United States · Grade 9 · Practice Sheet 16

1. 1.

   A value changes from 86 to 33. 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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2. 2.

   A current of 5 A flows through a 48 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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3. 3.

   A cone has base radius 3 cm and height 9 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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4. 4.

   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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5. 5.

   Find the volume of a sphere of radius 11 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

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6. 6.

   A cylinder has radius 10 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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7. 7.

   A force of 10 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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8. 8.

   Find the gravitational potential energy of a 20 kg object raised 8 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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9. 9.

   A wave has frequency 853 Hz and wavelength 3.94 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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10. 10.

    $1,100 is invested at 5% compound interest per annum for 5 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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11. 11.

    $3,400 is invested at 6% 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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12. 12.

    $2,100 is invested at 4% compound interest per annum for 5 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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13. 13.

    Find the volume of a sphere of radius 2 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

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

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14. 14.

    A wave has frequency 847 Hz and wavelength 2.13 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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15. 15.

    Find the circumference of a circle whose radius is 24 m. (Use π ≈ 3.14159)

    Formula:Circumference of a Circle

    $C = 2\pi r$

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16. 16.

    A wave has frequency 476 Hz and wavelength 4.34 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    A right-angled triangle has legs of 5 cm and 3 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 418 N acts on an area of 9.1 m². Find the pressure.

    Formula:Pressure

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

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19. 19.

    Solve for x: 9x + 19 = 127.

    Formula:Solving a Linear Equation

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

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20. 20.

    A cone has base radius 4 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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