United Kingdom · Year 10 · Practice Sheet 21

1. 1.

   Find the sum of the first 17 terms of an arithmetic series with first term a = 2 and common difference d = 5.

   Formula:Sum of an Arithmetic Series

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

   View formula →
2. 2.

   A cone has base radius 10 cm and height 10 cm. Find its volume. (π ≈ 3.14159)

   Formula:Volume of a Cone

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

   View formula →
3. 3.

   A right-angled triangle has legs of 5 cm and 7 cm. Find the length of the hypotenuse.

   Formula:Pythagorean Theorem

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

   View formula →
4. 4.

   Find the sum of the first 10 terms of an arithmetic series with first term a = 9 and common difference d = 1.

   Formula:Sum of an Arithmetic Series

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

   View formula →
5. 5.

   Solve for x: 8x + 16 = 104.

   Formula:Solving a Linear Equation

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

   View formula →
6. 6.

   Find the momentum of a 6 kg object moving at 29 m/s.

   Formula:Momentum

   $p = mv$

   View formula →
7. 7.

   An object with initial velocity 8 m/s accelerates at 1.1 m/s² for 5 s. Find the distance travelled.

   Formula:Kinematics (s = ut + ½at²)

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

   View formula →
8. 8.

   Solve for x: 3x + 17 = 44.

   Formula:Solving a Linear Equation

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

   View formula →
9. 9.

   Find the volume of a sphere of radius 6 cm. (π ≈ 3.14159)

   Formula:Volume of a Sphere

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

   View formula →
10. 10.

    A body starts at 11 m/s and accelerates at 4.3 m/s² for 5 s. Find its final velocity.

    Formula:Kinematics (v = u + at)

    $v = u + at$

    View formula →
11. 11.

    Solve using the quadratic formula: x² + 3x + 2 = 0.

    Formula:Quadratic Formula

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

    View formula →
12. 12.

    A cone has base radius 12 cm and height 16 cm. Find its volume. (π ≈ 3.14159)

    Formula:Volume of a Cone

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

    View formula →
13. 13.

    A current of 6.4 A flows through a 59 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
14. 14.

    A value changes from 55 to 127. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

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

    View formula →
15. 15.

    In a triangle, a = 12, b = 11 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 →
16. 16.

    A value changes from 124 to 101. Find the percentage change (to 2 d.p.).

    Formula:Percentage Change

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

    View formula →
17. 17.

    A current of 7.4 A flows through a 26 Ω resistor. Find the voltage across it.

    Formula:Ohm's Law

    $V = I R$

    View formula →
18. 18.

    A triangle has sides a = 16 cm and b = 17 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 →
19. 19.

    A device runs at 168 V drawing 5.7 A. Find its power consumption.

    Formula:Electrical Power

    $P = V I$

    View formula →
20. 20.

    An object with initial velocity 5 m/s accelerates at 4.7 m/s² for 6 s. Find the distance travelled.

    Formula:Kinematics (s = ut + ½at²)

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

    View formula →

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