Ashbourne Independent School GCSE Higher Mathematics
Primes, factors and multiples
Date:
Time: 25 minutes
Marks: 25 marks
Ashbourne Independent School 1 1.
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6.
Ashbourne Independent School 4 On the grid, enlarge the shape with a scale factor of 2 , centre P.
(Total 3 marks)
3.
(a) Express 45 as a product of its prime factors.
..............................................................
(2)
(b) Find the Highest Common Factor (HCF) of 45 and 30
.............................
(2)
Q3
(Total 4 marks)
4 7.
4.
Leave
blank
*P38964A0424*
(a) Find the highest common factor (HCF) of 24 and 30
.....................................
(1)
(b) Find the lowest common multiple (LCM) of 4, 5 and 6
.....................................
(2)
8.
5.
Melissa is 13 years old.
Becky is 12 years old.
Ashbourne ndependent Daniel
is 10Iyears
old. School Melissa, Becky and Daniel share £28 in the ratio of their ages.
Q4
(Total 3 marks)
5 21 Prove that
(2n + 3)2 – (2n – 3)2 is a multiple of 8
for all positive integer values of n.
(Total for Question 21 is 3 marks)
9.
22 Solve 3x2 – 4x – 2 = 0
5 Give
Writeyour
525solutions
as a product
of its
factors.
correct
to 3prime
significant
figures.
.................................................................................
(Total for Question 22 is 3 marks)
19
*P40647A01924*
..........................................
Turn over
(Total for Question 5 is 3 marks)
6 10.
Ed has 4 cards.
There is a number
on each
card. Ashbourne Independent School 12
6 6
15
?
..........................................
(Total for Question 8 is 3 marks)
9
Matt and Dan cycle around a cycle track.
Each lap Matt cycles takes him 50 seconds.
Each lap Dan cycles takes him 80 seconds.
Dan and Matt start cycling at the same time at the start line.
Work out how many laps they will each have cycled when they are next at the start line
together.
Matt.......................................... laps
Dan.......................................... laps
(Total for Question 9 is 3 marks)
8
*P43598A0828*
Ashbourne Independent School 7