Poland · Klasa 10 · Practice Sheet 48

1. 1.

   A bag has 16 equally likely marbles, of which 7 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.

   A value changes from 134 to 45. 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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3. 3.

   Find the force needed to accelerate a 26 kg mass at 5.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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4. 4.

   A force of 136 N acts on an area of 6.8 m². Find the pressure.

   Formula:Pressure

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

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5. 5.

   A force of 25 N moves an object 20 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   A triangle has sides a = 15 cm and b = 8 cm with an included angle C = 90°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

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7. 7.

   Find the force needed to accelerate a 23 kg mass at 1.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   A bag has 25 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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9. 9.

   zł 2,500 is invested at 4% compound interest per annum for 5 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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10. 10.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 11 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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11. 11.

    A cone has base radius 10 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

    $V = \tfrac{1}{3} \pi r^2 h$

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12. 12.

    An object with initial velocity 9 m/s accelerates at 1.9 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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13. 13.

    A body starts at 7 m/s and accelerates at 2 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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14. 14.

    Find the sum of the first 11 terms of an arithmetic series with first term a = 4 and common difference d = 3.

    Formula:Sum of an Arithmetic Series

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

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15. 15.

    An object has mass 62.7 g and volume 19 cm³. Find its density.

    Formula:Density

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

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16. 16.

    zł 2,500 is invested at 4% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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17. 17.

    A body starts at 8 m/s and accelerates at 5.8 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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18. 18.

    Find the force needed to accelerate a 9 kg mass at 6.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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19. 19.

    Find the gravitational potential energy of a 47 kg object raised 23 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    Find the sum of the first 5 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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