Finland · Grade 10 · Practice Sheet 37

1. 1.

   A bag has 27 equally likely marbles, of which 17 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.

   Solve for x: 4x + 6 = 22.

   Formula:Solving a Linear Equation

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

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3. 3.

   An object has mass 56.7 g and volume 9 cm³. Find its density.

   Formula:Density

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

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4. 4.

   A wave has frequency 700 Hz and wavelength 1.69 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   A population of 7,300 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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6. 6.

   Find the force needed to accelerate a 55 kg mass at 8.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A wave has frequency 244 Hz and wavelength 2.12 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   Find the sum of the first 7 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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9. 9.

   A force of 6 N moves an object 38 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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10. 10.

    Find the gravitational potential energy of a 16 kg object raised 26 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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11. 11.

    A force of 66 N moves an object 9 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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12. 12.

    €2,800 is invested at 7.5% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

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

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13. 13.

    A population of 1,000 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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14. 14.

    Find the volume of a sphere of radius 3 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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15. 15.

    In a triangle, a = 9, b = 5 and the included angle C = 40°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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16. 16.

    A 14 kg object moves at 8 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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17. 17.

    Find the momentum of a 32 kg object moving at 26 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A population of 8,000 grows 10% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    A 13 kg object moves at 4 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    A triangle has sides a = 6 cm and b = 14 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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