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Sha Tin College Mathematics Department
Key Stage 4 CORE Level Course
Unit 6 Assignment: Algebra II
Total
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A: Number Patterns
#1(no calc)
Fill in the blanks to continue the patterns in this number square.
1
2
4
2
4
8
4
8
16
8
[2]
#2(no calc)
Four rectangles are outlined in the diagram.
The area of the innermost one is 2 cm2, and its perimeter is 6 cm.
(a)
Working outwards, write down the area and perimeter of the other three
rectangles.
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Algebra II
1
Rectangle
Area (cm2)
Perimeter (cm)
1st
1 2  2
2 1  2  6
2nd
3 4 
2  3  4 
3rd


2
4th


2


[6]
(b)
Write down the area and perimeter of the next two rectangles in the
sequence (not shown in the diagram).
Answer (b)(i) 5th rectangle.
Area =
cm2. Perimeter =
cm.
cm2. Perimeter =
cm.
(b)(ii) 6th rectangle.
Area =
(c)
[4]
Write down the area and perimeter of the fiftieth rectangle in the sequence
Answer (c)
50th rectangle.
Area =
cm2. Perimeter =
cm.
[2]
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Algebra II
2
#3(no calc)
The number triangle below is made up of consecutive odd whole numbers.
Row
Number triangle
Total of
row (T)
Number of odd
numbers in row (R)
Average of
Row (T  R )
1st
1
1
1
1
2nd
3 5
2
3rd
7 9 11
3
4th
13 15 17 19
(a)
64
4
5th
5
6th
6
16
Fill the fifth and sixth rows of the number triangle.
[2]
(b)
Fill in the blanks in the “Total of row” and “Average of row” columns.
[4]
(c)
Write down the “Total of row” and “Average of row” for the 10th row.
Answer (c) Total of 10th row
(d)
Average of 10th row
[2]
Write down formulae, in terms of n, for “Total of nth row” and
“Average of nth row”.
Answer (d) Total of nth row
Average of nth row
Total for Section A
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Algebra II
[2]
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3
B:Linear Sequences
#1Calc For the number pattern, fill in the 5th term and then write a general
formula to find any term, in terms of n.
Term number (n)
1
2
3
4
5
n
General Formula : V =
Value (V)
5
7
9
11
[3]
#2 No calcs Draw an accurate graph of the information in #1
[2]
#4 What is the name of the shape of the graph drawn in #2?
[1]
#5 What kind of function (formula) is V?
[1]
Total for Section B
/7
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Algebra II
4
C: Quadratic Sequences
#1Calc
(i)
a) fill in the 5th term.
b) Fill in the 1st difference and the 2nd difference
c) What type of general formula links n and V?
_______________________________________________________________[1]
Term number (n) Value (V)
1st
2nd difference
Simultaneous
difference
Equation
1
8
2
14
3
22
4
32
5
n
d) By writing and solving a set of simultaneous equations or otherwise:
Write a general formula to find any term, in terms of n.
[4]
General Formula : V =
[2]
(ii)
a) fill in the 5th term.
b) Fill in the 1st difference and the 2nd difference
c) What type of general formula links n and V?
_______________________________________________________________[1]
Term number (n)
Value
1
2
3
4
5
n
2
9
22
41
1st
difference
2nd difference
Simultaneous
Equation
[4]
d) By writing and solving a set of simultaneous equations or otherwise:
Write a general formula to find any term, in terms of n.
General Formula : V =
[2]
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Algebra II
5
#2 Draw a sketch of what the graph of the formulae found in #1 would look like.
V
n
[2]
#3 What is the name of the shape of the graph drawn in #2?
[1]
#4 What kind of function (formula) is V?
[1]
Total for Section C
CAN DO STATEMENTS
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TICK HERE
RECAP Continue a sequence of numbers or patterns and find the nth
term
Investigating – working systematically, making predictions, proving
algebraically
Investigating – working systematically, looking for patterns,
making predictions, generalising
RECAP Use a difference method to find the formula for a linear
sequence
NEW Use a difference method to find the formula for a quadratic
sequence
Investigating – working systematically, generalizing, proving
algebraically
Sha Tin College Mathematics Department KS 4 CORE ASSIGNMENT Algebra II
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