Maths for Science 37 selecting answers.

  

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Maths for Science learning outcomes
This EMA is designed to assess the following learning outcomes:
Knowledge and understanding
Demonstrate knowledge and understanding of some of the mathematical and statistical concepts
and principles relevant to the study of science. In particular, the basic principles of:
Arithmetic with whole numbers, fractions, percentages and powers
Scientific notation, SI units, orders of magnitude and significant figures
The use of scientific formulae
Unit conversions
Rearranging, simplifying and combining algebraic equations
The use of algebra to solve scientific problems
The interpretation of graphs
Differentiation
Angles and trigonometry
Logarithms
Probability and descriptive statistics
Statistical hypothesis testing
Cognitive skills
Use techniques from Maths for Science to solve problems in a range of mathematical and scientific
contexts.
Key skills
Process and present data using appropriate techniques and methods of presentation.
Practical and Professional skills
Use a basic scientific calculator.
………………………………………………………….
1Evaluate -6 – ( -8)
-6 – ( -8) =
………………………………..
2What is 3 / 5 + 4 / 7
expressed as a single fraction? You should give your answer in the simplest possible form.
3/5+4/7=
Enter two values, numerator and denominator
…………..
3What is 3 / 2 ÷ 9 expressed as a single fraction? You should give your answer in the simplest possible
form.
3/2÷9=
Enter two values, numerator and denominator
…………….
4Evaluate (3^8)^1/4. You should give your answer as a single number (without the use of fractions,
brackets or exponents).
(3^8)^1/4 =
……..
5-
A child’s mass increases from 30 kg to 36 kg. What is the percentage increase?
Percentage increase in mass =
……
%
6Express 0.008348 in scientific notation to three significant figures.
X^2
If you want any text or numbers to appear as a superscript in your answer, click on the x2 button
before entering this text, and then click on this button again afterwards to return to normal text.
Alternatively use the up and down arrows on your keyboard. So if you wish to use scientific notation
in your answer then this should be entered as, for example, 5.2×102.
………….
7A distance (the wavelength of blue light) is given as 475 nm. Express this value in metres in scientific
notation.
475 nm =
m
……………….
8Enter a number into each of the four boxes in the table below to indicate the number of decimal
places and the number of significant figures in each of the figures given.
Number of decimal places
0.0143
5.150
………………..
9-
From the list below select the six equivalent expressions.
(b × a^2) ÷ c
Number of significant figures
b × a^2 × c-1
…………….
10Estimate the value of the following expression. You should give your answer to the nearest order of
magnitude. You may choose to do the calculation either with or without a calculator.
~ 10
………………
11If V = 1.7 × 10^-5 m^3 and
r = 1.63 × 10^-2 m calculate h in the equation
You should give your answer in scientific notation, with the correct number of significant figures and
the correct SI base units.
h=
……………
12Do the following calculations and express your answers to an appropriate number of significant
figures or decimal places.
(a) 4.4 + 0.57 =
(b)
………………..
13A jug has a volume of 1.41 × 10^3 cm^3. Express this value in dm^3.
Volume of jug =
dm3
………………
14A pyroclastic flow from an erupting volcano travels at a speed of 65 km hour^-1. Express this
value in m s^-1.
65 km hour^-1 =
m s^-1
…………………
15Rearrange
to make h the subject of the equation.
Give your answer in the simplest form and without brackets. Use the ‘/’ key to format your
answer, as appropriate.
h= ?
…………….
16Rearrange
to give an expression for m
. Select the one correct answer.
………………….
17-
Which three of the following expressions are equivalent?
,
,
,
……………….
18Combine the following two equations to give an equation for
which does not involve
.
You should give your answer in the simplest possible form and without brackets.
Equation 1
Equation 2
= ?
………….
19Find the two solutions of the equation
X^2 – 3x = 0
The solutions are x = ?
and
x= ? .
………………..
20You have been given the equation
If b is measured in newtons (N), c in seconds (s) and d in metres (m), what are the SI base units
of a? You should use the standard abbreviation for the simplest form of the units.
The SI base units of a are= ?
x^2
…………………..
21The graph shows the variation with time of the distance of an object from a fixed point. Find the
gradient of the graph. You should give your answer to 2 significant figures and include the
symbols for the appropriate SI unit.
gradient =
?
…………………….
22A graph of z against w is shown. What is the equation of this line? It may help you to know that
