Jordan · Grade 11 · Practice Sheet 18

1. 1.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 3 and common difference d = 7.

   Formula:Sum of an Arithmetic Series

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

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2. 2.

   Solve using the quadratic formula: x² − 4x + 0 = 0.

   Formula:Quadratic Formula

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

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3. 3.

   A wave has frequency 188 Hz and wavelength 1.12 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   JD 2,900 is invested at 8% compound interest per annum for 3 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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5. 5.

   A wave has frequency 307 Hz and wavelength 3.13 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

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

   Formula:Exponential Growth

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

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7. 7.

   A triangle has sides a = 8 cm and b = 19 cm with an included angle C = 45°. 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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8. 8.

   A force of 12 N moves an object 3 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   A population of 1,100 grows 10% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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10. 10.

    A cylinder has radius 5 cm and height 25 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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11. 11.

    Find the gravitational potential energy of a 48 kg object raised 6 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A population of 6,900 grows 3% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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13. 13.

    Find the sum of the first 3 terms of a geometric series with first term a = 4 and common ratio r = 4.

    Formula:Sum of a Geometric Series

    $S_n = \dfrac{a(r^{n} - 1)}{r - 1}$

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14. 14.

    A right-angled triangle has legs of 11 cm and 15 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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15. 15.

    Two masses 8,200 kg and 430 kg are 8 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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16. 16.

    A triangle has sides a = 12 cm and b = 7 cm with an included angle C = 120°. 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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17. 17.

    An object has mass 343 g and volume 49 cm³. Find its density.

    Formula:Density

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

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18. 18.

    Two masses 7,600 kg and 650 kg are 4 m apart. Find the gravitational force between them. (G = 6.674×10⁻¹¹)

    Formula:Newton’s Law of Gravitation

    $F = G\dfrac{m_1 m_2}{r^2}$

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19. 19.

    A 15 kg object moves at 25 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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20. 20.

    Find the force needed to accelerate a 50 kg mass at 1.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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