Sweden · Grade 10 · Practice Sheet 3

1. 1.

   Find the momentum of a 8 kg object moving at 7 m/s.

   Formula:Momentum

   $p = mv$

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2. 2.

   Find the force needed to accelerate a 26 kg mass at 6.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   A 29 kg object moves at 12 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

   $KE = \tfrac{1}{2} m v^2$

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4. 4.

   Find the sum of the first 12 terms of an arithmetic series with first term a = 2 and common difference d = 6.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   A force of 94 N moves an object 15 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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6. 6.

   Find the gravitational potential energy of a 3 kg object raised 22 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A right-angled triangle has legs of 19 cm and 20 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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8. 8.

   A body starts at 2 m/s and accelerates at 5.9 m/s² for 9 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   Solve for x: 4x + 2 = 34.

   Formula:Solving a Linear Equation

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

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10. 10.

    A value changes from 160 to 235. 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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11. 11.

    Find the momentum of a 20 kg object moving at 4 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    Solve using the quadratic formula: x² + 0x − 9 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    A bag has 14 equally likely marbles, of which 10 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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14. 14.

    Find the momentum of a 5 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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15. 15.

    kr 3,200 is invested at 7.5% simple interest per year for 3 years. Find the interest earned.

    Formula:Simple Interest

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

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16. 16.

    A triangle has sides a = 20 cm and b = 10 cm with an included angle C = 30°. 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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17. 17.

    A device runs at 76 V drawing 2.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Find the gravitational potential energy of a 27 kg object raised 13 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Solve using the quadratic formula: x² − 3x + 2 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    A force of 5 N moves an object 13 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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