United States · Grade 9 · Practice Sheet 22

1. 1.

   Find the force needed to accelerate a 3 kg mass at 1.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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2. 2.

   A cylinder has radius 14 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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3. 3.

   Solve for x: 4x + 7 = 19.

   Formula:Solving a Linear Equation

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

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4. 4.

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

   Formula:Volume of a Cone

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

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5. 5.

   Find the gravitational potential energy of a 16 kg object raised 6 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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6. 6.

   $108 is shared in the ratio 4 : 2. Find each share.

   Formula:Dividing in a Ratio

   $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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7. 7.

   A circle has a radius of 23 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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8. 8.

   Solve for x: 6x + 12 = 72.

   Formula:Solving a Linear Equation

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

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9. 9.

   $4,200 is invested at 10% 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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10. 10.

    Find the force needed to accelerate a 52 kg mass at 5.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    $4,100 is invested at 7.5% 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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12. 12.

    A current of 4.9 A flows through a 31 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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13. 13.

    A wave has frequency 881 Hz and wavelength 2.2 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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14. 14.

    A device runs at 17 V drawing 1.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    $30 is shared in the ratio 2 : 1. Find each share.

    Formula:Dividing in a Ratio

    $\text{share} = \dfrac{\text{part}}{\text{total parts}} \times T$

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16. 16.

    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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17. 17.

    A right-angled triangle has legs of 17 cm and 17 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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18. 18.

    A force of 42 N moves an object 19 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A device runs at 51 V drawing 8.3 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    A current of 1.4 A flows through a 18 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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