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Federal (FBISE) · Full book test (board pattern) · Free

10th Class Mathematics Full Book Paper

75 marks · 3 hours · 32 questions. Covers: 12 chapters (01. Complex Numbers to 12. Basic Statistics).

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10th Class Mathematics Full Book Paper

10th Class · Mathematics · Federal (FBISE)

Name: ____________Roll No: ________Class/Section: ________Date: ________Total marks: 75Time: 3 hours

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

  1. CV is given by the formula:
    1. SDrange×100\frac{\text{SD}}{\text{range}} \times 100
    2. meanSD×100\frac{\text{mean}}{\text{SD}} \times 100
    3. 100mean×SD\frac{\text{100}}{\text{mean}} \times SD
    4. SD100× mean \frac{\text{SD}}{\text{100}} \times \text { mean }
  2. If f(x)=12xf(x) =\frac{1}{2} x , what is f2(x)f^2 (x) ?
    1. 14x \frac{1}{4x}
    2. 14x \frac{1}{4} x
    3. 2x
    4. 14x2 \frac{1}{4} x^2
  3. Direct common tangents of equal circles are:
    1. parallel
    2. intersecting
    3. converging
    4. not parallel
  4. Which of the following vectors represents a position vector?
    1. OP→\overrightarrow{OP}
    2. −OP→-\overrightarrow{OP}
    3. PO→\overrightarrow{PO}
    4. PQ→\overrightarrow{PQ}
  5. Which ordered pair is a solution of the system 2x - y ≤ 5 and x + 2y > 2?
    1. (1 , -1)
    2. (4 , 1)
    3. (2 , 0)
    4. (3 , 2)
  6. In right △ABC, a = 2 cm , c = 4 cm, what is α?
    1. 30°
    2. 45°
    3. 60°
    4. 120°
  7. An expression which is the ratio of two polynomials but the polynomial in denominator is non-zero is called.
    1. polynomial
    2. rational Expression
    3. compound Expression
    4. irrational Expression
  8. If a circle is divided into ten equal arcs, then central angle of each arc is …………
    1. 10°
    2. 36°
    3. 60°
    4. 90°
  9. If A and B are two matrices, conformable for the product AB then (AB)t=(AB)^t =
    1. AtBtA^tB^t
    2. (BA)t(BA)^t
    3. BtAtB^tA^t
    4. AB
  10. Which of the following is a quadratic equation?
    1. ax + b = c
    2. ax² + bx + c
    3. ax² + bx + c = 0
    4. ax² + bx + c = 0, a = 0
  11. 21−i\frac{2}{1 - i} =?
    1. 1+i2\frac{1 + i}{2}
    2. (1+i)22\frac{(1+i)^2}{2}
    3. 1−i1 - i
    4. 1+i1 + i
  12. Angle subtended by an arc at centre of circle is called ………… angle.
    1. reflex
    2. inscribed
    3. straight
    4. central
  13. Which of the following divides the data into two equal parts?
    1. decile
    2. quartile
    3. percentile
    4. median
  14. Which of the following is an exponential function?
    1. (13)x\left(\frac{1}{3}\right)^x
    2. exe^x
    3. 2x2^x
    4. All of these
  15. Angle between tangent and radial segment of a circle is:
    1. 30°
    2. 45°
    3. 60°
    4. 90°

Q2. Short questions (Attempt any 9 of 12 · 9 × 4 = 36)

  1. Sketch the graph of the quadratic function y = −x²− 4x. Will it open upward or downward?
  2. Raabi and Jerry are hoping on their play circles of four sectors each painted in red, green, yellow and blue colours. Find the probability that they will jump on: (1) At the same colour (2) At the different colours.
  3. Draw a circle with the help of any round object, then find its centre.
  4. Find the values of unknown in the figure.Question diagram
  5. Find z .zˉ:z=14−7i\bar{z} : {z} = 14 - 7i
  6. Prove that r2=4Rcos⁡α2cos⁡γ2sin⁡β2 r_2 = 4R \cos \frac{\alpha}{2} \cos \frac{\gamma}{2} \sin \frac{\beta}{2}
  7. Simplify the following.x2−255−x4÷3x20\frac{x^2 - 25}{5} - \frac{x}{4} \div \frac{3x}{20}
  8. Draw vectors a⃗\vec{a} = 3 units west and b⃗\vec{b} = 3 unit north on graph paper. Draw the following vector on the graph paper. a⃗−2b⃗\vec{a} - 2\vec{b}
  9. Find all roots of 8x³− 7x³− 1 = 0
  10. In the figure, AB‾=4BC‾\overline{AB} = 4 \overline{BC} and , ∠AOB find: ∠OAB + ∠ABC + ∠BCO + ∠COAQuestion diagram
  11. Verify A(B + C) = AB + AC A=[52],B=[64] and C=[12]. A = \begin{bmatrix} 5 & 2 \end{bmatrix}, B = \begin{bmatrix} 6 \\ 4 \end{bmatrix} \text{ and } C = \begin{bmatrix} 1 \\ 2 \end{bmatrix}.
  12. Solve the inequalities, if possible, graph the solution. 23x−4≥1\frac{2}{3}x - 4 ≥ 1

Q3. Long questions (Attempt any 3 of 5 · 3 × 8 = 24)

  1. Data shows scores of Huffaz in a Hifz Quran test: scores41−5051−6061−7071−8081−9091−100f3172030182 \begin{array}{|c|c|c|c|c|c|c|} \hline \text{scores} & 41 - 50 & 51 - 60 & 61 - 70 & 71 - 80 & 81 - 90 & 91 - 100 \\ \hline f & 3 & 17 & 20 & 30 & 18 & 2 \\ \hline \end{array} Find standard deviation of the data.
  2. The daily sum of labour and the material costs of Haani's and Massab's Home Industries are Rs. 20,000 and Rs. 40,000 respectively. If labour and the material rate, for both the Home Industries is same but Hanni's Home Industry has 6 workers who make 80 items and Massab's Home Industry has 12 workers who make 160 items, find the labour and the material cost.
  3. Ifg(x)=12x3+x2+2, find g(−13).g(x) = \frac{1}{2x^3} + \frac{x}{2} + 2, \, \text{find } g\left(-\frac{1}{3}\right).
  4. The difference of a positive number and its square is 380. Find the number.
  5. Represent z₁÷ z₂ graphically when z₁= -4 − 6i and z₂= 1 + i