The document discusses concepts related to forming and solving equations, particularly through the use of angle, area, and perimeter facts. It provides examples of problems along with methods for finding values through equations based on geometric principles. Additionally, it includes exercises and exam-style questions to enhance understanding of mathematical equations.

1. Forming and Solving Equations
LO 1: To be able to form and solve equations using angle facts
Foundation Starter
Simplify:
Solve:
3) Write 60 as a product of primes
4) List the factors of 24
Foundation Plus/Higher Starter
Simplify:
1)
Solve:
3) Write 440 as a product of primes
4) What is the HCF of 24 and 36?
3 𝑥+7 𝑦
9 𝑥3
−12𝑥2
1 2 𝑎8
6 𝑎2
7
− 3
𝑐= 4
𝑐= 2
60=22
×3× 5
440=23
× 5×11
1,2,3 ,4,6,8 ,12,24
12
1517 0.00021

2. Forming and Solving Equations
LO 1: To be able to form and solve equations using angle facts
What angle facts can we use to find x and y?
3
𝑥
2 𝑥
𝑥
𝑦
2
𝑦
𝑦 +20
𝑦+10
Angles in a triangle add up to 180°
So
6 𝑥 =180
𝑥 =30
Angles in a quadrilateral add up to 360°
So
5 𝑦 + 30=360
5 𝑦=330
𝑦 =66

3. 1.
2.
3.
4.
7.
6.
8.
5.
11.
10.
9.
3
𝑥
5
𝑥
2
𝑥
2
𝑥
2 𝑥+30
𝑥+50
3
𝑥
3
𝑥
𝑥
2
𝑥
3 𝑥+50
2 𝑥
2 𝑥+30
3 𝑥
3
𝑥
2
𝑥
9 𝑥+9
5 𝑥−5
6 𝑥+20
5 𝑥+11
2
𝑥
2
𝑥
3
𝑥
4
𝑥
𝑥
+10
2
𝑥
3 𝑥
𝑦
80 − 𝑥
2 𝑥+8
4 𝑥+17
𝑥
2
𝑥
80 − 𝑥
80 +𝑥
6 𝑥−10
5 𝑥−10
𝑦
𝑥=18 𝑥=15
𝑥=40 𝑥=13
Y=10
𝑥=20
𝑥=22.5
𝑥=45
𝑥=28
12.
2
𝑥
+5
3 𝑥+5
𝑥=20
30 0
2 𝑥−5
5
𝑥=15
Y=50

4. Forming and Solving Equations
LO 1: To be able to form and solve equations using angle facts
What angle facts can we use to solve the following:
3 𝑥−18 2 𝑥+2
3 𝑥+3
5 𝑥−1
4 𝑥−20
3 𝑥+10
3 𝑥−15
𝑥+25
Vertically opposite
angles are equal
So
𝑥 =20
Angles in a
straight line add
up to 180°
So
8 𝑥 +92=1
8 𝑥 = 8
𝑥 =1
Corresponding angles are equal
So
3 𝑥 − 20= 10
3 𝑥 =30
𝑥 =10
Alternate angles are equal
So
2 𝑥 − 15=25
2
𝑥 =20

5. 5 𝑥 5 5
7 𝑥+403 𝑥+40
5 𝑥
1 20
8 𝑥
56
-30 1 17
7 𝑥+11 5 𝑥+19
1 25
3 𝑥+35
3 𝑥−28
𝑥+22
5 𝑥−42 3 𝑥+78
4 𝑥−30
3 𝑥+20
3 𝑥−17
𝑥+29
1.
2.
3.
4.
7.
6.
8.
5.
11.
10.
12.
9.
7
𝑥
2
𝑥
𝑥=11 𝑥=21 𝑥=60
𝑥=20 𝑥=10
𝑥=5
𝑥=24 𝑥=30
𝑥=50
𝑥=7 𝑥=25
𝑥=23

6. Forming and Solving Equations
LO 1: To be able to form and solve equations using angle facts
Exam Style Questions!

7. Forming and Solving Equations
LO 2: To be able to form and solve equations using area and perimeter facts
𝑥+5+𝑥+𝑥+5+𝑥
4 𝑥+10
4 𝑥+10=38
4 𝑥=28
𝑥=7
length

8. Forming and Solving Equations
LO 2: To be able to form and solve equations using area and perimeter facts
2 𝑥+9+2 𝑥−4+4 𝑥+6
8 𝑥 +11
8 𝑥 +11=39
8 𝑥 =28
𝑥 =7

9. 3 𝑥
2 𝑥
8 𝑥
5 𝑥
a) Form an expression
for the perimeter
b) The perimeter is
52m find x
8
3 𝑥+16
a) Form an
expression for the
perimeter
b) The perimeter is
220cm find x
2 𝑥−5
This is a regular polygon
a) Form an expression
for the perimeter
b) The perimeter is
78m find x
3 𝑥+3
2 𝑥
2 𝑥+2
3 𝑥
a) Form an expression
for the perimeter
b) The perimeter is
75cm find x A rectangle has it’s length twice it’s
width. If it’s perimeter is 42cm, find
the width
1.
2.
3.
4.
5.
10 𝑥+5
𝑥=7
12𝑥 −30
𝑥=9
11 𝑥
=20
=42 w=7
2 6 𝑥 𝑥=2

10. Forming and Solving Equations
LO 2: To be able to form and solve equations using area and perimeter facts
3
2 𝑥 −6 a) Form an expression for the area
b) The area is 42cm find x
3 𝑥+ 5
8 a) Form an expression for the area
b) The area is 80cm find x
3 (2 𝑥 − 6)
6 𝑥 − 18
6 𝑥 − 18=42
6 𝑥 =60
𝑥 =10
1
2
× 8(3 𝑥 +5)
4( 3 𝑥 +5)
1 2 𝑥 +20
1 2 𝑥 +20=80
1 2 𝑥= 60
𝑥 =5

11. Forming and Solving Equations
LO 2: To be able to form and solve equations using area and perimeter facts
5
2 𝑥+7 a) Form an
expression for the
area
b) The area is 70cm
find x
3 𝑥 −7
10
a) Form an expression for
the area
b) The area is 115cm find x
The area of a square is
49cm find the perimeter
1.
2.
3.
10 𝑥+35
𝑥=3.5
15 𝑥−35
𝑥=10
28 𝑐𝑚

12. Forming and Solving Equations
Exam Style Questions!
LO 2: To be able to form and solve equations using area and perimeter facts

13. 𝑥+10
5
𝑥
−
7
3
𝑥
+
3
2𝑡+10
2 𝑥+4
9 𝑥+28
2 𝑥 −3 − 𝑥 +9
1.
2.
3. 7.
6.
5.
11.
10.
9.
3
𝑥
+
8
5
𝑥
+
4
𝑥=4 𝑥=2 𝑥=4
𝑥=2 𝑥=5 𝑥=5
𝑥=4
𝑥=4
𝑥=10
3 𝑥+2
4 𝑡+2
6 𝑥− 4
2 𝑥+15 5 𝑥+3
16 𝑥−7
9 𝑥+83 18 𝑥−7

14. 𝑥 +1
3
𝑥=29
𝑥=9.5
𝑥=−6
𝑥 −9
2
4 𝑥− 3
5
2 𝑥 − 5
2
𝑥 +16
2
9 − 𝑥
3