Singapore · Grade 10 · Practice Sheet 47

1. 1.

   Find the force needed to accelerate a 30 kg mass at 8.1 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   $3,800 is invested at 8% 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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3. 3.

   A device runs at 74 V drawing 9.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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4. 4.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 9 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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5. 5.

   A population of 1,300 grows 8% per year. Find its size after 4 years (nearest whole number).

   Formula:Exponential Growth

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

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6. 6.

   A wave has frequency 572 Hz and wavelength 0.38 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the sum of the first 9 terms of an arithmetic series with first term a = 5 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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8. 8.

   An object with initial velocity 2 m/s accelerates at 1 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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9. 9.

   Find the momentum of a 53 kg object moving at 26 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    A population of 1,100 grows 3% per year. Find its size after 5 years (nearest whole number).

    Formula:Exponential Growth

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

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11. 11.

    A 22 kg object moves at 17 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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12. 12.

    Solve for x: 6x + 6 = 30.

    Formula:Solving a Linear Equation

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

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13. 13.

    Find the gravitational potential energy of a 11 kg object raised 6 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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14. 14.

    Solve for x: 5x + 2 = 47.

    Formula:Solving a Linear Equation

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

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15. 15.

    In a triangle, a = 13, b = 10 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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16. 16.

    An object with initial velocity 7 m/s accelerates at 2.9 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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17. 17.

    A population of 6,200 grows 10% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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18. 18.

    Find the volume of a sphere of radius 5 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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19. 19.

    A force of 409 N acts on an area of 1.4 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    Find the momentum of a 20 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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