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Punjab (PTB) · Quarter book test · Free

10th Class Mathematics 3rd Quarter Book Paper

40 marks · 1 hour · 28 questions. Covers: UNIT 7: TRIGONOMETRY, UNIT 8: CHORDS AND ARCS OF A CIRCLE, UNIT 9: TANGENT AND ANGLES OF A CIRCLE.

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10th Class Mathematics 3rd Quarter Book Paper

10th Class · Mathematics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 40Time: 1 hour

Q1. Multiple choice questions (Attempt all · 12 × 1 = 12)

  1. If  then ?

  2. Distance of a point on the circumference to the centre of the circle is called:

    1. Radius

    2. Arc

    3. Chord

    4. Tangent

  3. Any two angles in the same segment of the circle are:

    1. Supplementary

    2. Complementary

    3. Equal

    4. Zero

  4. What is true about sec ?

  5. Perpendicular from the centre of a circle on a chord ...... it:

    1. Bisect

    2. equal

    3. Greater

    4. Less

  6. An angle in a segment greater than a semicircle is ...... angle:

    1. An acute

    2. Right

    3. An obtuse

    4. Straight

  8. If two circles have three points is common, what can be concluded about them?

    1. They are concentric

    2. They are tangent

    3. They coincide

    4. They are non-collinear

  9. If r=6cm and  radians, then arc length is:

    1. 12 cm

    2. 8 cm

    3. 6 cm

    4. 3 cm

  11. Any part of a circumference is called:

    1. Chord

    2. Diameter

    3. Radius

    4. Arc

  12. ...... tangents can be drawn to a circle from a point outside the circle:

    1. One

    2. Two

    3. Three

    4. Many

Q2. Short questions (Attempt any 8 of 12 · 8 × 2 = 16)

  1. In the given, find the value of x.

  2. An architect designs a circular dome on a building. A lighting rod is placed 12 m away from the centre of the dome which has a radius of 5m. Support cables are attached from the rod to the dome, touching the dome at two points. What is the length of each cable?

  3. The diagram shows a cuboid ABVDEFGH in which , , calculate the size of the angle between  and the plane ABCD. Give your answer correct to 1 decimal place.

  4. In the given figure  units and  units. Find the value of x.

  5. Find , when: 

  6. What is the formula to find the area of a triangle when two sides and their included angle are given?

  7. Define a semi circle.

  8. Find the angles marked in the given figure, where O is the centre of the circle.

  9. A ligthhouse is located on a cliff 80 m above sea level. A ship is spotted at an angle of depression of . How far is the ship from the base of the cliff?

  10. What is the sum of all the central angles of a circle?

  11. S,T,U and V are points on the circumference of a circle. Find the angles x and y.

  12. In an isometric game, the camera is placed at a  angle from the ground. If the player is 10 units in front and 10 units above, what is the direct line of sight distance?

Q3. Long questions (Attempt any 3 of 4 · 3 × 4 = 12)

  1. The diagram shows a prism. Trinagle PQR is a cross section of the prism, where  and . Calculate the size of the angle that the line MR makes with the plane RQLN.

  2. A pyramid-shaped sculpture is placed in the center of a circular plaza with a radius of 10m. A decoractive pole stands 26 m from the center of the circle. Two guide wires are attached from the pole to the plaza edge, just touching the circle. Find the length of each wire.

  3. Find the values of x and y in the given figure, such that .

  4. The diagram shows 3 places A,B and C. (i) A from C (ii) C from A (iii) C from A (iv) B from C