United States · Grade 12 · Practice Sheet 34

1. 1.

   A cone has base radius 9 cm and height 14 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

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2. 2.

   A force of 81 N moves an object 35 m in the direction of the force. Find the work done.

   Formula:Work Done

   $W = F d$

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3. 3.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 10 and common difference d = 8.

   Formula:Sum of an Arithmetic Series

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

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4. 4.

   Find the force needed to accelerate a 9 kg mass at 3.2 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 9 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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6. 6.

   Find the sum of the first 7 terms of a geometric series with first term a = 1 and common ratio r = 4.

   Formula:Sum of a Geometric Series

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

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7. 7.

   Find the force needed to accelerate a 32 kg mass at 1.5 m/s².

   Formula:Newton's Second Law

   $F = ma$

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8. 8.

   Find the sum of the first 6 terms of an arithmetic series with first term a = 5 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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9. 9.

   A force of 25 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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10. 10.

    A body starts at 4 m/s and accelerates at 4.5 m/s² for 4 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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11. 11.

    In a triangle, a = 9, b = 5 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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12. 12.

    A body starts at 12 m/s and accelerates at 1.4 m/s² for 3 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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13. 13.

    An object with initial velocity 14 m/s accelerates at 4.3 m/s² for 5 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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14. 14.

    A triangle has sides a = 14 cm and b = 9 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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15. 15.

    A population of 7,100 grows 5% per year. Find its size after 4 years (nearest whole number).

    Formula:Exponential Growth

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

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16. 16.

    Find the force needed to accelerate a 10 kg mass at 2.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    A triangle has sides a = 6 cm and b = 11 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 39 kg object moves at 11 m/s. Find its kinetic energy.

    Formula:Kinetic Energy

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

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19. 19.

    Find the force needed to accelerate a 15 kg mass at 7.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

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20. 20.

    A force of 97 N moves an object 4 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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