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Class 10 Mathematics Full Unit Test Chapter 7 Trigonometry| Punjab Board 2027 Model Papers
Class 10 Mathematics Chapter 7 Full unit Test Trigonometry
Unit 7: Trigonometry Class 10 Mathematics Full Unit Test is prepared according to the Punjab Board 2027 Model Papers pattern. This full unit test covers important Class 10 Mathematics Trigonometry questions, including trigonometric ratios, signs and quadrants, exact values, law of sines, law of cosines, area of triangles, bearings, and related problem-solving questions. Students can use this Punjab Board 2027 Mathematics model paper for chapter-wise preparation, revision, and practice according to the new board examination pattern.
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Full Unit Test
Unit 7: Trigonometry
Model Paper
Objective Type
Time Allowed: 20 Min.
Max. Marks: 15
Note: Four possible answer A, B, C and D to each question are given.
The choice which you think is correct, fill that circle in front of
that question with Marker or ink pen in the answer book. Cutting
filling two or more circles will result in zero mark in that question.
(i)
adj. / opp. =
(ii) tan 90° =
(iii)
In which quadrant sinθ > 0 and cosθ < 0?
(iv)
If θ = 90° then which of the following function has value equals 1.
(v)
cos (180° − θ) =
(vi)
If θ = 120° then:
(vii)
sin 150° =
(viii)
The law of cosines states that:
(ix)
Area of a triangle can be found by the formula A =
(x)
Area of the triangle is:
(xi)
Area of the triangle is A =
(xii)
Bearing of P from Q is:
(xiii)
Bearing of the point P is:
(xiv)
All trigonometric ratios are positive in:
(xv)
cot (−θ) =
Here is Subjective part of Model Paper 2027.
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Subjective Type
Time Allowed: 2:10 hours
(Part-I)
Max. Marks: 60
2. Write short answers to any six (06) questions:
(2 × 6 = 12)
(i) Find the signs of the following:
(i) cos 75° (ii) cot 250°
(ii) Without using calculator, find the exact values of the trigonometric functions:
(i) sin120° (ii) cot 150
(iii) Find the signs of cosec 88°
(iv) Without using calculator, find the exact values of the trigonometric functions:
sec 150°
(v) Define Oblique Triangle.
(vi) Can we use law of sines, when two sides and included angle or the three sides of a triangle are given?
(vii) Without using calculator, find the exact values of the trigonometric functions:
cos 120°
(viii) Define Law of sines.
(ix) Define Law of cosines.
3. Write short answers to any six (06) questions:
(2 × 6 = 12)
(i) Write the formulae for Area of a triangle.
(ii) Calculate area of triangle ABC in which
a = 4.2, b = 3.2 and γ = 70°.
(iii) Calculate area of ΔABC, in which
β = 50°, γ = 40°, c = 10cm.
(iv) Calculate area of ΔABC, in which
a = 6.1cm, b = 2.3cm, γ = 80°.
(v) Calculate area of ΔABC in which
a = 4cm, b = 3cm, c = 5cm.
(vi) Calculate area of each triangle ABC, if
a = 7cm, b = 8cm, γ = 38°.
(vii) A boat crosses a river 80m wide, at a 60° angle to the current.
What distance does the boat actually travel?
(viii) In the diagram, the bearing of Q from P is 060°.
Find the bearing of P from Q.
(ix) Find bearing of point P in each of the following:
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4. Write short answers to any six (06) questions:
(2 × 6 = 12)
(i) The diagram shows the positions of two ships P and Q.
What is the bearing of ship P from ship Q?
(ii) Abdul Hadi walks 100m North and then 300m East.
How far is he from his starting position?
(iii) A ship sails 20km on a bearing of 120°.
How far to the South has the ship moved from its original position?
(iv) An aircraft flies 150km east, then 100km northeast
(45° from East). What is the total displacement?
(v) Calculate the area of ΔABC, in which
a = 4cm, b = 6cm, c = 8cm.
(vi) Hashim walks 4km due North, then turns and walks
3km due East. What is the bearing from the starting point to his final position?
(vii) Define Angle of Elevation.
(viii) Write the formula of Area of a triangle for two angle and one side.
(ix) Find area of ΔABC, in which
a = 8cm, b = 9cm, c = 10cm.
(Part-II)
Note: Attempt any two (02) questions.
(2 × 8 = 16)
5:(a) In a triangle ABC, β = 45°, γ = 30°,
a = 6cm, calculate b and c.
(b) Solve ΔABC, in which
α = 77°, β = 66°, a = 2cm.
6:(a) In ΔABC, a = 3, b = 5,
c = 7. Find the values of α, β, γ.
(b) Solve the triangle ABC, in which
a = 12.2cm, c = 15.8cm, γ = 50°.
7:(a) The diagram shows a pyramid. The base, PQRS,
is a horizontal square of side of 10cm. The vertex, V, is vertically
above the midpoint, M and m VM = 12cm.
Calculate the size of angle VPM.
(b) A lighthouse is located on a cliff 80m above sea level.
A ship is spotted at an angle of depression of 12°.
How far is the ship from the base of the cliff?
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(Part-III)
Note: Attempt any one (01) question.
(1 × 8 = 8)
8:(a) A ship sails 100km on a bearing of 045°,
then changes course and sails 120km on a bearing of 135°.
Find the distance between the starting point and the final position.
(b) Solve the triangle ABC, in which:
a = 5.4cm, b = 3.4cm, α = 49°.
9:(a) A pilot flies 200km on a bearing of 045°,
then turns and flies 150km on a bearing of 135°.
How far is the plane from its original position?
(b) The diagram shows a cuboid ABCDEFGH in which
m AB = 5cm, m BC = 7cm,
m AE = 3cm.
