Tanzania · Grade 12 · Practice Sheet 10

1. 1.

   A triangle has sides a = 17 cm and b = 10 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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2. 2.

   A force of 466 N acts on an area of 9.3 m². Find the pressure.

   Formula:Pressure

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

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3. 3.

   Find the sum of the first 5 terms of a geometric series with first term a = 7 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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4. 4.

   Find the gravitational potential energy of a 48 kg object raised 16 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

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5. 5.

   A cone has base radius 3 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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6. 6.

   Find the momentum of a 41 kg object moving at 19 m/s.

   Formula:Momentum

   $p = mv$

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7. 7.

   Find the sum of the first 3 terms of a geometric series with first term a = 6 and common ratio r = 3.

   Formula:Sum of a Geometric Series

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

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8. 8.

   A force of 58 N moves an object 6 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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9. 9.

   In a triangle, a = 16, b = 10 and the included angle C = 60°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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10. 10.

    TSh 3,900 is invested at 6% 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.

    Find the gravitational potential energy of a 4 kg object raised 3 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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12. 12.

    A device runs at 65 V drawing 1.1 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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13. 13.

    A triangle has sides a = 5 cm and b = 16 cm with an included angle C = 30°. 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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14. 14.

    In a triangle, a = 11, b = 17 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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15. 15.

    A population of 3,300 grows 2% per year. Find its size after 6 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    A force of 410 N acts on an area of 2.6 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    A triangle has sides a = 19 cm and b = 9 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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18. 18.

    A force of 118 N moves an object 36 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    A force of 186 N acts on an area of 5.9 m². Find the pressure.

    Formula:Pressure

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

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20. 20.

    A cone has base radius 3 cm and height 17 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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