Testing conjectures. Exemplar questions and answers

1.

Testing conjectures
Year 9
#MathsEveryoneCan

2.

Which of the numbers are factors of 12, and which are
multiples of 12?
1
6
36
12
4
48
30
Are any of the numbers both factors and multiples of 12?
©White Rose Maths

3.

Which of the numbers are factors of 12, and which are
multiples of 12?
1
6
36
12
Factors of 12
1
6
12
4
48
30
Multiples of 12
4
36
12
48
Are any of the numbers both factors and multiples of 12?
12 is both a factor and a multiple of 12.
©White Rose Maths

4.

List the first 10 prime numbers.
Which numbers between 40 and 60 are prime?
Explain how you can tell by looking at some numbers
whether or not they are prime.
©White Rose Maths

5.

List the first 10 prime numbers.
2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Which numbers between 40 and 60 are prime?
41, 43, 47, 53, 59
Explain how you can tell by looking at some numbers
whether or not they are prime.
All numbers ending in a 0 are not prime.
Numbers with an even final digit are not prime, 2 is the exception.
Numbers with 5 as the final digit are not prime, 5 is the exception.
©White Rose Maths

6.

A fair die numbered 1 to 9 is rolled once.
Find the probability that it shows:
a prime number
a multiple of 4
a factor of 36
a common factor of 9 and 18
a common multiple of 2 and 4
©White Rose Maths

7.

A fair die numbered 1 to 9 is rolled once.
Find the probability that it shows:
a prime number
a multiple of 4
a factor of 36
2
9
4
9
(2,3,5,7)
(4,8)
6
2
or
9
3
(1,2,3,4,6,9)
a common factor of 9 and 18
a common multiple of 2 and 4
3
1
or
9
3
2
9
(1,3, 9)
(4, 8)
©White Rose Maths

8.

By drawing a factor tree or otherwise, express 72 as a product of prime
factors, giving your answer in index form.
Use your answer to express these numbers as products of prime factors.
Explain your reasoning.
144
216
720
360
©White Rose Maths

9.

By drawing a factor tree or otherwise, express 72 as a product of prime
factors, giving your answer in index form.
72
36
9
3
2
2
3
72 = 32 × 22
Use your answer to express these numbers as products of prime factors.
Explain your reasoning.
144
144 = 72 × 2
144 = 32 × 22 × 2
144 = 32 × 23
216
216 = 72 × 3
216 = 32 × 22 × 3
216 = 33 × 22
720
720 = 72 × 10
720 = 32 × 22 × 2 × 5
720 = 32 × 23 × 5
360
360 = 72 × 5
720 = 32 × 22 × 5
720 = 32 × 22 × 5
©White Rose Maths

10.

The HCF of two numbers is 6 and the LCM of the numbers is 24
What might the numbers be?
How many solutions can you find?
©White Rose Maths

11.

The HCF of two numbers is 6 and the LCM of the numbers is 24
What might the numbers be?
How many solutions can you find?