the mean deviation about the mean for the data 6, 7, 10, 12, 13, 4, 8, 12.
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Statistics
Find the variance and standard deviation of the data 2, 4, 6, 8, 10.
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Statistics
Define variance and standard deviation of a set of observations.
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Statistics
The mean of a data set is 6 and its standard deviation is 2 sqrt2. Find the coefficient of variation.
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Probability
A fair die is thrown once. Find the probability of getting a prime number.
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Probability
Two fair dice are thrown together. Find the probability that the sum of the numbers on them is 8.
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Probability
One card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that it is a king or a heart.
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