Argentina · Grado 10 · Practice Sheet 33

1. 1.

   A triangle has sides a = 18 cm and b = 19 cm with an included angle C = 30°. Find its area (to 2 d.p.).

   Formula:Area of a Triangle (Sine Rule)

   $A = \tfrac{1}{2} ab\sin C$

   View formula →
2. 2.

   Solve using the quadratic formula: x² + 9x + 18 = 0.

   Formula:Quadratic Formula

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

   View formula →
3. 3.

   Solve for x: 8x + 14 = 70.

   Formula:Solving a Linear Equation

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

   View formula →
4. 4.

   Find the momentum of a 56 kg object moving at 13 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
5. 5.

   A wave has frequency 505 Hz and wavelength 2.38 m. Find its speed.

   Formula:Wave Speed

   $v = f\lambda$

   View formula →
6. 6.

   A population of 5,300 grows 3% per year. Find its size after 5 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
7. 7.

   $4,800 is invested at 4% simple interest per year for 5 years. Find the interest earned.

   Formula:Simple Interest

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

   View formula →
8. 8.

   Find the gravitational potential energy of a 32 kg object raised 15 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
9. 9.

   $1,700 is invested at 8% simple interest per year for 3 years. Find the interest earned.

   Formula:Simple Interest

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

   View formula →
10. 10.

    An object with initial velocity 10 m/s accelerates at 1.3 m/s² for 10 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →
11. 11.

    A cylinder has radius 2 cm and height 7 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

    View formula →
12. 12.

    An object has mass 44 g and volume 40 cm³. Find its density.

    Formula:Density

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

    View formula →
13. 13.

    A value changes from 147 to 181. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

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

    View formula →
14. 14.

    In a triangle, a = 18, b = 9 and the included angle C = 70°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
15. 15.

    Find the force needed to accelerate a 23 kg mass at 4.3 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
16. 16.

    A cylinder has radius 2 cm and height 22 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cylinder

    $V = \pi r^2 h$

    View formula →
17. 17.

    A current of 3.5 A flows through a 60 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
18. 18.

    A triangle has sides a = 5 cm and b = 10 cm with an included angle C = 30°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

    $A = \tfrac{1}{2} ab\sin C$

    View formula →
19. 19.

    In a triangle, a = 18, b = 12 and the included angle C = 110°. Find side c (to 2 d.p.).

    Formula:Cosine Rule

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

    View formula →
20. 20.

    Find the volume of a sphere of radius 12 cm. (π ≈ 3.14159)

    Formula:Volume of a Sphere

    $V = \tfrac{4}{3} \pi r^3$

    View formula →

© FormulaWon — formulawon.app · Answers & step-by-step working available on the solutions sheet.