Employer numeracy aptitude tests.
Part I: Sample timed test
You will be given 5minutes to attempt the following two questions.
Question 1
The following data provides information on an endangered species which has
been protected since 1990.
100%
90%
80%
Year Population size
70%
1990 40,000
60% Seniles
1995 35,000 50% Adults
2000 30,000 40% Juveniles
2005 30,000 30%
20%
10%
0%
1990 1995 2000 2005
How many adults were there in the population in 1995?
A. 31500 B. 24500 C. 28000 D. 26250
If it is twice as expensive to protect the land that juveniles use compared with
protecting land used by adults and seniles, what is the ratio of the cost of
protecting land in 1990 to the cost of protecting land in 2000?
A. 9:11 B. 18:19 C. 12:11 D. None of these
In 2005, if 60% of adults produced on average 1.2 eggs, and 50% of the eggs
hatched into juveniles, how many viable juveniles were produced by the 2005
adults?
A. 7560 B. 12600 C. 15120 D. 25200
MASH: Mathematics Resources Centre
http://www.bath.ac.uk/study/mash
November 2007
Question 2
A local lottery allocates 100 prizes every month, each worth $10. The number
of entries per month is given in the figure below:
350
300
Number of entries 250
200
150
100
50
0
Jan Feb March April May June
Month
In March, what was the probability that an entry would win a prize?
2 3 1
A. B. C. D. None of these
3 2 2
If funds raised by the lotto in April were $750 more than in February, how much
did one entry cost?
A. $5 B. $12 C. $6 D. $10
Over the 6 month period, what was the net profit on the lotto?
A. $125 B. $375 C. -$375 D. -$125
MASH: Mathematics Resources Centre
http://www.bath.ac.uk/study/mash
November 2007
Part II: Key concepts tested in employer numeracy tests
Key areas:
Algebraic expression and solution
Percentage, ratio and fractions
Handling data.
Algebra
Translate word problem into algebraic expression
Solve resulting equation
Use solution to answer original question.
Examples
1. Claire is six years older than her sister Megan. In two years time, Claire
will be twice as old as Megan. How old will Megan be in 3 years time?
2. In Sainsburys, an offer on orange juice gives 3 cartons for the price of 2.
In Tesco, the offer on the same carton of orange juice is buy 1 carton,
get one carton half price. A customer wants to buy 6 cartons of orange
juice. If it is 30p cheaper to buy these in Sainsburys, what is the cost of
a single carton of juice?
http://www.mathcentre.ac.uk/students.php/mathematics/algebra/linearequa
tions/resources/
http://www.bbc.co.uk/schools/gcsebitesize/maths/algebra/
Percentage
How to calculate a percentage of a number
Conversion between percentage, fraction and decimal
Calculate increases (respectively decreases) by a given percentage.
Calculate percentage increases and reverse percentage increases.
Examples
1. Joshua has a voucher offering 20% off the price of chart CDs. If the
original price of the CD was 12 pounds, what price did Joshua pay?
2. The price of shares in St. Ives on October 18 2007 was 220p; on October
25 2007, the price was 240p. What percentage increase does this
represent?
3. A violin costs 75 pounds, which includes 17.5% VAT. If the violin is
purchased for educational purposes, VAT is not paid. What is the cost of
the violin in this case?
http://www.mathcentre.ac.uk/students.php/mathematics/arithmetic/percent
ages/resources/
http://www.bbc.co.uk/schools/gcsebitesize/maths/number/
MASH: Mathematics Resources Centre
http://www.bath.ac.uk/study/mash
November 2007
Ratio
What is a ratio
Conversion between ratio and fractions
Translating ratio problems into problems involving fractions
Examples
1. A recipe for pancakes includes 100g flour and 20g of sugar. Write down,
in simplest form, the ratio of flour to sugar.
2. Four sheets of paper can be purchased for 60p. How much would 9
sheets cost?
3. The angles in a triangle are in the ratio 2:3:4. What is the size of the
largest angle?
4. A cleaning solution is made in the ratio of concentrate to water to be
3:7 by volume. What is the total volume of the cleaning solution which
can be made from 16 litres of concentrate?
http://www.mathcentre.ac.uk/students.php/mathematics/arithmetic/ratio/re
sources/
http://www.bbc.co.uk/schools/gcsebitesize/maths/number/
Handling data
Obtaining relevant information from a graph or table
Examples
1. Data on population structure in Germany in 1985 provides the following
information:
a. Population at start of the year = 61.0 millions
b. Live births per 1000 population = 9.6
c. Deaths per 1000 population = 11.5
d. Percentage of population at start of year under 15 = 15%
e. Percentage of population at start of year aged 60 or over = 20%
How many people were aged under 15 at the start of the year?
How many live births occurred (to the nearest 1000)?
Approximately what percentage of the population were aged 60 or over
at the end of 1985?
2. Using the chart detailing sales of jeans, answer the following questions:
a. What was the selling price for a single pair of Levi jeans if the
sales income was 6000 pounds for this product in month 1?
b. If Levi jeans sell for twice as much as Wrangler jeans, in which
month was the total sales income highest?
c. What was the average income from sales of Levi jeans over the 6
month period?
MASH: Mathematics Resources Centre
http://www.bath.ac.uk/study/mash
November 2007
Jeans sales
300
250
200
Jeans sold per month
Levis
150
Wrangler
100
50
0
1 2 3 4 5 6
Month
http://www.bbc.co.uk/schools/gcsebitesize/maths/data/
Maths web resources
http://www.mathcentre.ac.uk/students.php/
http://www.mathtutor.ac.uk/
http://www.bbc.co.uk/schools/revision/
Test practice
http://www.shldirect.com/
http://www.kent.ac.uk/careers/tests/mathstest.htm
http://www.tda.gov.uk/skillstests/numeracy/practicematerials.aspx
http://www.edexcel.org.uk/sfc/onscreen/alan-test/
http://www.efinancialcareers.co.uk
MASH: Mathematics Resources Centre
http://www.bath.ac.uk/study/mash
November 2007