Kenya · Grade 10 · Practice Sheet 27

1. 1.

   Solve using the quadratic formula: x² − 7x + 6 = 0.

   Formula:Quadratic Formula

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

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2. 2.

   Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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3. 3.

   A wave has frequency 198 Hz and wavelength 0.79 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   A value changes from 74 to 96. 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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5. 5.

   A bag has 19 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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6. 6.

   A value changes from 30 to 211. 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 320 N acts on an area of 0.9 m². Find the pressure.

   Formula:Pressure

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

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8. 8.

   A right-angled triangle has legs of 16 cm and 13 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   A device runs at 27 V drawing 7.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A cone has base radius 5 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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11. 11.

    In a triangle, a = 6, b = 12 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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12. 12.

    A cylinder has radius 7 cm and height 30 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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13. 13.

    A wave has frequency 755 Hz and wavelength 2.07 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A cylinder has radius 14 cm and height 5 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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15. 15.

    Find the sum of the first 19 terms of an arithmetic series with first term a = 5 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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16. 16.

    Find the momentum of a 23 kg object moving at 12 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    An object with initial velocity 0 m/s accelerates at 4.2 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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18. 18.

    A 5 kg object moves at 10 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

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

    Formula:Density

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

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20. 20.

    A 11 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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