Singapore · Grade 12 · Practice Sheet 14

1. 1.

   $2,100 is invested at 3% 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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2. 2.

   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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3. 3.

   A force of 22 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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4. 4.

   Find the sum of the first 11 terms of an arithmetic series with first term a = 12 and common difference d = 3.

   Formula:Sum of an Arithmetic Series

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

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5. 5.

   A current of 6.3 A flows through a 56 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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6. 6.

   Find the sum of the first 7 terms of a geometric series with first term a = 1 and common ratio r = 2.

   Formula:Sum of a Geometric Series

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

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7. 7.

   A population of 6,400 grows 3% per year. Find its size after 6 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   A current of 7.7 A flows through a 9 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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9. 9.

   Find the gravitational potential energy of a 43 kg object raised 9 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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10. 10.

    A wave has frequency 875 Hz and wavelength 2.99 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    A triangle has sides a = 20 cm and b = 8 cm with an included angle C = 90°. 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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12. 12.

    Solve using the quadratic formula: x² − 7x + 10 = 0.

    Formula:Quadratic Formula

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

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13. 13.

    Find the sum of the first 8 terms of a geometric series with first term a = 5 and common ratio r = 2.

    Formula:Sum of a Geometric Series

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

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14. 14.

    Find the force needed to accelerate a 24 kg mass at 7.6 m/s².

    Formula:Newton's Second Law

    $F = ma$

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15. 15.

    A wave has frequency 233 Hz and wavelength 2.53 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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16. 16.

    A cone has base radius 5 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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17. 17.

    Find the sum of the first 3 terms of a geometric series with first term a = 7 and common ratio r = 3.

    Formula:Sum of a Geometric Series

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

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18. 18.

    A population of 4,100 grows 8% per year. Find its size after 2 years (nearest whole number).

    Formula:Exponential Growth

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

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19. 19.

    A wave has frequency 479 Hz and wavelength 3.58 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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20. 20.

    In a triangle, a = 16, b = 12 and the included angle C = 100°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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