AS PHYSICS
Maths Skills Booklet
ARK PUTNEY ACADEMY
MATHS SKILLS FOR PHYSICS
ALGEBRA, INTERPRETING EQUATIONS, SIGNIFICANT FIGURES, DECIMAL PLACES, STANDARD FORM, PREFIXES AND GRAPHS
1. Make ‘x’ the subject of the following equations:
a)
b)
c)
d)
2. Combining and interpreting equations.
a) s = (v+u)/2 and s = d/t Eliminate s; make v the subject.
b) E = mgh and E = mv2/2 Eliminate E; make h the subject
c) F=kQ1Q2/r2 and E=F/Q Eliminate F; make E the subject
d) F = ma If the value of the acceleration (a) decreases, how does this affect the value of F (force)?
e) F = ma If the value of the mass (m) increases, how will this affect the value of the acceleration (a)?
f) R=ρL/A The value of A is increased. How does this affect the value of R if ρ and L remain constant?
g) R=ρL/A The value of L is increased. How does this affect the value of A if R and ρ remain constant?
h) KE = ½ mv2 The value of the KE is doubled. How does this affect the value of v if m remains constant?
3. Express the following numbers to 3 significant figures:
a) 10.23
b) 10.28
c) 10.25
d) 0.0003184
e) 154,798
4. Express the following numbers to 2 decimal places:
a) 65.432
b) 45325.32115
c) 1800.0004
d) 0.00504
e) 0.0018
5. Express the following numbers to two significant figures in standard form:
a) 10.23
b) 3,000,578
c) 1,400,220,000
d) 0.00000498
e) 65,480,389,594
6. Without using a calculator, work out the value of
a) 103 x 103
b) 5 x 102 x 0.02
c ) 8.3 x 104 x 107
d) 102 x 105 x 107
e) 4x104 x 7x105
7. Without using a calculator, work out the value of
a) 107 / 103
b) 104 / 103
c) 5042 / 102
d) 4 x 105 / (2 x 103)
e) 8 x 104 / (2 x 104)
8. Without using a calculator work out the following:
a) 102 / 10-2
b) 3 / 10-3
c) 3xl04 / 10-6
d) 3 x 10-3 / (2 x 10-4)
e) 0.22 x 10-6 / (0.88 x 10-9)
UNITS AND PREFIXES
1. Here are five basic SI quantities. Fill in the units and their abbreviations.
QUANTITY / UNIT / ABBREVIATIONMass
TimeLength
Electric Current
Temperature
2. Scientists normally work in SI units. All other units can be derived from the basic SI units. Work out the basic units in which the following derived units can be expressed:
Newton Ohm Pascal Volt
3. In front of units, standard prefixes may be used e.g. “kilo”, “milli”. Write down the prefixes for the following indices:
INDEX / PREFIX / INDEX / PREFIX10-3 / milli / 103 / kilo
10-6 / 106
10-9 / 109
10-12 / 1012
10-15 / 1015
4. Write the following using the above prefixes:
a) 6543337 m as megametres
b) 10003 m as kilometres
c) 33 mm as metres
d) 10 mg as kilograms
e) 10 m2 as millimetres2
5. Show that one year is approximately 30 million seconds. Write this as a power of ten and with the appropriate prefix.
6. The Earth is about 150 million kilometres from the Sun. Write this in metres, as a power of ten and with the appropriate prefix
7. A microbe is typically 1/1000 of a millimetre in dimensions. Write this in metres as a power of ten, and with the appropriate prefix.
8. How long does it take light to cross a 3 m wide room?
(speed of light = 3 x 108 m s–1)?
9. Suggest an object which is about 1 nm in size.
10. Suggest an object which is around 1 Mm in dimensions.
GRAPHS
LINEAR GRAPHS
Directly Proportional (goes through origin) Linear Relationship (straight line, but y-intercept not zero)
2. Plot graphs and draw the best straight lines for the following. Then work out the gradients.
a)
X / 2.2 / 2.3 / 2.4 / 2.5 / 2.6 / 2.7 / 2.8Y / 0.31 / 0.33 / 0.34 / 0.36 / 0.37 / 0.39 / 0.4
b)
X / 29 / 34 / 38 / 42 / 47 / 55 / 63Y / 9.7 / 11.3 / 12.7 / 14 / 15.7 / 18.3 / 21
3. Plot a graph of y against x and estimate the gradient of the curve at points
a) x=2 b) x = 5 and c) x = 7.4
X / 1 / 2 / 3.4 / 4.6 / 5.5 / 6.3 / 7.6 / 8.3 / 9.2Y / 1 / 4 / 11.6 / 21.2 / 30.3 / 39.7 / 57.8 / 68.8 / 84.6
The following graphs are useful for A2, in particular when it comes to coursework. You are unlikely to encounter graphs like these during your AS studies.
POWER LAW
To get a straight line, the graph should be plotted as a LOG-LOG graph.
EXPONENTIAL
To get a straight line, the graph should be plotted as a LOG-LINEAR graph (see below).