Chile · Grado 10 · Practice Sheet 19

1. 1.

   A 15 kg object moves at 11 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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2. 2.

   Solve using the quadratic formula: x² + 1x + 0 = 0.

   Formula:Quadratic Formula

   $x = \dfrac{-b \pm \sqrt{b^2 - 4ac}}{2a}$

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3. 3.

   A cylinder has radius 14 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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4. 4.

   A bag has 12 equally likely marbles, of which 11 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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5. 5.

   A wave has frequency 667 Hz and wavelength 2.2 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A value changes from 54 to 136. 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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7. 7.

   A force of 68 N moves an object 30 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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8. 8.

   Find the sum of the first 16 terms of an arithmetic series with first term a = 9 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

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9. 9.

   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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10. 10.

    In a triangle, a = 13, b = 13 and the included angle C = 60°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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11. 11.

    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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12. 12.

    A value changes from 86 to 100. 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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13. 13.

    Find the momentum of a 60 kg object moving at 10 m/s.

    Formula:Momentum

    $p = mv$

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14. 14.

    A force of 52 N moves an object 38 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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15. 15.

    $1,100 is invested at 6% 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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16. 16.

    Find the momentum of a 41 kg object moving at 7 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    A device runs at 164 V drawing 1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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18. 18.

    Solve for x: 7x + 16 = 30.

    Formula:Solving a Linear Equation

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

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19. 19.

    An object with initial velocity 13 m/s accelerates at 4.6 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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20. 20.

    Find the force needed to accelerate a 45 kg mass at 1.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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