China · Grade 10 · Practice Sheet 50

1. 1.

   A triangle has sides a = 18 cm and b = 15 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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2. 2.

   Solve using the quadratic formula: x² − 5x − 6 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   A cylinder has radius 13 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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4. 4.

   A triangle has sides a = 6 cm and b = 12 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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5. 5.

   In a triangle, a = 5, b = 18 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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6. 6.

   A force of 58 N moves an object 29 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   Find the momentum of a 25 kg object moving at 5 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   A bag has 24 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.

   An object with initial velocity 6 m/s accelerates at 1.1 m/s² for 10 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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10. 10.

    A 36 kg object moves at 22 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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11. 11.

    A body starts at 16 m/s and accelerates at 5.6 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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12. 12.

    A population of 1,500 grows 5% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    A right-angled triangle has legs of 5 cm and 4 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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14. 14.

    Find the sum of the first 19 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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15. 15.

    A wave has frequency 333 Hz and wavelength 1.3 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    Solve for x: 6x + 5 = 65.

    Formula:Solving a Linear Equation

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

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17. 17.

    Find the gravitational potential energy of a 12 kg object raised 39 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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18. 18.

    Find the momentum of a 39 kg object moving at 25 m/s.

    Formula:Momentum

    $p = mv$

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19. 19.

    An object with initial velocity 6 m/s accelerates at 4.3 m/s² for 2 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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20. 20.

    Find the gravitational potential energy of a 3 kg object raised 6 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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