Tunisia · Grade 10 · Practice Sheet 6

1. 1.

   A bag has 22 equally likely marbles, of which 5 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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2. 2.

   Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   A wave has frequency 519 Hz and wavelength 3.24 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Find the gravitational potential energy of a 5 kg object raised 31 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   Find the force needed to accelerate a 57 kg mass at 4.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   A right-angled triangle has legs of 8 cm and 10 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

   $c = \sqrt{a^2 + b^2}$

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7. 7.

   Find the force needed to accelerate a 60 kg mass at 0.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   Solve for x: 9x + 7 = 52.

   Formula:Solving a Linear Equation

   $x = \dfrac{c - b}{a}$

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9. 9.

   Find the momentum of a 54 kg object moving at 3 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A right-angled triangle has legs of 14 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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11. 11.

    A force of 63 N moves an object 6 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    A right-angled triangle has legs of 6 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

    $c = \sqrt{a^2 + b^2}$

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13. 13.

    Find the sum of the first 10 terms of an arithmetic series with first term a = 3 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    DT 3,500 is invested at 6% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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15. 15.

    Find the momentum of a 59 kg object moving at 13 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 4 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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17. 17.

    Solve for x: 5x + 2 = 22.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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18. 18.

    A current of 4.6 A flows through a 48 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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19. 19.

    An object has mass 222.6 g and volume 42 cm³. Find its density.

    Formula:Density

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

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20. 20.

    A value changes from 83 to 136. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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