New Zealand · Year 10 · Practice Sheet 39

1. 1.

   A triangle has sides a = 11 cm and b = 6 cm with an included angle C = 90°. 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 for x: 3x + 20 = 44.

   Formula:Solving a Linear Equation

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

   View formula →
3. 3.

   Find the gravitational potential energy of a 13 kg object raised 19 m. (g = 9.8 m/s²)

   Formula:Gravitational Potential Energy

   $PE = mgh$

   View formula →
4. 4.

   A 28 kg object moves at 20 m/s. Find its kinetic energy.

   Formula:Kinetic Energy

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

   View formula →
5. 5.

   A current of 6.5 A flows through a 7 Ω resistor. Find the voltage across it.

   Formula:Ohm's Law

   $V = I R$

   View formula →
6. 6.

   Find the volume of a sphere of radius 10 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
7. 7.

   An object with initial velocity 0 m/s accelerates at 2.7 m/s² for 3 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
8. 8.

   A population of 7,000 grows 5% per year. Find its size after 2 years (nearest whole number).

   Formula:Exponential Growth

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

   View formula →
9. 9.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 7 and common difference d = 4.

   Formula:Sum of an Arithmetic Series

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

   View formula →
10. 10.

    Solve for x: 4x + 6 = 30.

    Formula:Solving a Linear Equation

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

    View formula →
11. 11.

    A bag has 21 equally likely marbles, of which 8 are red. Find the probability of drawing a red marble (to 3 d.p.).

    Formula:Simple Probability

    $P(E) = \dfrac{\text{favourable}}{\text{total}}$

    View formula →
12. 12.

    A force of 40 N moves an object 7 m in the direction of the force. Find the work done.

    Formula:Work Done

    $W = F d$

    View formula →
13. 13.

    $1,100 is invested at 6% compound interest per annum for 2 years. Find the final amount (to 2 d.p.).

    Formula:Compound Interest

    $A = P\left(1 + \dfrac{r}{100}\right)^{t}$

    View formula →
14. 14.

    A current of 6 A flows through a 29 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
15. 15.

    A body starts at 3 m/s and accelerates at 4.5 m/s² for 2 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
16. 16.

    A triangle has sides a = 8 cm and b = 12 cm with an included angle C = 45°. Find its area (to 2 d.p.).

    Formula:Area of a Triangle (Sine Rule)

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

    View formula →
17. 17.

    Find the force needed to accelerate a 24 kg mass at 5.1 m/s².

    Formula:Newton's Second Law

    $F = ma$

    View formula →
18. 18.

    Find the gravitational potential energy of a 45 kg object raised 23 m. (g = 9.8 m/s²)

    Formula:Gravitational Potential Energy

    $PE = mgh$

    View formula →
19. 19.

    Find the momentum of a 37 kg object moving at 22 m/s.

    Formula:Momentum

    $p = mv$

    View formula →
20. 20.

    Find the sum of the first 9 terms of an arithmetic series with first term a = 1 and common difference d = 7.

    Formula:Sum of an Arithmetic Series

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

    View formula →

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