the gradient of the line is -4. Your answer should not include brackets.
Z=
?
…………………………
23-
? and L are related by the equation
where all the other quantities in the equation are constant. Which two of the following graphs
would be straight lines going through the origin:
,
,
,
……………….
24The graph shows the way in which a variable y changes as another variable x increases.
Identify (by clicking on the boxed letters on the graph) the three points at which
=0
please look at the image below to see the boxed letters on the graph below
……………….
25If
where n, R and T are constants, what is
? Select the correct answer.
,
,
,
,
……………………………………………………….
26If z = 3t^2 + 6t + 4, what is the gradient of a graph of z against t at t = 2.
You should enter your answer as a number not in scientific notation.
Gradient = ?
…………
27Find the second derivative of
with respect to t. Chose the correct option.
,
,
,
………………………………
28An angle measures 0.11 in radians. What is this angle when measured in degrees? Give your
answer to two significant figures.
Angle =
?
o
…………………………………….
29Find the distance D shown in the diagram. The overall height of the flagpole is 7.4 m and the man’s
eyes are 1.5 m above ground level. Angle theta
is 35°. Give your answer in metres to two significant figures.
A flag pole is 7.4 m high. Angle to horizontal of a man’s eyes to top of flag pole is 35°. Man’s eyes are
1.5 m above ground level. Horizontal distance of man from base of flag pole is D. Vertical distance of
top of flagpole above man’s eyes is H.
D=
? m
………………….
30A vector has components Fx = 2.8 N and Fy = 3.4 N. Find the magnitude of the vector. You should
give your answer to two significant figures.
Magnitude F =
?
N to two significant figures.
………………………..
31log10 x = -8. What is the value of x?
x= ?
…………………………….
32Which two of the following expressions are equivalent to log10 (6y^-4)?
,
,
,
…………………………………..
33If a graph is plotted of ln z against t for the equation z = 4 e^3t, what will be the gradient of the
graph?
Hint: You should start by taking the log to base e of both sides of the equation.
Gradient =
? response
………………………….
34Ten Dunlin (small wading birds) are trapped and the length of their bills measured. The results are
listed below. What is the median of these data
Bill length/mm
34.0
38.0
32.5
37.5
32.0
33.5
31.0
36.5
34.5
35.5
median =
?
mm
……………………..
35A game starts by drawing one card from a shuffled pack of playing cards and simultaneously
throwing a die. The highest possible score corresponds to drawing an ace and throwing a six. What is
the probability, expressed as the simplest possible fraction, of achieving this highest possible score?
Note that in a pack of 52 playing cards, there are four aces.
Probability= ? / ?
……………………….
36A length is measured 10 times. The results are listed below. Calculate the standard deviation of
these measurements to four decimal places, giving your answer as a decimal number (i.e. not in
scientific notation). It may help you to know that the mean of these data is 3.3839 m.
Reading
1
2
3
4
5
Standard deviation = ?
Length/m
3.462
3.406
3.452
3.359
3.355
m
Reading
6
7
8
9
10
Length/m
3.357
3.403
3.355
3.349
3.341
……………………………..
Information:- A population geneticist makes the prediction that, if a population of wild plants is in
so-called Hardy-Weinberg equilibrium, then the ratio of red-, pink- and white-flowered plants in the
population will be 0.64 : 0.32 : 0.04.
The five questions for Chapter 12 take you through the steps of a ?^2-test for a set of data given in
the first question, in order to determine whether or not the population represented by the data is in
Hardy-Weinberg equilibrium.
The questions for Chapter 12 are linked and so you must attempt them in order. You will not be able
to attempt the second question until you have completed the first question, and so on. If you get an
incorrect answer to one question you will be given the correct answer to enable you to move on to
the following question. You do not need to remember values from screen to screen; all the
information required will be provided at each stage.
37If the population is in Hardy–Weinberg equilibrium, then the ratio of red-, pink- and white-flowered
plants in the population will be 0.64 : 0.32 : 0.04. 182 red-flowered plants, 64 pink-flowered plants
and 16 white-flowered plants are counted in a representative sample drawn from the population.
What are the expected numbers of red-flowered plants, pink-flowered plants and white-flowered
plants if the population is in Hardy–Weinberg equilibrium? Give your answers, to two decimal
places, in the boxes provided.
Expected number of red-flowered plants =
?
Expected number of pink-flowered plants =
?
Expected number of white-flowered plants = ?
………………………..
38-

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