Properties of numbers
Revision Test
September 14, 2014
Aim to answer all questions in full, showing all your working. The allocated time for
this test is: 45 minutes.
1 Sequences and Patterns
Fill in the missing numbers for the following sequences:
(a) 0, 2, , 6, 8, 10, , , 16, etc. (1 mark)
(b) 1, , 5, 7, , 11, 13, , 17, etc. (1 mark)
(c) 1, , 7, 10, 13, , , 22, etc. (1 mark)
(d) 10, 8, 6, , 2, 0, , -4, -6, etc. (1 mark)
(e) 2, 3, 5, , 11, 13, , 19, etc. (1 mark)
(f) 1, 4, 9, , 25, 36, , 64, , 100, etc. (1 mark)
(g) 1, 10, 100, , 10000, etc. (2 marks)
(h) 1, 2, 4, 8, , 32, , 128, etc. (2 marks)
(i) 1, 2, 3, 5, 8, , 21, 34, , etc. (3 marks)
2 Prime numbers, Factors, Prime factors and Multiples.
Fill in the following gaps and delete as appropriate for the following statements to hold
true:
(a) The number 13 is / is not a prime number because it has . . . factors. (1 mark)
(b) The factors of the number 13 are . . . . . . . . . Out of these factors only . . . is a prime
factor. (1 mark)
Properties of numbers (revision test) Name:. . . . . . . . . . . . . . . . . . . . . . . . . . . Form:. . . . . .
(c) The factors of the number 99 are . . . . . . . . . (1 mark)
(d) The number 99 is / is not a prime number because it has . . . factors. (1 mark)
(e) The prime factors of the number 99 are . . . . . . . . . (1 mark)
(f) Draw a factor tree for the number 99, making sure you circle the . . . . . . factors.
(2 marks)
(g) Looking at the factor tree, you can write the . . . . . . . . . . . . . . . . . . of the number 99
as: 99 = × × , which then further simplifies to 99 = × using the
. . . . . . notation. (4 marks)
(h) The prime numbers greater than 10, but less than 20 are . . .. . . . . . (1 mark)
(i) Prime numbers are generally odd / even numbers, the only exception being the
number . . ., which is odd /even. (1 mark)
(j) The number 1 is /is not prime and has . . . . . . factor(s). (1 mark)
3 Multiples and Number sets
Fill in the following gaps and delete as appropriate for the following statements to hold
true:
(a) The first five positive multiples of 4 are . . . . . . . . . . (1 mark)
(b) The number 0 is / is not a multiple of 4, because 4 is not/ is a factor of the number
0. This means that we can / cannot write 0 as a product of 4 and another number.
However, the number 0 is / is not a positive number. (1 mark)
(c) The set 0, 3, 6, 9, 12, etc represents positive/ non-negative multiples of . . .. (1 mark)
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Properties of numbers (revision test) Name:. . . . . . . . . . . . . . . . . . . . . . . . . . . Form:. . . . . .
(d) Examples of negative/ non-positive multiples of 5 include 0, -5, -10, etc. (1 mark)
(e) The following numbers 0,1,2,3,4,5, etc. are part of the whole numbers / counting
numbers set. Alternatively, we can say that these numbers are non-negative/ positive
integers. (1 mark)
4 HCF and LCM
Fill in the following gaps and delete as appropriate for the following statements to hold
true:
(a) List the all the positive factors of 12 in ascending order: . . . . . . . . . . . . . (1 mark)
(b) List the all the positive factors of 20 in ascending order: . . . . . . . . . . . . . (1 mark)
(c) HCF is an abbreviation for . . . . . . . . . . . . (1 mark)
(d) Comparing the list of factors for 12 and 20, you notice that the HCF is (1 mark)
(e) List the first seven positive multiples of 12: . . . . . . . . . . . . . (1 mark)
(f) List the first seven positive multiples of 20: . . . . . . . . . . . . . (1 mark)
(g) LCM is an abbreviation for . . . . . . . . . . . . (1 mark)
(h) Comparing the list of multiples for 12 and 20, you notice that the LCM is (1
mark)
(i) Instead of writing down and comparing lists for all the factors and multiples of two
or more numbers, we can also find the HCF and LCM easier using . . . . . . diagrams.
To do so, we first need to draw . . . . . . . . . . . . in order to find the prime factorisation
of the numbers 12 and 20: (1 mark)
(j) Using the drawings above we can write 12 = × × and 20 = × × . Now
we can fill in the diagrams on the next page: (2 marks)
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Properties of numbers (revision test) Name:. . . . . . . . . . . . . . . . . . . . . . . . . . . Form:. . . . . .
(k) Using the diagram above, the HCF of 12 and 20 is given by × = , while the
LCM is given by × × × = . (2 marks)
(l) Repeat the above process (i)-(k) to find the HCF and LCM of three numbers (instead
of just two): 15, 20 and 24. Note that now you will need the fill the diagram below:
(5 marks)
HCF(15,20,24)=. . . . . . . . . . . . and LCM(15,20,24)=. . . . . . . . . . . . . . . . . . . . .
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Properties of numbers (revision test) Name:. . . . . . . . . . . . . . . . . . . . . . . . . . . Form:. . . . . .
5 Understanding negative numbers in context
Fill in the following gaps and delete as appropriate for the following statements to hold
true.
Hint. Draw a number line (horizontal/vertical) or similar in case you need help to answer
the following questions:
(a) The outside temperature in London during one of the coldest nights last winter
reached a minimum of −4◦ C. The following day, altough still cold outside, the
thermometer indicated +3◦ C. This was good news as the temperature increased by
◦ C. Children were eager to go out and play in the snow. (2 marks)
(b) The sea level is taken as a reference for measuring land elevation. Hence at sea level
we are at . . . . . . altitude which we write as 0 m (meters). Above the sea level we
use positive/ negative numbers to indicate height (altitude) of a hill or mountain,
whereas below the sea we use positive/ negative numbers to describe the depth of the
ocean and seas. Hence, the measurements indicate that the highest point on Earth
measured from the sea level is the peak of Mount Everest at an elevation of +8,848/
-8,848 m, while the lowest point underwater is Challenger Deep at the bottom of
the Mariana trench which lies at 10,911m below the sea level. The elevation of
Challenger deep is hence written mathematically using our convention as . . . . . . m.
(2 marks)
(c) Given that 1000 m = 1km, we can say that the elevation of the peak of Mount
Everest is roughly +9 / -9 km, while the elevation of Challenger Deep is circa +11/
-11 km. Starting from Challenger Deep we need to go up . . . . . . km to reach the
same elevation as that of the peak of Mount Everest. (2 marks)
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