Questions
Use algebra to write:
1) 2 less than w w – 2
2) 3 more than d d + 3 or 3+d
3) Sum of 5 and c c + 5 or 5+c
4) f more than g f + g
5) p less than double q
6) 7 less than square m m-7
7) Square the sum of 4 and k
Tuesday, 07 July 2020
2
(4+k)
Page 1
Adding and Subtracting like
terms
3a + a -2a = 2a
3b + b -6b = -2b
3c + 4b – 5c + 2b = -2c + 6b
Tuesday, 07 July 2020
Page 2
Simplify each expression…
1) 5a – 4y – 11a + 2y
6) 3d – 5e – 4d + 2e
2) -4f + 6g – 7f – 3g
7) p + 8r – 7p + 2r + 3p
3) 4m + 9n – 6m - 14n
8) 9x + 3x – 8 - 2x + 3
4) -4t + 7y – 10t + 5y
9) a – 6b + 2a + 3b - 3a
5) 1 + 2r – 7 – 7r
10) 3g + 2h – 3h + 2g
-6a - 2y
-11f + 3g
-2m – 5n
-14t + 12y
-6 – 5r
Tuesday, 07 July 2020
-d – 3e
-3p + 10r
10x – 5
-3b
5g – h
Page 3
Multiplying
Simplify:
2a x 4b = 8ab or 8ba
10c x 2de = 20cde
3w x 4y x 5z = 60wyz
Tuesday, 07 July 2020
Page 4
Dividing Algebraic Terms
Simplify:
8a ÷ 4 = 2a
-10ab ÷ 2a = -5b
-20pq
-pq = 20
Tuesday, 07 July 2020
Page 5
Indices (1)
2a^3 x a^6 x 3a^2 = 6a^11
C^2 x -2c^3 x 4c = -8c^6
2y^2 x 4y^5 =8y^7
3m^3 x 4m^5 = 12m^8
Tuesday, 07 July 2020
Page 6
Indices (2)
Q1.
2a3b6 x a6b2 = 2a9b8
Q2. 3c5d4 x 5c2d4 = 15c7d8
Q3. 2ab4 x 4a2C3 = 8a3b4 c3
Q4. 3mnp3 x 4mn2p5 = 12m2n3p8
Tuesday, 07 July 2020
Page 7
Indices (3)
Q1. (a2)4 x (a3)2
Tuesday, 07 July 2020
=
a14
Q2.
4(a2)3 = 4a6
Q3.
(2a2)3 = 8a6
Q4.
(5ab3)2 = 25a2b6
Page 8
Zero Indices
Tuesday, 07 July 2020
Q1.
-30
=
-1
Q2.
(-5)0
=
1
Q3.
a0
=
1
Page 9
Expanding the Brackets
Expand these expressions:
3(a + b) = 3a + 3b
4(y + 6) = 4y + 24
2(2a + 3b – 4c) = 4a + 6b – 8c
Tuesday, 07 July 2020
Page 10
Expand the brackets…
1) 4(2p – 12) = 8p - 48
2) 5(2a + 4b) = 10a + 20b
3) 3(4c – 4b) = 12c – 12b
4) 7(3e + 2f – 4g) = 21e + 14f – 28g
5) 9(6w + 2y – 7z) = 54w + 18y – 63z
6) -10(3b – 9m) = -30b + 90m
Tuesday, 07 July 2020
Page 11
Adding Bracketed Expressions
4(a + 5b) + 3(7a – b) =
4a + 20b + 21a – 3b =
25a + 17b
Tuesday, 07 July 2020
Page 12
Subtracting Bracketed
Expressions
3(2a – 4b) – 2(a + 2b) =
6a – 12b – 2a – 4b =
4a – 16b
Tuesday, 07 July 2020
Page 13
Subtracting Bracketed
Expressions
3(2p + 3q) – 4(p – 2q) =
6p + 9q - 4p + 8q =
2p + 17q
Tuesday, 07 July 2020
Page 14
Invisible 1
7(m – 2n) – (m – 3n) =
7m – 14n – m + 3n =
6m - 11n
Tuesday, 07 July 2020
Page 15
Questions
1) 7(2a – 4b) + 2(2a + b) 18a – 26b
2) 2(3y – w) - 3(2y + 5w)
-17w
3) 4(p + q) + 5(2p – 3q) 14p – 11q
4) 6(2n + m) - 2(n – m) 10n + 7m
5) 2(4s + r) + 7(2s – 3r) 22s – 19r
Tuesday, 07 July 2020
Page 16
If a = 3 and b = 5 what is the
value of
2a + b ?
