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Roll No.
FAZAIA SCHOOLS & COLLEGES SEND-
UP EXAM: MATHEMATICS HSSC-I
(Session 2017 – 18)
Name of Candidate
Time Allowed : 2:35 Hours Total Marks: 80
NOTE: Sections ‘B’ and ‘C’ comprise pages 1-2 and questions therein are to be answered
on the separately provided Answer Book. Use supplementary answer sheet i.e.
Sheet – B if required. Write your answers neatly and legibly.
SECTION – B (Marks 40)
Q. 2 Attempt any TEN parts. All parts carry equal marks. (10 X 4 = 40)
(i) Simplify 2
by expressing in the form of a + ib .
5 + − 8
(ii) Construct truth table for the statement: (P∧ ~ P) → q
(iii) Verify that
a +
l a
a
a
a +
l a
a
a
a + l
=
2
(3a + )
(iv) Determine that p is tautology, absurdity or contingency.
(v) Find the values of the trigonometric function:
− 71π
6
(vi) Reduce cos
4
θ to an expression involving only function of multiples of θ, raised to
(vii)
the first power.
m
2
− 1
If cotθ =
2m
(0 < θ < π ) find the value of remaining trigonometric ratios.
(viii) Draw the graph of y = tan x, x ∈[−π , π ]
(ix)
Show that
1
=
2rR
1
+
1
+
1
ab bc ca
(x) Solve the triangle ABC, by using law of cosine given that b = 3, c = 5,α = 120
.
(xi) Show that cos
−1
(−x) = π − cos
−1
x
(xii) Solve the equation: sin 2x = cos x](https://image.slidesharecdn.com/math-hssc-i-bc-180206055500/75/Math-hssc-i-bc-1-2048.jpg)
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Math hssc-i-bc
This document contains a mathematics exam for HSSC-I (Higher Secondary School Certificate Part 1) with questions covering various topics: 1) Simplifying expressions involving complex numbers, trigonometric functions, and logarithms. 2) Evaluating trigonometric functions for given angles. 3) Proving trigonometric identities and relationships between inverse trigonometric functions. 4) Solving triangles using trigonometric functions, laws of sines and cosines. 5) Solving systems of linear equations using Cramer's rule. The exam is divided into two sections with a total of 80 marks and includes short answer questions as well as multi-step proof questions.
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Math hssc-i-bc
- 1. 2 Roll No. FAZAIA SCHOOLS& COLLEGES SEND- UP EXAM: MATHEMATICS HSSC-I (Session 2017 – 18) Name of Candidate Time Allowed : 2:35 Hours Total Marks: 80 NOTE: Sections ‘B’ and ‘C’ comprise pages 1-2 and questions therein are to be answered on the separately provided Answer Book. Use supplementary answer sheet i.e. Sheet – B if required. Write your answers neatly and legibly. SECTION – B (Marks 40) Q. 2 Attempt any TEN parts. All parts carry equal marks. (10 X 4 = 40) (i) Simplify 2 by expressing in the form of a + ib . 5 + − 8 (ii) Construct truth table for the statement: (P∧ ~ P) → q (iii) Verify that a + l a a a a + l a a a a + l = 2 (3a + ) (iv) Determine that p is tautology, absurdity or contingency. (v) Find the values of the trigonometric function: − 71π 6 (vi) Reduce cos 4 θ to an expression involving only function of multiples of θ, raised to (vii) the first power. m 2 − 1 If cotθ = 2m (0 < θ < π ) find the value of remaining trigonometric ratios. (viii) Draw the graph of y = tan x, x ∈[−π , π ] (ix) Show that 1 = 2rR 1 + 1 + 1 ab bc ca (x) Solve the triangle ABC, by using law of cosine given that b = 3, c = 5,α = 120 . (xi) Show that cos −1 (−x) = π − cos −1 x (xii) Solve the equation: sin 2x = cos x
- 2. (xiii) Find themeasure of greatest angle, if sides of the triangle are 16, 20, 33. (xiv) Prove that Z = Z if and only if Z is real. SECTION – C (Marks 40) Note: Attempt any FIVE questions. All questions carry equal marks. (5 X 8= 40) 1 − 5 3i Q. 3 Find out real and imaginary parts of : 1 + 3i Q. 4 Solve the system of linear equations by Cramer’s rule 2x + 2y + z = 3 3x − 2y − 2z = 1 5x + y − 3z = 2 Q. 5 Q. 6 Prove that: 1 cosecθ − cotθ − 1 sinθ = 1 sinθ − 1 cosecθ + cotθ Q. 7 Prove without using tables / calculator that sin19 cos11 + sin 71 sin11 = 1 2 Q. 8 The sides of a triangle are triangle is120 . x 2 + x + 1, 2x + 1 and x 2 − 1 . Prove that greatest angle of the Q. 9 Prove that: sin −1 5 + sin −1 13 7 = cos −1 253 25 325 Prove that cot ሺ� + �ሺ= 𝐶𝑜� � 𝐶𝑜� �−1 𝐶𝑜� �+𝐶𝑜� �