Download GCSE Mathematics Foundation Level Topics covered in the

GCSE Mathematics
Foundation Level
Topics covered in the following questions are:
-Types of Numbers (Factors, Multiples, Cube, etc)
-Prime Factors
-LCM & HCF
Q1.
From the numbers in the cloud,
(a) write down a square number,
(b) write down a multiple of 7,
(c) write down a factor of 30
(Total for Question is 3 marks)
Q2.
Here is a list of numbers.
5
15
30
50
60
90
100
125
From the numbers in the list, write down
(i) two different numbers that add up to an even number
(ii) a multiple of 20
(iii) a factor of 45
(iv) a cube number
(Total for Question is 4 marks)
Q3.
Here is a list of numbers.
1
2
4
5
7
11
13
14
15
17
From the list, write down three different prime numbers that add together to make 20
(Total for Question is 3 marks)
Q4.
Jan writes down
one multiple of 9
two different factors of 40
Jan adds her three numbers together.
The answer is greater than 20 but less than 30
What three numbers could Jan have written down?
(Total for Question is 3 marks)
Q5.
Michael writes down 4 different factors of 60
He adds the 4 factors together.
He gets a number greater than 20 but less than 35
What 4 factors could Michael have written down?
(Total for Question is 3 marks)
Q6.
Rita is going to make some cheeseburgers for a party.
She buys some packets of cheese slices and some boxes of burgers.
There are 20 cheese slices in each packet.
There are 12 burgers in each box.
Rita buys exactly the same number of cheese slices and burgers.
(i) How many packets of cheese slices and how many boxes of burgers does she buy?
Rita wants to put one cheese slice and one burger into each bread roll.
She wants to use all the cheese slices and all the burgers.
(ii) How many bread rolls does Rita need?
(Total for Question is 4 marks)
Q7.
Here is a list of numbers.
From the list, write down
(a) a factor of 24
(b) a multiple of 7
(c) a square number
(Total for Question is 3 marks)
Q8.
Veena bought some food for a barbecue.
She is going to make some hot dogs.
She needs a bread roll and a sausage for each hot dog.
There are 40 bread rolls in a pack.
There are 24 sausages in a pack.
Veena bought exactly the same number of bread rolls and sausages.
(i) How many packs of bread rolls and packs of sausages did she buy?
(ii) How many hot dogs can she make?
(Total for Question is 5 marks)
Q9.
Write 525 as a product of its prime factors.
(Total for Question is 3 marks)
Q10.
Find the Lowest Common Multiple (LCM) of 8 and 12
(Total for Question is 2 marks)
Q11.
(a) Express 54 as a product of its prime factors.
(b) Find the Lowest Common Multiple (LCM) of 45 and 54
(Total for Question is 4 marks)
Mark Scheme
Question
Working
Answer
Mark
Notes
111
B1 for 4 or
16 (or both)
B1 cao B1
10 or 15 (or
both)
Answer
Mark
Notes
5,15 or
5,125 or
15,125 or
30,50 or
30,60 or
30,90 or
30,100 or
50,60 or
50,90 or
50,100 or
60,90 or
60,100 or
90,100 60
or 100 5 or
15 125
4
B1 for 2
numbers,
from the list,
whose sum
is an even
number.
Answer
Mark
Notes
3 primes
that total 20
3
M1 for
identifying
at least 2
different
prime
numbers
from the list,
could
indicate on
the list (not
more than
one
incorrect)
16 or 4 21
10 or 15
(a) (b) (c)
Q1.
Q2.
Working
(i)
(ii)
(iii) (iv)
B1 for 60
or 100 or
both B1 for
5 or 15 or
both B1 cao
Q3.
Working
M1 for
any 3
numbers
from the list
that total 20
A1 for 2,
7, 11 or 2,
5, 13 or
both (in any
order)
Q4.
Q5.
Question
Q6.
Working
Answer
Mark
Notes
eg. 10, 12,
5, 2
3
M1 for at
least 2
factors of
60 clearly
identified
M1 for 20
< sum of '4
distinct
natural
numbers' <
35
A1 cao
Question
Working
(a) (b) (c)
Answer
Mark
Notes
12 14 16
111
B1 cao B1
cao B1 cao
Q7.
Q8.
Question
Working
Answer
LCM (40, 24) = Rolls (packs) 3
120
Sausages
Rolls 120 ÷
(trays) 5
40 =
Hot dogs 120
Sausages
120 ÷ 24 =
OR
Rolls 40 is 2 ×
2 × 2 (×5)
Sausages 24
is 2 × 2 × 2
(×3) 40, 80,
120, 160, 200,
240, 280 24,
48, 72, 96,
120, 144, 168
Mark
Notes
5
M1 attempts
multiples of
either 40 or 24
(at least 3 but
condone errors
if intention is
clear)
M1 attempts
multiples of
both 40 and 24
(at least 3 of
each but
condone errors
if intention is
clear)
M1 (dep on
M1) division by
40 or 24 or
counts up
multiples.
(implied if one
answer correct
or answers
reversed)
A1 rolls
(packs) 3,
sausages
(trays) 5 OR
any multiple of
3,5
A1 hot dogs
120 or ft on
both of their
packs or ft
'common
multiple'
OR
M1 expansion
of either
number into
factors
M1
demonstrates
one of the
expansions
that includes 8
oe
M1
demonstrates
a 2nd
expansion that
includes 8 oe
A1 cao for
rolls (packs) 3,
sausages
(trays) 5
A1 hot dogs
120
Working
5|525
5|105
3|21
7
Answer
Mark
Notes
3
M1 for
continual
prime
factorisation
(at least first
2 steps
correct) or
first two
stages of a
factor tree
correct
M1 for fully
correct
factor tree
or list 3, 5,
5, 7
A1 3 × 5 ×
5 × 7 or 3 ×
52 × 7
3×5×5×
7
Q9.
Q10.
Question
Working
Question
(a)
(b)
Answer
Mark
Notes
24
2
M1 for list of at
least 3
multiples of 8
and 2
multiples of 12
or
correct
method to
write either 8
or 12 as
product of
prime factors
A1 cao
Working
Answer
Mark
Notes
54 ÷ 2 = 27
27 ÷ 3 = 9
9÷3=3
3÷3=1
2×3×3×
3
2
M1 for
attempt at
prime
factorization
2
45, 90,
135, 180,
225,
270,..
54, 108,
162, 216,
270, ..
270
(at least two
correct
divisions):
could be
shown as a
factor tree
OR sight of
at least one
of each of
2, 3 as
factors of
54 A1 for 2
×3×3×3
or 2 × 3³ M1
for at least
3 multiples
of 45 and
54 (can
include 45,
54) or a
correct
method to
write 45 as
3×3×5 or
32×5
A1 cao