Singapore · Grade 10 · Practice Sheet 5

1. 1.

   A cylinder has radius 2 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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2. 2.

   A body starts at 3 m/s and accelerates at 4.9 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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3. 3.

   A wave has frequency 171 Hz and wavelength 3.58 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   $5,000 is invested at 6% 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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5. 5.

   $700 is invested at 4% 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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6. 6.

   An object has mass 36.3 g and volume 33 cm³. Find its density.

   Formula:Density

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

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7. 7.

   A cone has base radius 10 cm and height 18 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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8. 8.

   A right-angled triangle has legs of 8 cm and 17 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   A current of 1.6 A flows through a 34 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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10. 10.

    A force of 45 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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11. 11.

    A wave has frequency 290 Hz and wavelength 1.6 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A body starts at 19 m/s and accelerates at 4.9 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    A wave has frequency 106 Hz and wavelength 1.53 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 8 and common difference d = 5.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    A current of 2.7 A flows through a 13 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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17. 17.

    A value changes from 158 to 210. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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18. 18.

    Find the sum of the first 16 terms of an arithmetic series with first term a = 10 and common difference d = 2.

    Formula:Sum of an Arithmetic Series

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

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19. 19.

    A force of 69 N moves an object 10 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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20. 20.

    A value changes from 175 to 110. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

    $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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