Tanzania · Grade 10 · Practice Sheet 5

1. 1.

   In a triangle, a = 16, b = 17 and the included angle C = 110°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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2. 2.

   An object with initial velocity 12 m/s accelerates at 1.2 m/s² for 6 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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3. 3.

   A wave has frequency 28 Hz and wavelength 4.46 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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4. 4.

   Solve for x: 2x + 18 = 36.

   Formula:Solving a Linear Equation

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

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5. 5.

   Find the force needed to accelerate a 37 kg mass at 5.8 m/s².

   Formula:Newton's Second Law

   $F = ma$

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6. 6.

   An object with initial velocity 1 m/s accelerates at 2.8 m/s² for 7 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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7. 7.

   Find the force needed to accelerate a 53 kg mass at 4.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   Find the sum of the first 20 terms of an arithmetic series with first term a = 1 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

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9. 9.

   A device runs at 180 V drawing 9.6 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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10. 10.

    An object has mass 130 g and volume 20 cm³. Find its density.

    Formula:Density

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

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11. 11.

    A population of 7,400 grows 10% per year. Find its size after 7 years (nearest whole number).

    Formula:Exponential Growth

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

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12. 12.

    TSh 1,100 is invested at 6% simple interest per year for 5 years. Find the interest earned.

    Formula:Simple Interest

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

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13. 13.

    A force of 289 N acts on an area of 3.6 m². Find the pressure.

    Formula:Pressure

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

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14. 14.

    A 17 kg object moves at 24 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

    $KE = \tfrac{1}{2} m v^2$

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15. 15.

    A triangle has sides a = 19 cm and b = 5 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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16. 16.

    Find the momentum of a 26 kg object moving at 28 m/s.

    Formula:Momentum

    $p = mv$

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17. 17.

    An object has mass 201 g and volume 30 cm³. Find its density.

    Formula:Density

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

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18. 18.

    A triangle has sides a = 7 cm and b = 15 cm with an included angle C = 60°. 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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19. 19.

    TSh 2,900 is invested at 5% compound interest per annum for 2 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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20. 20.

    A population of 3,800 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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