1. Algebra 1
Level 4
1. Number chains
(a) A number chain starts
1 2 5 ...
To find the next number you use the rule × 3 t h e n – 1
Write the next two numbers in the number chain.
1 2 5 ............. .............
1 mark
(b) Here is a different number chain.
3 9 27 81 ...
What could the rule be to find the next number?
1 mark
2. Count on
(a) I count on in equal steps.
My fourth number is 42, my fifth number is 47
? 4 2 4 7
What is my first number?
...................
1 mark
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2. (b) I count on in equal steps.
My first number is –3, my fifth number is 5
– 3 ? 5
What is my third number?
...................
2 marks
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3. 3. Number sequence
Here is part of a number sequence.
7 1 1 1 9 3 5
To get the next number you
multiply by 2 then subtract 3
Fill in the two missing numbers in the sequence.
1 17 1 9 3 5
2 marks
4. Flats
The diagram shows part of a block of flats.
There are four flats on each floor.
1 2 3 4
8765
9 1 0 1 1 1 2
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4. (a) What are the numbers of the flats on the 10th floor?
.................... , .................... , .................... , ....................
1 mark
(b) On what floor is flat number 60?
......................
1 mark
5. Using rules
(a) The rule in a number sequence is add 8
Use this rule to write the missing numbers in the sequence.
1 9 2 71 1
1 mark
(b) The rule in a different number sequence is double, then add 1
Use this rule to write the missing numbers in the sequence.
2 3 4 71 1
2 marks
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5. 6. Thinking of rules
(a) I can think of three different rules to change 6 to 18
6 1 8
Complete these sentences to show what these rules could be.
first rule:
second rule:
third rule:
add ..................
multiply by ......................
multiply by 2 then ........................
1 mark
1 mark
1 mark
(b) Now I think of a new rule.
The new rule changes 10 to 5 and it changes 8 to 4
1 0 5 8 4
Write what the new rule could be.
...............................
1 mark
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6. 7. Rules
(a) A rule changes 1
2
1
to 4
2
1
1
1
2
? 4
1
2
What could the rule be?
Tick ( ) the two correct answers below.
+ 3 – 3 × 3 ÷ 3
1 mark
(b) A rule changes 10 to 5
What could the rule be? Give two different answers.
1 0 5
1 mark
1 0 5
1 mark
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7. 8. Number sequence
The rule for this sequence is to add the same number each time.
Use this rule to write the missing numbers in the sequence.
3 1 9
1 mark
9. Using rules
(a) These rules show how to get from one number to the next in these sequences.
Use the rules to write the next two numbers in each sequence.
Rule: Add 8
4 12 ................ ................
1 mark
Rule: Multiply by 3
4 12 ................ ................
1 mark
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8. Rule: Divide by 4 then add 11
4 12 ................ ................
1 mark
(b) A sequence of numbers starts like this:
30 22 18
Could the rule be Subtract 8?
Yes No
Explain your answer.
1 mark
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9. 10. Shapes on a grid
Here is a sequence of shapes made with grey and white tiles.
S h a p e
n u m b e r 1
S h a p e
n u m b e r 2
S h a p e
n u m b e r 3
S h a p e
n u m b e r 4
The number of grey tiles = 2 × the shape number
The number of white tiles = 2 × the shape number
(a) Altogether, how many tiles will be in shape number 5?
........................ tiles
1 mark
(b) Altogether, how many tiles will be in shape number 15?
........................ tiles
1 mark
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10. (c) Write the missing number below.
The total number of tiles = ..................... × the shape number
1 mark
11. Chains
(a) The number chain below is part of a doubling number chain.
Fill in the two missing numbers.
. ... .. .. .. .. .. .. . .. ... .. .. .. .. .. ..
4 0 8 0 1 6 0
1 mark
(b) The number chain below is part of a halving number chain.
Fill in the two missing numbers.
. .. .. ... .. .. .. .. . .. ... .. .. .. .. .. ..
4 0 2 0 1 0
1 mark
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11. 12. Patterns on a grid
I put square tiles on a large grid so that the tiles touch at the corners.
The diagram shows part of my diagonal pattern.
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 x
y
1
2
3
4
5
6
7
(a) The bottom right-hand corner of tile 2 is marked with a •
Write the coordinates of this point.
( , )
1 mark
(b) Tile 4 touches two other tiles.
Write the coordinates of the points where tile 4 touches two other tiles.
( , ) ( , )
1 mark
(c) Write the coordinates of the points where tile 17 touches two other tiles.
( , ) ( , )
1 mark
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12. (d) I have 30 tiles to make a pattern on a grid.
The pattern is a series of squares.
7
6
5
4
3
2
1
0
0 1 2 3 4 5 6 7 x
y
I have used some of the 30 tiles to make my pattern.
Do I have enough tiles left to make the next square, of side length 4?
Show working to explain your answer.
2 marks
Brewood CE C Middle School 12