Switzerland · Grade 10 · Practice Sheet 23

1. 1.

   A current of 2.6 A flows through a 48 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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2. 2.

   A value changes from 145 to 23. 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.

   In a triangle, a = 16, b = 16 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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4. 4.

   A population of 7,500 grows 3% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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5. 5.

   An object has mass 221 g and volume 26 cm³. Find its density.

   Formula:Density

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

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6. 6.

   Find the gravitational potential energy of a 30 kg object raised 14 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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7. 7.

   A force of 65 N moves an object 3 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   A cylinder has radius 7 cm and height 27 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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9. 9.

   An object has mass 58.8 g and volume 42 cm³. Find its density.

   Formula:Density

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

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10. 10.

    Find the gravitational potential energy of a 16 kg object raised 25 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    Find the force needed to accelerate a 58 kg mass at 5.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    An object has mass 63 g and volume 9 cm³. Find its density.

    Formula:Density

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

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13. 13.

    Find the sum of the first 6 terms of an arithmetic series with first term a = 5 and common difference d = 4.

    Formula:Sum of an Arithmetic Series

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

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14. 14.

    Find the force needed to accelerate a 38 kg mass at 6.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    Find the gravitational potential energy of a 2 kg object raised 35 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    CHF 2,000 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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17. 17.

    A population of 1,900 grows 2% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    Find the momentum of a 17 kg object moving at 18 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    A right-angled triangle has legs of 10 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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20. 20.

    A bag has 9 equally likely marbles, of which 8 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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