Singapore · Grade 10 · Practice Sheet 22

1. 1.

   A right-angled triangle has legs of 3 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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2. 2.

   A wave has frequency 598 Hz and wavelength 1.32 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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3. 3.

   A body starts at 6 m/s and accelerates at 3 m/s² for 5 s. Find its final velocity.

   Formula:Kinematics (v = u + at)

   $v = u + at$

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4. 4.

   Find the force needed to accelerate a 38 kg mass at 1.6 m/s².

   Formula:Newton's Second Law

   $F = ma$

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5. 5.

   An object with initial velocity 15 m/s accelerates at 3.3 m/s² for 9 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

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6. 6.

   Solve for x: 8x + 16 = 80.

   Formula:Solving a Linear Equation

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

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7. 7.

   A wave has frequency 331 Hz and wavelength 4.83 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

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8. 8.

   A right-angled triangle has legs of 18 cm and 6 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

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9. 9.

   Find the sum of the first 7 terms of an arithmetic series with first term a = 8 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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10. 10.

    $3,100 is invested at 7.5% 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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11. 11.

    A cylinder has radius 11 cm and height 13 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

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12. 12.

    In a triangle, a = 17, b = 9 and the included angle C = 80°. 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.

    Solve using the quadratic formula: x² − 1x − 2 = 0.

    Formula:Quadratic Formula

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

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14. 14.

    A device runs at 17 V drawing 3.6 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

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15. 15.

    A force of 81 N acts on an area of 1 m². Find the pressure.

    Formula:Pressure

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

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16. 16.

    A triangle has sides a = 13 cm and b = 11 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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17. 17.

    A wave has frequency 626 Hz and wavelength 3.01 m. Find its speed.

    Formula:Wave Speed

    $v = f\lambda$

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18. 18.

    A body starts at 9 m/s and accelerates at 4.1 m/s² for 7 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

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19. 19.

    An object with initial velocity 6 m/s accelerates at 2.4 m/s² for 8 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

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20. 20.

    Find the force needed to accelerate a 11 kg mass at 0.5 m/s².

    Formula:Newton's Second Law

    $F = ma$

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