New Zealand · Year 10 · Practice Sheet 12

1. 1.

   A cone has base radius 9 cm and height 18 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 right-angled triangle has legs of 8 cm and 19 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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3. 3.

   $3,300 is invested at 6% simple interest per year for 2 years. Find the interest earned.

   Formula:Simple Interest

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

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4. 4.

   A value changes from 193 to 132. 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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5. 5.

   A device runs at 55 V drawing 0.3 A. Find its power consumption.

   Formula:Electrical Power

   $P = V I$

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6. 6.

   In a triangle, a = 9, b = 12 and the included angle C = 100°. Find side c (to 2 d.p.).

   Formula:Cosine Rule

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

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7. 7.

   Solve for x: 3x + 5 = 23.

   Formula:Solving a Linear Equation

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

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8. 8.

   Solve using the quadratic formula: x² + 0x − 4 = 0.

   Formula:Quadratic Formula

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

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9. 9.

   Find the force needed to accelerate a 16 kg mass at 1.9 m/s².

   Formula:Newton's Second Law

   $F = ma$

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10. 10.

    An object has mass 229.6 g and volume 28 cm³. Find its density.

    Formula:Density

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

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11. 11.

    Find the momentum of a 12 kg object moving at 9 m/s.

    Formula:Momentum

    $p = mv$

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12. 12.

    A cylinder has radius 3 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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13. 13.

    Find the sum of the first 7 terms of an arithmetic series with first term a = 5 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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14. 14.

    A population of 7,800 grows 8% per year. Find its size after 8 years (nearest whole number).

    Formula:Exponential Growth

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

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15. 15.

    A force of 118 N moves an object 6 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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16. 16.

    Find the force needed to accelerate a 50 kg mass at 6.8 m/s².

    Formula:Newton's Second Law

    $F = ma$

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17. 17.

    Find the momentum of a 42 kg object moving at 4 m/s.

    Formula:Momentum

    $p = mv$

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18. 18.

    A force of 34 N moves an object 25 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

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19. 19.

    $2,900 is invested at 3% compound interest per annum for 4 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 device runs at 92 V drawing 2.8 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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