Nigeria · Grade 10 · Practice Sheet 13

1. 1.

   A cone has base radius 11 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   A right-angled triangle has legs of 14 cm and 8 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   Solve using the quadratic formula: x² + 3x − 10 = 0.

   Formula:Quadratic Formula

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

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4. 4.

   A cylinder has radius 12 cm and height 24 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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5. 5.

   Find the volume of a sphere of radius 8 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   A force of 93 N moves an object 2 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   ₦2,000 is invested at 10% simple interest per year for 6 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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8. 8.

   A device runs at 198 V drawing 6.7 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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9. 9.

   In a triangle, a = 7, b = 8 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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10. 10.

    A wave has frequency 115 Hz and wavelength 0.86 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A force of 232 N acts on an area of 7 m². Find the pressure.

    Formula:Pressure

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

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12. 12.

    A value changes from 58 to 194. 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.

    ₦1,000 is invested at 8% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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14. 14.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 1 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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15. 15.

    ₦3,900 is invested at 5% simple interest per year for 4 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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16. 16.

    Find the sum of the first 18 terms of an arithmetic series with first term a = 12 and common difference d = 8.

    Formula:Sum of an Arithmetic Series

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

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17. 17.

    ₦2,400 is invested at 6% simple interest per year for 2 years. Find the interest earned.

    Formula:Simple Interest

    $I = \dfrac{P \times r \times t}{100}$

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18. 18.

    A body starts at 0 m/s and accelerates at 2.1 m/s² for 9 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    An object has mass 55.3 g and volume 7 cm³. Find its density.

    Formula:Density

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

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20. 20.

    A current of 2.8 A flows through a 7 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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