United States · Grade 9 · Practice Sheet 43

1. 1.

   A circle has a radius of 11 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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2. 2.

   A 14 kg object moves at 21 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

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3. 3.

   Solve for x: 7x + 14 = 63.

   Formula:Solving a Linear Equation

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

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4. 4.

   Find the force needed to accelerate a 36 kg mass at 3.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   A right-angled triangle has legs of 19 cm and 12 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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6. 6.

   Find the force needed to accelerate a 38 kg mass at 6.4 m/s².

   Formula:Newton's Second Law

   $F = ma$

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7. 7.

   A cylinder has radius 14 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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8. 8.

   Find the force needed to accelerate a 9 kg mass at 4.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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9. 9.

   A circle has a radius of 25 cm. Find its area. (Use π ≈ 3.14159)

   Formula:Area of a Circle

   $A = \pi r^2$

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10. 10.

    Solve for x: 5x + 14 = 49.

    Formula:Solving a Linear Equation

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

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11. 11.

    Find the force needed to accelerate a 8 kg mass at 4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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12. 12.

    A cylinder has radius 13 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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13. 13.

    $154 is shared in the ratio 3 : 4. Find each share.

    Formula:Dividing in a Ratio

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

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14. 14.

    A bag has 14 equally likely marbles, of which 12 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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15. 15.

    A current of 3.4 A flows through a 16 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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16. 16.

    A device runs at 119 V drawing 5.4 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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17. 17.

    Find the force needed to accelerate a 52 kg mass at 7.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    $3,800 is invested at 3% compound interest per annum for 4 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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19. 19.

    An object has mass 24.3 g and volume 27 cm³. Find its density.

    Formula:Density

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

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20. 20.

    A bag has 30 equally likely marbles, of which 18 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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