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

9th Class Mathematics Second half Book Paper

75 marks · About 2 hours 40 minutes · 47 questions. Covers: 6 chapters (UNIT 8: Logic to UNIT 13: Probability).

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9th Class Mathematics Second half Book Paper

9th 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. Which one tells us how often a specific event occurs relative to the total number of frequency event or trials?

    1. Expected frequency

    2. Sum of relative frequency

    3. Relative frequency

    4. Frequency

  2. The circumference of a circle with radius r is:

    4. None of these

  3. In a reciprocal function  as x approaches zero, what happens to y? 

    1. It approaches infinity

    2. It approaches zero

    3. It becomes undefined

    4. It remains constant

  4. What is the formula for the weighted mean? 

    1. Weighted=

    2. Weighted mean = ?(wx) × Ew

    3. Weighted mean = ?(wx) – S? 

    4. Weighted mean = ?(wx) + Ew

  5. What is the angle formed by two intersecting rays from a vertex in a triangle called? 

    1. Complementary angle

    2. Opposite angle

    3. Vertical angle

    4. Exterior angle

  6. In an equilateral triangle, what is the measure of each angle?

  7. The relative frequency of selecting a red ball from 80 students is: 

    1. 0.29

    2. 0.19

    3. 0.31

    4. 0.12

  9. Which of the following represents an exponential decay function? 

    1. y = 2x

  10. What is the arithmetic mean of the data set: 4, 6, 10, 12, 15, 20, 25, 28, 30? 

    1. 16.67

    2. 18.00

    3. 20.00

    4. 22.00

  11. A triangle with all sides and angles equal is called a: 

    1. Right triangle

    2. Isosceles triangle

    3. Equilateral triangle

    4. Scalene triangle

  12. What is the condition for two polygons to be similar?

    1. Corresponding angles are equal and Corresponding sides are equal

    2. Corresponding angles are equal and Corresponding sides are proportional

    3. Corresponding angles are proportional and Corresponding sides are equal

    4. Corresponding angles are proportional and Corresponding sides are proportional

  13. If six dice are rolled 50 times, the expected frequency of a number appearing is given by: 

    1. NP(B)

    2. NP(A)

    3. NP(X)

    4. None of these

  14. The statement " A straight line can be drawn between any two points" is:

    1. Theorem

    2. Conjecture

    3. Axiom

    4. Logic

  15. For the function , what is the vertex of the parabola? 

    1. (0,0)

    4. (1,1)

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

  1. A toy manufacturer produces model cars which are similar in every way to the actual cars. If the ratio of the door area of the model to the door area of the car is 1 cm to 2500 cm, find: the ratio of the capacities of their petrol tanks.

  2. Formulate simple deductive proof's of the following algebraic expression, prove that L.H.S is equal to the R.H.S.

  3. Find the missing value in the following similar solid:

  4. Define tautology.

  5. Define regular polygon.

  6. The sum of the interior angles of a triangle is 180o.

  7. Two polygons are similar with a ratio of corresponding sides being . If the area of the smaller polygon is 54 cm2, find the area of the larger polygon.

  8. If x and y are positive real numbers and then .

  9. Find the ratio of the areas of similar figures if the ratio of their corresponding lengths are: 1:3

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

  1. A company manufactures school bags. The function of producing x bags is C(x)= 1200 + 800x and the revenue from selling x bags is R(x)=50x. Determine the profit or loss when 250 bags are sold.

  2. Construct the following triangles and find whether there exists any ambiguous case: and .

  3. How do you identify an exponential function from a table of values?

  4. Construct with the given measurements and verify that the perpendicular bisectors of the triangle are concurrent: and

  5. What is the axis of symmetry of a quadratic function?

  6. What is an ambiguous case in triangle construction?

  7. What is an exponential function?

  8. Define scalene triangle.

  9. What is a reciprocal function.

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

  1. The arithmetic mean of 45 numbers is 80. Find their sum.

  2. What is a favorable outcome?

  3. Following are the number of telephone calls made in a week to 30 teachers of high school:

    5 8 11 25 13 16 20 17 15 16 30 21 14 18 19
    6 22 26 15 19 35 29 31 23 25 20 10 9 7 26

    Construct a frequency distribution with number of classes?

  4. What is the probability of rolling a double six with two dice?

  5. Usman rolled a fair dice eight times. Each time their sum was recorded as 8,5,6,6,9,4,3,11. Find the median and mode of the sum.

  6. The probability that Ayesha will pass the examination is 0.85. What will be the probability that Ayesha will not pass the examination?

  7. The following distribution represents the scores achieved by a group of chemistry students in the chemistry laboratory:

    Scores 24-28 29-33 34-38 39-43 44-48 49-53 Total
    No. of students 3 6 12 23 15 6 65

    What is the upper limit of the last class?

  8. A ball contains 5 blue balls and 8 green balls. Find the probability of selecting at random: not a green ball.

  9. Differentiate between discrete and continuous data.

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

  1. A tessellation is created by repeatedly reflecting a basic shape. The basic shape is a right-angled triangle with sides of lengths 3, 4 and 5 units. Find: The minimum number of reflections needed to create a tessellation that covers a square with an area of 3600 square units.

  2. The heights (in inches) of 200 students are recorded in the following frequency distribution. Find the mean height of the student by short formula:

    Height (x) (in inches) 51 52 53 54 55 56 57 58 59 60
    Frequency (f) 2 5 8 24 55 45 38 16 6 1

  3. Construct a triangle ABCD with and . Draw the locus of all points which is: equidistant from A and B. Label the point P inside the rectangle which is 3.1 cm from point A and equidistant from A and B.

  4. Let A,B and C are the missiles and they are fired at a target, if the probabilities of hitting the target, , respectively. Find the probabilities of missile A does not hit the target.

  5. Prove the following statement: If x is an even integer then show that is even.