Kuwait · Grade 10 · Practice Sheet 37

1. 1.

   Find the sum of the first 5 terms of an arithmetic series with first term a = 12 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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2. 2.

   A bag has 28 equally likely marbles, of which 7 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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3. 3.

   Solve for x: 3x + 16 = 28.

   Formula:Solving a Linear Equation

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

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4. 4.

   Find the gravitational potential energy of a 15 kg object raised 3 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A device runs at 116 V drawing 8.9 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   An object with initial velocity 6 m/s accelerates at 4.9 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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7. 7.

   In a triangle, a = 13, b = 12 and the included angle C = 40°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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8. 8.

   Find the force needed to accelerate a 47 kg mass at 7.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   KD 2,800 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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10. 10.

    A force of 102 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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11. 11.

    A wave has frequency 379 Hz and wavelength 4.48 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A 31 kg object moves at 20 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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13. 13.

    A cone has base radius 7 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    A value changes from 162 to 57. 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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15. 15.

    KD 1,600 is invested at 3% 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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16. 16.

    Find the sum of the first 13 terms of an arithmetic series with first term a = 8 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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17. 17.

    A 8 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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18. 18.

    A body starts at 12 m/s and accelerates at 1.8 m/s² for 8 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    Find the gravitational potential energy of a 44 kg object raised 31 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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20. 20.

    A wave has frequency 732 Hz and wavelength 2.71 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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