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KS3 SatsMuncher 1 Answers

SatsMunchers 1 Answers

Special Numbers & Sequences

 

Q1.  Which multiple of 7 lies between 30 and 40?

A1.  35     
There's loads of multiples of 7:  7, 14, 21, 28, 35, 42 .
.. but only 35 lies between 30 and 40!

Q2.  Which factor of 24 lies between 10 and 20?

A2.  12     

24 can be made from:  1 x 24,  2 x 12,  3 x 8,  4 x 6

So, 24 has 8 factors:    1, 2, 3, 4, 6, 8, 12, 24
... but only 12 fits the question.

 

Q3.  What's the square of 8?

A3.  64     
The 'square of 8' means '8 times itself' or '8 x 8'


Q4.  Can you complete this sequence:   

       13,  9,  5,  1, __ ,  __ ?

A4.  -3 and -7         
The sequence is going down (or decreasing) by 4 each time.

Q5. Can you complete this sequence:     

       3, __ ,  15,  21,  27 ?

A5.  9         
The sequence is going up (or increasing) by 6 each time.

Q6.  The first four numbers of a sequence are: 

       11, 15, 19, 23 ...

Which description fits this sequence:

A.  The first number is 4 and the sequence increases by 11 each time?

B.  The first number is 11 and the sequence  increases by 5 each time?

C.  The first number is 11 and the sequence decreases by 4 each time?

D.  The first number is 11 and the sequence increases by 4 each time?

A6.  D         
Did you choose one of the other three choices?  
They were VERY similar - try to read questions more slowly.

Q7.  I'm thinking of a number - 

      Clue 1: It is less than 30. 

      Clue 2: It is both a multiple of 6 and 9

      What number am I thinking of ?

A7.  18:         
18 is a multiple of both 6 and 9 - so it's a 'common multiple':

1st few Multiples of 6: 6, 12, 18, 24, 30, 36, 42 ...

Ist few Multiples of 9: 9, 18, 27, 36, 45, 54, 63 ...

Y
ou can see that 6 and 9 have both 18 and 36 in common
(And that 18 is the LOWEST common multiple)

Q8.  2 and 24 are a factor pair of 48.

       Which is the correct list for the remaining factor pairs?

       A.  3 and 16,      4 and 12

       B.  3 and 16,      4 and 12,      6 and 7

       C.  1 and 48,      3 and 16,      4 and 12,      6 and 8

       D.  3 and 16,      4 and 12,      6 and 8

A8.  C
A misses out 1 x 24 (the most common mistake)
B misses these AND 6 x 8
D misses out LOADS


It's just too easy to miss out just one factor ...
So, it's safer to work them out in order, starting with 1, then 2, then 3 ...

1 X 48   2 X 24   3 X 16   4 X 16   6 X 8   (8 X 6 is a repeat so you know to stop).

Q9.  The nth term of a sequence is n(n + 2).  

        What is the 4th term of this sequence?

A9.  24

First, think of n as the position number. 
For example, in the sequence: 1, 4, 7, 10 ... 7 is the 3rd position number.

So, when n = 3, the nth term is 7


Now turn the question into plain English:
'nth term = n(n + 2) '   becomes ...

' any term in this sequence will always equal the position number multiplied by 2 more than the position number '

(OK, so it's long - but it does make sense if you read it enough times!)

So
The 4th number = n x (n + 2) 
                            
= 4 x (4 + 2) 
                            = 4 x 6
                            = 24

(If you wanted to know which sequence it is, then:
1st term  = 1 x 3 = 3
2nd term = 2 x 4 = 8
3rd term  = 3 x 5 = 15
4th term  = 4 x 6 = 24

So, sequence is:  3, 8, 15, 24)

Q10.  A sequence starts with 1, 4, 7, 10 ...

         What is the nth term of this sequence? 

A10.  3n-2
The clue here is that the sequence goes up in threes - just like the 3 times tables.  The only question them is 'how far  awayis the 3 times tables from this sequence? -


Position
Number:
     1st    2nd    3rd    4th
x3:               3        6       9      12     try subtracting 2?
-2:                1        4       7       10     correct

Using words:     
'Any term is 3 times the position number and subtract 2'

Using maths:  nth term = 3 x n - 2  or  3n - 2

How did you get on?  The last few were quite challenging, but don't worry about this because you may not have learned it yet.

Your Score

0 - 1  
You found these hard going but you're persistent - which is what will make you a winner in the long run!  - And don't worry, you will revise these topics again in school.

2 - 4  
A fabulous start! - you're working to at least Level 4... now is the time when a little extra effort into your Year 9 maths will pay giant bonuses in your grades.

5 - 8 
An astounding result! - you're clearly going places as a competent mathematician - and you've picked up some really demanding Level 5 topics.  What a star.

9 - 10 
A brilliant score! - You've learned some quite challenging Level 6 maths and perhaps these weekly challenges may prove too easy for you.

 

What Next? - You Can:

- Leave this challenge 

... and come back later if you want to see if you can improve your score

- Try SatsMuncher 2: the Chancy Numbers Challenge!

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