Singapore · Grade 10 · Practice Sheet 4

1. 1.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 12 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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2. 2.

   A cylinder has radius 13 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.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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4. 4.

   A cone has base radius 5 cm and height 15 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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5. 5.

   In a triangle, a = 5, b = 12 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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6. 6.

   Find the momentum of a 33 kg object moving at 24 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A device runs at 138 V drawing 2.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   A body starts at 6 m/s and accelerates at 4.1 m/s² for 3 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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9. 9.

   A force of 96 N moves an object 11 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 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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11. 11.

    A device runs at 191 V drawing 8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    Find the gravitational potential energy of a 27 kg object raised 24 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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13. 13.

    $800 is invested at 6% compound interest per annum for 2 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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14. 14.

    A right-angled triangle has legs of 11 cm and 20 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    Find the momentum of a 30 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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16. 16.

    $1,800 is invested at 4% 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 cylinder has radius 13 cm and height 29 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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18. 18.

    Find the gravitational potential energy of a 22 kg object raised 15 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    A device runs at 96 V drawing 4.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    An object has mass 172.2 g and volume 41 cm³. Find its density.

    Formula:Density

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

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