United States · Grade 10 · Practice Sheet 27

1. 1.

   A force of 112 N moves an object 16 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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2. 2.

   A 9 kg object moves at 6 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   A body starts at 17 m/s and accelerates at 5.8 m/s² for 2 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   An object with initial velocity 9 m/s accelerates at 3.5 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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5. 5.

   A device runs at 127 V drawing 10 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A right-angled triangle has legs of 3 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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7. 7.

   A triangle has sides a = 7 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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8. 8.

   $3,700 is invested at 3% compound interest per annum for 4 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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9. 9.

   A population of 3,800 grows 10% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    An object has mass 148.5 g and volume 33 cm³. Find its density.

    Formula:Density

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

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11. 11.

    A device runs at 203 V drawing 9.9 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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12. 12.

    A force of 41 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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13. 13.

    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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14. 14.

    A bag has 23 equally likely marbles, of which 18 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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15. 15.

    A cone has base radius 7 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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16. 16.

    Find the gravitational potential energy of a 6 kg object raised 3 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    A force of 48 N acts on an area of 2.8 m². Find the pressure.

    Formula:Pressure

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

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18. 18.

    A device runs at 43 V drawing 9.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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19. 19.

    A value changes from 86 to 186. 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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20. 20.

    Find the sum of the first 5 terms of an arithmetic series with first term a = 3 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

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