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Algebra
Sequences
Equations
Sequences Help
How many sticks are there in each pattern?
Pattern
no. n
Number
of sticks
4 times
table
1
2
3
4
5
6
5
9
13 17 21 25
4
8
12 16 20 24
+4 +4 +4 +4 +4
What
pattern
do
you
notice
in the
number
of sticks?
So
the
rule
for
the
number
of
sticks
is
What must you add to the 4 times table to get the
How
manyofsticks
are there in the next 3 patterns?
number
sticks?
Multiply by 4 then add 1 or x4 + 1 or 4n + 1
1
Back
Sequences Help
How many tiles are in each shape?
Pattern
no. n
No. of
tiles
1 2 3 4 5
3 8 15 24 35
Each shape can be seen as the square of the next
Draw
theminus
next
shape.
th and 5th shapes?
+5
+7 in
+9
+11
How many
tiles
are
the
4
pattern
number
1.
(n + 1)2 – 1 or n2 + 2n
What
The pattern
difference
do you
increases
notice by
in the
2 each
number
time.of tiles?
Home
Try some on your own.
Away
Sequences Home
• Draw a table of values.
• Find the 4th, 5th, and 10th terms.
• Find the rule for the following sequences.
1.
2.
7, 10, 13……..
3.
4.
1, 5, 9 ……..
Away
Answers
Home Answers
1. Pattern no.
No. of sticks
2. Pattern no.
Sequence no.
3. Pattern no.
No. of sticks
4. Pattern no.
Sequence no.
New topic.
1
2
3
4
5
10
7
12
17
22
27
52
1
2
3
4
5
10
7
10
13
16
19
34
1
2
3
4
5
10
4
9
14
19
24
49
1
2
3
4
5
10
1
5
9
13
17
37
Back to
questions
Rule: 5n + 2
Rule: 3n + 4
Rule: 5n -1
Rule: 4n - 3
Away
Sequences Away
• Draw a table of values for the first five results
• Work out the 10th term
• Find a rule for the sequences
1.
2. 4, 10, 18, 28 ……….
3.
Home
Answers
Away Answers
1. Pattern No.
No. white of
1
4
2 3 4 5
12 24 40 60
Rule: 2n2 + 2n
1
4
2 3 4 5
10 18 28 40
Rule: n2 + 3n
1
1
2
6
tiles
2. Pattern No.
Sequence
no.
3.
Pattern No.
No. white of
3 4 5
15 28 45
Rule: 2n2 - n
tiles
New topic.
Back to
questions
Simplification Help
Collect together the like terms.
7a + 2c – 3a – 4c =
4a + 2c – 4c
But
4a + 2c – 4c =
4a – 2c
And
4(2d–+g)
f) means
– 2(3d – 2f)2means
2 (3c
lots of (3c – 1g)
4 lots of (2d + f)
OR
THEN TAKE (3c
AWAY
– g) + (3c – g)
Which equals 26clots
– 2g
of (3d – 2f)
BUT
4 lots of 2d + f = 8d + 4f
AND
= – 6d – – 4f
= – 6f + 4f
So 4(2d + f) – 2(3d – 2f) = 8d + 4f - 6f + 4f
THEN TAKE AWAY 2 lots of (3d -2f)
= 2d + 8f
Solving equations Help
3(c + 5) = 7c - 9
3c + 15 = 7c - 9
We need ‘c’Take
on one
thesides
equation and
3c side
from of
both
numbers on the other
3c +15 = 3c
7c
4c - 9
Add 9 to both sides
+9
+11
+24
+20 = 4c - 9
Divide both sides by 4
24 = 4c
4
4
6=c
+9
Simultaneous equations Help
3a – 2b = 1 ……… 1
2a + b = 10 ……… 2
Multiply equation 2 by 2 to make the coefficients of
‘b’ the same (ignoring the signs).
3a – 2b = 1 …….. 1
4a + 2b = 20 …… 2
Add equation
1
to equation
2
7a = 21
Divide both sides by 7
a=3
Substitute a = 3 into either equation
Home
2(3) + b = 10
6 + b = 10
So b = 4
Away
Algebra Home
1. Simplify: 2 – 4t – 5 + 9t
2. If c = 4 and r = 3, find the value of 6c + r2
11
3. If y = 3x + 5, and x = -2, what is the value of y?
What is the value of x if y =17?
4.
Solve 3d + 20 = 7d
5. Simplify: 3m2 + 2m – 6m –m2 + m
6.
3(4s – 5) = 9
Away
Answers
Home answers
1)
2)
3)
-3 + 5t
3
y = -1, x = 4
4)
D=5
5)
2m2 - 3m
6)
s=2
New topic
Back to
questions
Away
Algebra Away
1. Solve : 4(3x + 2) – 3(x – 6) = 8
2. Solve: 2x + 3x + 2 = 5
3
6
3.
The triangle
is not drawn
to scale
What is the value of each
angle in this triangle?
4. Solve: 2x + 3y = 16
3x – 2y = 11
Answers
Away Answers
1. X = -2
2. X = 4
3. The angles are 60, 90, 30
4. x = 5, y = 2
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questions
Home
New topic