Pakistan · Class 10 · Practice Sheet 48

1. 1.

   Solve using the quadratic formula: x² + 6x + 5 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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2. 2.

   An object has mass 125.8 g and volume 37 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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3. 3.

   In a triangle, a = 5, b = 6 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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4. 4.

   A population of 8,100 grows 8% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

   $N = N_0 (1 + r)^{t}$

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5. 5.

   Find the force needed to accelerate a 37 kg mass at 5.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   In a triangle, a = 12, b = 5 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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7. 7.

   An object has mass 74 g and volume 37 cm³. Find its density.

   Formula:Density

   $\rho = \dfrac{m}{V}$

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8. 8.

   A force of 245 N acts on an area of 8 m². Find the pressure.

   Formula:Pressure

   $P = \dfrac{F}{A}$

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9. 9.

   A bag has 9 equally likely marbles, of which 3 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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10. 10.

    An object has mass 176 g and volume 40 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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11. 11.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 9 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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12. 12.

    An object has mass 252.3 g and volume 29 cm³. Find its density.

    Formula:Density

    $\rho = \dfrac{m}{V}$

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13. 13.

    A force of 77 N moves an object 27 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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14. 14.

    Find the force needed to accelerate a 57 kg mass at 4.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

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16. 16.

    A wave has frequency 820 Hz and wavelength 0.34 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    In a triangle, a = 17, b = 12 and the included angle C = 80°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

    $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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18. 18.

    Find the momentum of a 15 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 3 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

    $S_n = \tfrac{n}{2}\left(2a + (n-1)d\right)$

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20. 20.

    A force of 301 N acts on an area of 7.6 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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