Maths and Physics Quiz – Worked Solutions

Please complete the following questions to the best of your ability (use your Maths GCSE notes if you are having difficulties !)

1. Express the following quantities in Standard Form:
e.g. The speed of light in free space is 300,000,000 m/s or 3x10⁸ m/s in standard form.

• 23,000 Kg = 2.3 x 10⁴ Kg
• 876,000,000 m = 8.76 x 10⁸ m
• 0.000123 F = 1.23 x 10^-4 F
• 1/1000 C = 0.001 C = 1 x 10^-3 C
• 20⁵ Km = 3,200,000 Km = 3.2 x 10⁶ Km

2. Light travels at 3x10⁸ m/s. How far will it have travelled in 16x10¹⁵ s ?

distance = speed x time

distance = (3 x 10⁸) x (16 x 10¹⁵)

distance = 4.8 x 10²⁴ m

3. The reading on a scale is 35.346 Kg. The scale is only accurate to 3 Significant Figures. Write the reading to the correct degree of accuracy.

Answer: 35.3 Kg

4. A bottle contains 500 cm³ of a liquid. Write this volume in m³.

There are (100)³ cm³ in 1m³ so
500/100³ = 5 x 10^-4 m³

5. If k=100 N/m and m=4 Kg then calculate frequency, f

using the equation

 

= 0.8 Hz

 

6. An experiment on a metal-filament lamp gave the following values of resistance R (ohms) at various voltages V (volts):

Plot a graph of R (y-axis) against V (x-axis).

Draw a line of best-fit and calculate

1. the gradient of the graph = 1.3
2. the intercept on the y-axis = 20

7. John’s car travels a distance of 750 m in a straight line up a hill. The angle of inclination of the hill is 14 degrees to the horizontal AC. Calculate the vertical height BC.

Sin 14 = opposite / hypotenuse

Sin 14 = BC / 750

BC = Sin 14 x 750

BC = 181.4 m

 

8. Rearrange the formula v²=u² + 2as so that a is the subject.

v²-u² = 2as