South Korea · Grade 10 · Practice Sheet 27

1. 1.

   In a triangle, a = 6, b = 17 and the included angle C = 50°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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2. 2.

   A population of 4,600 grows 5% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   Solve for x: 5x + 3 = 53.

   Formula:Solving a Linear Equation

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

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4. 4.

   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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5. 5.

   Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   A device runs at 183 V drawing 2.4 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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7. 7.

   In a triangle, a = 11, b = 17 and the included angle C = 70°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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8. 8.

   An object with initial velocity 5 m/s accelerates at 2.4 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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9. 9.

   In a triangle, a = 5, b = 14 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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10. 10.

    A wave has frequency 744 Hz and wavelength 1.21 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    Find the momentum of a 24 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A cone has base radius 8 cm and height 8 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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13. 13.

    A population of 8,300 grows 8% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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14. 14.

    A body starts at 17 m/s and accelerates at 3.9 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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15. 15.

    An object with initial velocity 4 m/s accelerates at 2.6 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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16. 16.

    A current of 4.8 A flows through a 49 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    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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18. 18.

    Find the momentum of a 57 kg object moving at 5 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    ₩3,900 is invested at 5% 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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20. 20.

    Find the gravitational potential energy of a 48 kg object raised 35 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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