Singapore · Grade 10 · Practice Sheet 2

1. 1.

   Find the sum of the first 15 terms of an arithmetic series with first term a = 6 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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2. 2.

   Find the gravitational potential energy of a 6 kg object raised 36 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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3. 3.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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4. 4.

   A cylinder has radius 4 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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5. 5.

   A population of 5,000 grows 8% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   Find the momentum of a 16 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   A value changes from 158 to 239. 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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8. 8.

   A 19 kg object moves at 3 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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9. 9.

   A wave has frequency 631 Hz and wavelength 2.42 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    A right-angled triangle has legs of 19 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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11. 11.

    $1,600 is invested at 3% simple interest per year for 6 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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12. 12.

    Solve for x: 9x + 17 = 89.

    Formula:Solving a Linear Equation

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

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13. 13.

    Find the gravitational potential energy of a 39 kg object raised 2 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    A device runs at 237 V drawing 4.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    Find the force needed to accelerate a 13 kg mass at 6.7 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    A device runs at 173 V drawing 7.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    A triangle has sides a = 11 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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18. 18.

    An object with initial velocity 7 m/s accelerates at 2.9 m/s² for 3 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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19. 19.

    In a triangle, a = 7, b = 17 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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20. 20.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 3 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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