11
28
16
If c = -3 and d = 2 what is the
value of
c – 2d ?
-9
-7
5
Solving Equations (1)
a) X - 4 = 10 + 4 b) 4X = 12
X
= 10 + 4
X = 12 ÷ 4
X
= 14
X =3
Tuesday, 07 July 2020
Page 19
Solving Equations (2)
a) 5x + 2 = 4x + 5
5x – 4x = 5 - 2
x=3
x = -1/3
Tuesday, 07 July 2020
Page 20
Solving Equations (3)
•
•
•
•
4(d - 2)= 12
4d-8=12
4d=20
D=5
Tuesday, 07 July 2020
• 2d – 1 = 3
5
• 2d = 15 +1
• 2d =16
• d =8
Page 21
Questions
Find X in each equation:
1. 2x+3=23
x=10
2. 3x +2=11 x=3
3. 4x+5=17
x=3
4. 6x+4=34
x=5
5. 10x+8=98 x=9
6. 5x-4=26
x=6
7. 3x-2=22
x=8
8. 12x-2=46 x=4
9. 9x-3=60
x=7
10.11x-12=87 x=9
Tuesday, 07 July 2020
Star questions:
1. 2(x+3)=16 X=5
2. 3(x+4)=27 X=5
3. 5(x-3)=55 X=14
4. 6(x-4)=18 X=7
5. 7(x-4)=0 X=4
Page 22
Line 1
1: X=4
0
1
5
5
9
0
2
5
7
4
10
10 13
6
14
15
14
16
15
17
Line 1: y=6
11
13
Line 2
6
5
4
2
1
0
Write the equation of the lines:
Line 1: X=4
Line 2: y= 6
Tuesday, 07 July 2020
Page 23
Finding the first 3 terms
4n + 2
1st term
=
4×1+2
=6
2nd term
=
4×2+2
= 10
3rd term
=
4×3+2
= 14
6 10 14
Tuesday, 07 July 2020
Page 24
Find Nth Rule
3
7
11
15
19
23
27
4
1) The difference = 4
2) The first term - The difference = 3 – 4 = -1
Tuesday, 07 July 2020
Page 25
Find term to term rule:
1) 4,8,12,??…..
1) Add 4
2) 27,24,…?..,18
2) Subtract 3
3) 100,…??..,400,800 3) Multiply by 2
Find Nth rule:
1) 4,8,12,16
2) 27,24,21,18
--3
1) 4n
2) -3n+30
If the nth rule is 2n+3 find:
1)The first three terms 1) 5 ,7,9
2) The 6th term
2) 2x6+3=15
Tuesday, 07 July 2020
Page 26
Expand the brackets
(y+2)(y+1)=y^2+3y+2
(y-2)(y+1) =y^2-y-2
(b-2)(b-1)= b^2-3b+2
Factorise
12ab - 6a = 6a(2b -1)
9K- 6 =3(3k-2)
Tuesday, 07 July 2020
Page 27
2x + 2y =3
2x - y = 6
( 1,3)
Tuesday, 07 July 2020
2x + y = 8
x-y=4
Substitution
( 4,3) ( 4,0)
Page 28
Simultaneous Graphically
(x,y)
Y
x
Gradient
(3,6)( 5,8)
Tuesday, 07 July 2020
Page 29
y-intercept
+4
(0,4)(6,1)
x
Gradient
x
• Quadratic Function
• Plot a grapy of the equation ‘y = x2 + 1
x
y
-3
10
-2
-1
0
1
2
3
5
2
1
2
5
10
Vertex point (0,1)
Equation Of Line of Symmetry x=0
Make h subject
5h-3b=12c
5h=12c+3b
h=12c+3b
5
Make s subject
4 = g(s – 7)
g(s – 7) = 4

gs – 7g = 4 
Tuesday, 07 July 2020
s = 4 + 7g
g
Page 32
Rearrange the formula to make p the subject
m=p+n
2
p=n-m
2
P=2(m – n)
Our answer should say ... p = 2(m – n)