United States · Grade 10 · Practice Sheet 28

1. 1.

   A cone has base radius 12 cm and height 10 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.

   Solve for x: 7x + 1 = 71.

   Formula:Solving a Linear Equation

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

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3. 3.

   A triangle has sides a = 17 cm and b = 6 cm with an included angle C = 60°. 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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4. 4.

   A wave has frequency 514 Hz and wavelength 1.64 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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5. 5.

   Find the momentum of a 11 kg object moving at 4 m/s.

   Formula:Momentum

   $p = mv$

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6. 6.

   Find the force needed to accelerate a 5 kg mass at 3.7 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   Find the momentum of a 25 kg object moving at 23 m/s.

   Formula:Momentum

   $p = mv$

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8. 8.

   $1,100 is invested at 6% 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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9. 9.

   A force of 92 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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10. 10.

    A device runs at 49 V drawing 4.2 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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11. 11.

    A wave has frequency 860 Hz and wavelength 2.83 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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12. 12.

    A population of 4,300 grows 2% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    $4,400 is invested at 5% 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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14. 14.

    $1,500 is invested at 8% compound interest per annum for 2 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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15. 15.

    $1,800 is invested at 8% 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 gravitational potential energy of a 37 kg object raised 2 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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17. 17.

    $4,300 is invested at 8% 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.

    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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19. 19.

    A body starts at 19 m/s and accelerates at 4.7 m/s² for 10 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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20. 20.

    A value changes from 67 to 132. 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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