Plus One Maths Annual Exam Answer Key

Plus One Maths Answer Key - March 2025 Examination

Section 1: Answer any 6 questions from 1 to 8 (3 scores each)

Question 1

(a) Write the set A = {1, 4, 9, 16, .... 100} in set builder form.

A = {x | x = n², n ∈ ℕ, 1 ≤ n ≤ 10}

(b) Write all subsets of the set {1, 2, 3}.

Subsets: ∅, {1}, {2}, {3}, {1,2}, {1,3}, {2,3}, {1,2,3}

Question 2

(a) The degree measure of \(\frac{4\pi}{3}\) = ______.

240°

(b) If \(\cos x = \frac{3}{5}\), \(x\) lies in third quadrant. Find the values of the trigonometric functions \(\sin x\) and \(\tan x\).

sin x = -4/5, tan x = 4/3

Question 8

(a) Write the equation of y-axis.

x = 0

(b) Find the slope of a line which passes through the origin and the midpoint of the line segment joining the points P(0, -4) and Q(8, 0).

Slope = 1/2

Section 2: Answer any 6 questions from 9 to 16 (4 scores each)

Question 9

(a) Write the set-builder form of the subset (−1, 2) of ℝ.

{x ∈ ℝ | -1 < x < 2}

(b) Let U = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} be the universal set having subsets A = {1, 3, 5, 7, 9} and B = {5, 6, 7, 8, 9, 10}, then find (3)

(i) A∪B = {1,3,5,6,7,8,9,10}
(ii) A' = {2,4,6,8,10}, B' = {1,2,3,4}
(iii) (A∪B)' = {2,4} = A'∩B'

Question 16

If A and B are two events such that P(A) = 0.42, P(B) = 0.48 and P(A and B) = 0.16, then find the following:

(i) P(not A) = 0.58
(ii) P(not B) = 0.52
(iii) P(A or B) = 0.74

Section 3: Answer any 3 questions from 17 to 20 (6 scores each)

Question 17

(a) \(\sin(765^\circ) = \underline{\hspace{2cm}}\)

(C) 1/√2

(b) Find the value of \(\cos(75^\circ)\).

(√6 - √2)/4

(c) Show that \(\tan 3x \tan 2x \tan x = \tan 3x - \tan 2x - \tan x\).

Proof: Using tan(3x) = tan(2x + x) identity

Question 20

Find Mean, Variance and Standard Deviation of the following data:

Mean: 62
Variance: 201.6
Standard Deviation: √201.6 ≈ 14.2