Lebanon · Grade 10 · Practice Sheet 5

1. 1.

   LL 2,000 is invested at 4% 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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2. 2.

   A bag has 14 equally likely marbles, of which 12 are red. Find the probability of drawing a red marble (to 3 d.p.).

   Formula:Simple Probability

   $P(E) = \dfrac{\text{favourable}}{\text{total}}$

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3. 3.

   A right-angled triangle has legs of 6 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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4. 4.

   A population of 5,900 grows 3% per year. Find its size after 3 years (nearest whole number).

   Formula:Exponential Growth

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

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5. 5.

   A wave has frequency 703 Hz and wavelength 1.5 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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6. 6.

   A 35 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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7. 7.

   A device runs at 228 V drawing 7.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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8. 8.

   Solve using the quadratic formula: x² + 0x − 36 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   Find the momentum of a 29 kg object moving at 22 m/s.

   Formula:Momentum

   $p = mv$

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10. 10.

    Find the force needed to accelerate a 3 kg mass at 3.9 m/s².

    Formula:Newton's Second Law

    $F = ma$

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11. 11.

    A triangle has sides a = 7 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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12. 12.

    In a triangle, a = 17, b = 16 and the included angle C = 50°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

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13. 13.

    A cylinder has radius 8 cm and height 12 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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14. 14.

    A current of 3.5 A flows through a 50 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

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15. 15.

    Find the sum of the first 17 terms of an arithmetic series with first term a = 11 and common difference d = 6.

    Formula:Sum of an Arithmetic Series

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

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16. 16.

    A wave has frequency 544 Hz and wavelength 4.87 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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17. 17.

    Solve for x: 8x + 8 = 64.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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18. 18.

    LL 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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19. 19.

    A device runs at 118 V drawing 8.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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20. 20.

    Solve for x: 9x + 20 = 128.

    Formula:Solving a Linear Equation

    $x = \dfrac{c - b}{a}$

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