Belgium · Year 11 · Practice Sheet 15

1. 1.

   A triangle has sides a = 19 cm and b = 13 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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2. 2.

   A population of 8,700 grows 3% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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3. 3.

   A force of 107 N moves an object 32 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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4. 4.

   A current of 3 A flows through a 33 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   A device runs at 94 V drawing 3.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   A force of 85 N moves an object 24 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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7. 7.

   Find the sum of the first 3 terms of a geometric series with first term a = 4 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 population of 3,300 grows 5% per year. Find its size after 8 years (nearest whole number).

   Formula:Exponential Growth

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

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9. 9.

   A cone has base radius 5 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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10. 10.

    Find the momentum of a 57 kg object moving at 29 m/s.

    Formula:Momentum

    $p = mv$

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11. 11.

    Find the sum of the first 14 terms of an arithmetic series with first term a = 7 and common difference d = 1.

    Formula:Sum of an Arithmetic Series

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

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12. 12.

    A force of 106 N moves an object 38 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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13. 13.

    A cone has base radius 4 cm and height 19 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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14. 14.

    An object has mass 70.2 g and volume 13 cm³. Find its density.

    Formula:Density

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

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15. 15.

    A population of 7,100 grows 8% per year. Find its size after 3 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    A right-angled triangle has legs of 11 cm and 18 cm. Find the length of the hypotenuse.

    Formula:Pythagorean Theorem

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

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17. 17.

    Find the force needed to accelerate a 36 kg mass at 5.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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18. 18.

    €3,700 is invested at 8% 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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19. 19.

    A triangle has sides a = 6 cm and b = 11 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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20. 20.

    Find the momentum of a 7 kg object moving at 15 m/s.

    Formula:Momentum

    $p = mv$

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