Nigeria · Grade 12 · Practice Sheet 14

1. 1.

   A population of 5,100 grows 3% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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2. 2.

   Find the force needed to accelerate a 14 kg mass at 4.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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3. 3.

   In a triangle, a = 17, b = 10 and the included angle C = 80°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

   $c = \sqrt{a^2 + b^2 - 2ab\cos C}$

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4. 4.

   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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5. 5.

   A cone has base radius 9 cm and height 23 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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6. 6.

   A wave has frequency 528 Hz and wavelength 3.23 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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7. 7.

   Find the gravitational potential energy of a 15 kg object raised 14 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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8. 8.

   A current of 4.1 A flows through a 59 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 1 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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10. 10.

    Find the force needed to accelerate a 9 kg mass at 5.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    Two masses 6,600 kg and 270 kg are 20 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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12. 12.

    Find the force needed to accelerate a 18 kg mass at 3.4 m/s².

    Formula:Newton's Second Law

    $F = ma$

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13. 13.

    ₦2,100 is invested at 6% 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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14. 14.

    An object with initial velocity 12 m/s accelerates at 3.9 m/s² for 7 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

    $s = ut + \tfrac{1}{2}at^2$

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15. 15.

    Find the force needed to accelerate a 32 kg mass at 7.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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16. 16.

    ₦1,200 is invested at 6% 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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17. 17.

    A current of 5.2 A flows through a 27 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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18. 18.

    ₦1,400 is invested at 4% 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.

    Solve using the quadratic formula: x² + 5x + 0 = 0.

    Formula:Quadratic Formula

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

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20. 20.

    Find the sum of the first 8 terms of a geometric series with first term a = 3 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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