Kuwait · Grade 10 · Practice Sheet 33

1. 1.

   A value changes from 110 to 245. Find the percentage change (to 2 d.p.).

   Formula:Percentage Change

   $\%\,\text{change} = \dfrac{\text{new} - \text{old}}{\text{old}} \times 100$

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2. 2.

   In a triangle, a = 16, b = 11 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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3. 3.

   A triangle has sides a = 13 cm and b = 16 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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4. 4.

   A current of 7.7 A flows through a 52 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

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5. 5.

   A cylinder has radius 4 cm and height 21 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cylinder

   $V = \pi r^2 h$

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6. 6.

   A cone has base radius 3 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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7. 7.

   A population of 4,300 grows 10% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

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8. 8.

   KD 2,600 is invested at 4% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

   $I = \dfrac{P \times r \times t}{100}$

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9. 9.

   A device runs at 168 V drawing 2.1 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    A wave has frequency 881 Hz and wavelength 2.5 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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11. 11.

    An object with initial velocity 13 m/s accelerates at 4.9 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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12. 12.

    A cone has base radius 10 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

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13. 13.

    Find the force needed to accelerate a 10 kg mass at 1.2 m/s².

    Formula:Newton's Second Law

    $F = ma$

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14. 14.

    An object has mass 111 g and volume 30 cm³. Find its density.

    Formula:Density

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

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15. 15.

    Find the gravitational potential energy of a 19 kg object raised 14 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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16. 16.

    A force of 281 N acts on an area of 9.8 m². Find the pressure.

    Formula:Pressure

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

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17. 17.

    A wave has frequency 107 Hz and wavelength 0.53 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    Find the gravitational potential energy of a 47 kg object raised 7 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

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19. 19.

    Find the sum of the first 15 terms of an arithmetic series with first term a = 2 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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20. 20.

    Solve for x: 6x + 2 = 44.

    Formula:Solving a Linear Equation

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

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