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Punjab (PTB) · Half book test (board pattern) · Free

10th Class Mathematics Second half Book Paper

75 marks · About 2 hours 40 minutes · 47 questions. Covers: 6 chapters (UNIT 7: TRIGONOMETRY to UNIT 12: PROBABILITY).

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10th Class Mathematics Second half Book Paper

10th Class · Mathematics · Punjab (PTB)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 75Time: About 2 hours 40 minutes

Q1. Multiple choice questions (Attempt all · 15 × 1 = 15)

  1. The range is the ...... of min. value of a data set:

    1. Product

    2. Sum

    3. Difference

    4. Mean

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

    1. Supplementary

    2. Complementary

    3. Equal

    4. Zero

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

    1. Radius

    2. Arc

    3. Chord

    4. Tangent

  4. What is called a visual representation to show all possible outcomes:

    1. A free diagram

    2. A tail diagram

    3. Sample diagram

    4. A tree diagram

  5. If  then ?

  6. To draw a tangent at middle point of an arc, first step is to:

    1. Join endpoints of an arc

    2. Draw radius

    3. Draw a line perpendicular to chord

    4. Draw an angle

  7. Second quartile represents:

    1. Mean

    2. Mode

    3. Median

    4. Variance

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

    1. An acute

    2. Right

    3. An obtuse

    4. Straight

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

    1. Bisect

    2. equal

    3. Greater

    4. Less

  10. In a random experiment, each possible outcome is called:

    1. An event

    2. Sample space

    3. Probability

    4. Rolling a dice

  11. What is true about sec ?

  12. Two equal tangents from a point to a circle can be drawn when the point is ...... the cirlce:

    1. On

    2. Inside

    3. Outside

    4. At centre of

  13. The box in Box-and-Whisker plot represents:

    4. IQR

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

    1. 12 cm

    2. 8 cm

    3. 6 cm

    4. 3 cm

  15. 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

Q2. Short questions (Attempt any 6 of 9 · 6 × 2 = 12)

  1. 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.

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

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

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

  5. 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?

  6. Define a semi circle.

  7. 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?

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

  9. Calculate area of the following triangle ABC. 

Q3. Short questions (Attempt any 6 of 9 · 6 × 2 = 12)

  1. 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?

  2. Construct a circle with the help of given radius and verify its centre by construction: r = 1.5 cm.

  3. Find , when: 

  4. ABC an arc of a fountain, complete a circle without finding its centre.

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

  6. Draw a circle of radius 1.5cm and draw a tangent at point P, when P is at a distance of 8 cm from its centre.

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

  8. Draw tangent to  at point P, when P is endpoint of the arc.

  9. Find the angles x and y in the following figure:

Q4. Short questions (Attempt any 6 of 9 · 6 × 2 = 12)

  1. Hashim rolled a dice and tossed a coin simultaneously. Draw possibility diagram.

  2. The sum of 5 numbers is 45 and the sum of their squares is 421. Find the mean and standard deviation of the data.

  3. A bag contains 4 red and 3 green balls, Kabeer draw two balls one after the other with replacement (the second is drawn after the first is replaced). Find the probability that the first ball is red and the second ball is also red.

  4. Find the range of the following data set: 63,89,98,125,79,108,117,60

  5. If the probability of an event A is , then find the probability of the event Not A.

  6. A company forecasts monthly sales (rupees in millions): 15,18,14,20,13. Find the variability in sales predictions.

  7. Two coind are tossed together. What is the probability of getting different faces on the coins?

  8. Find  median, minimum and maximum values for the following box-and-whisker plot.

  9. Majid dealt two cards successively (without replacement) from a well shuffled deck of 52 playing card. Find the probability that the first card is a king and the second card is a queen.

Q5. Long questions (Attempt any 3 of 5 · 3 × 8 = 24)

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

  2. Draw the cumulative frequency polygon for the following frequency distribution of the weekly wages (rupees in thousands) of number of workers by more than method. Also locate  on it.

    Weekly wages (rupees in thousands) 0-20 20-40 40-60 60-80 80-100
    No. of workers 30 48 61 40 21

  3. 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.

  4. 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.

  5. A dice is rolled and coin is tossed together: (i) Find sample space by drawing possibility diagram. (ii) Find sample space by sketching tree diagram. (iii) What is the probability of getting a tail and an even number?