Malaysia · Year 11 · Practice Sheet 30

1. 1.

   A right-angled triangle has legs of 14 cm and 5 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A cylinder has radius 12 cm and height 6 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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3. 3.

   In a triangle, a = 18, b = 16 and the included angle C = 100°. 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.

   Find the volume of a sphere of radius 9 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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5. 5.

   Find the population standard deviation of: 9, 8, 14, 15, 8 (to 2 d.p.).

   Formula:Standard Deviation (Population)

   $\sigma = \sqrt{\dfrac{\sum (x - \bar{x})^2}{n}}$

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6. 6.

   Find the sum of the first 8 terms of a geometric series with first term a = 8 and common ratio r = 4.

   Formula:Sum of a Geometric Series

   $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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7. 7.

   A force of 61 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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8. 8.

   A wave has frequency 390 Hz and wavelength 4.76 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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9. 9.

   RM 2,100 is invested at 6% compound interest per annum for 5 years. Find the final amount (to 2 d.p.).

   Formula:Compound Interest

   $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

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10. 10.

    In a triangle, a = 12, b = 5 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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11. 11.

    A current of 1.4 A flows through a 31 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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12. 12.

    A body starts at 18 m/s and accelerates at 3.2 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    A device runs at 236 V drawing 2.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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14. 14.

    A right-angled triangle has legs of 17 cm and 12 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    A force of 227 N acts on an area of 2 m². Find the pressure.

    Formula:Pressure

    $P = \dfrac{F}{A}$

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16. 16.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 7 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

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17. 17.

    Find the sum of the first 8 terms of a geometric series with first term a = 3 and common ratio r = 4.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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18. 18.

    Two masses 4,300 kg and 430 kg are 7 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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19. 19.

    A force of 34 N moves an object 34 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A cylinder has radius 7 cm and height 25 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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