1. Senior 1 Annual Exam Revision

2. Triangles & Quadrilaterals
What you need to know?
Properties of Triangles
Properties of Quadrilaterals
How to use angles in a triangle add up to 180° to find missing angles
How to use angles in a quadrilateral add up to 360° to find missing angles
How to construct triangles using a compass, protractor and ruler (3 types of constructions)
Triangles & Quadrilaterals

3. Properties of Triangles
No Parallel Sides
Properties of Triangles
Angles & Sides
Types of Triangles
Isosceles triangle
2 equal sides
2 equal angles (base)
Equilateral Triangle
3 equal sides
3 equal angles.
Scalene triangle
3 unequal sides
3 unequal angles

4. Any triangle containing a 90o angle is a right-angled triangle
An isosceles or a scalene triangle may contain a right angle.
Right-angled
isosceles triangles.
Right-angled
scalene triangle.

5. 1) What is a Quadrilateral
1) What is a Quadrilateral?  A shape with 4 straight sides… 2) How many can you name?
Sides, Angles, Parallel?
Square
Equal sides
2 pairs of parallel sides
All angles 90˚
Rectangle
2 pairs of equal sides
2 pairs of parallel sides
All angles 90˚
Trapezium
1 pair of parallel sides
Rhombus
Equal sides
Opposite sides parallel
Opposite angles equal
Kite
2 pairs of equal sides
No parallel sides
One pair of equal angles
Parallelogram
2 pairs of equal sides
Opposite sides parallel
Opposite angles equal

6. (Ls in an isosceles triangle)
= 136°
x =180 – 136 = 44°
(Ls in a triangle)
= 245°
y = 360 – 245 = 115°
(Ls in a quad)
180 – 30 = 150°
150 ÷ 2 = 75°
(Ls in an isosceles triangle)

7. Constructions Use compass, protractor & ruler
You must be able to understand words about triangles and draw a sketch from those words
You must identify which type of construction it is (ASA, SSS, SAS) These are types of constructions NOT types of triangles!!
Once you do, try to remember the steps particular to that construction
You must ALWAYS start by constructing the base line.
Constructions Use compass, protractor & ruler

8. Construct the base line AB = 10 cm
Put protractor at A, draw an angle of 60° - line of any length
Open compass 8cm, pin at A and make an arc
Join where this arc cuts the line to B, call it C
Construct ∆ ABC having AB = 10cm, AC = 8cm and A = 60° - Measure BC from your drawing
9cm

9. Construct the base line XY = 8 cm
Put protractor at X, draw an angle of 45° - line of any length
Put protractor at Y, draw an angle of 60° - line of any length (must cut the other)
Where lines cut, is Z
Construct ∆ XYZ having XY = 8cm, X = 45° and Y= 60° Measure angle Z and state type of triangle - 77 Z X Y

10. Construct the base line PQ = 8 cm
Put compass on P, open 8cm make an arc
Put compass on Q, open 8cm make an arc which meets the other arc
Where the arcs meet is point R & join
Construct ∆ PQR having PQ = PR = RQ = 8cm Measure all three angles, did you make an accurate construction? R
8cm
8cm P Q
8cm

11. Decimals What you need to know? Identify place value Order decimals
Add & Subtract decimals
Multiply decimals
Divide decimals
Decimal by whole
Decimal by decimal
Rounding decimals
Decimals

12. Decimals warm up 1) Which number is biggest: 1.34 0.99 1.22)
3) Which number is smallest:
4) 2 x 1.2
5) Which number is closest to 5:
6) 3.5 – 2.5
7) Which number is biggest:
8) 3.6 ÷ 2
= 2.3
= 2.4
= 1
= 1.8

13. Decimals

14. Decimals
In the number
(a) how many tenths are there?
(b) how many hundredths are there?
(c) how many thousandths are there?
Write each of these as a number:
(a) one hundredth (b) seven hundredths
(c) six tenths (d) two tenths
(e) one tenth (f) three thousandths 8 4 5
0.07
0.1
0.01
0.2
0.003
0.6

15. Decimals
Order these decimals in ASCENDING order
0.165, 0.151, 0.56, 0.6, 0.605
Order these decimals in DESCENDING order
6.34, 7.2, 6.45, 6.2, 6.4, 7.24
0.151, 0.165, 0.56, 0.6, 0.605
7.24, 7.2, 6.45, 6.4, 6.34, 6.2

16. Decimals 3.6 0.69 45.2 24.904 1.38 10.56 Multiplying decimals
METHOD:
Count how many decimal places, then forget the decimal places and work out the whole numbers multiplication
Get your answer, put the point in from the back according to how many places you counted at the beginning
Multiplying decimals
1.2 x ) 0.23 x 3
3) 11.3 x ) x 2
5) 6 x ) 8 x 1.32
3.6
0.69
45.2
24.904
1.38
10.56

17. Decimals 1.6 1.475 0.83 0.518 Dividing decimals by whole numbers
METHOD:
Simple bus stop division, just remember to put the point above the point of the dividend.
Dividing decimals by whole numbers
4.8 ÷ ) 5.9 ÷ 4
3) 5.81 ÷ ) ÷ 14
1.6
1.475
0.83
0.518

18. Decimals 20 1.1 48 20.1 Dividing decimals by decimals
METHOD:
AIM: Change decimal divisor to whole number
How? Multiply by 10,100,1000
Work out using methods you already know: whole/whole or division/whole
Dividing decimals by decimals
30 ÷ ) 0.55 ÷ 0.5
3) 3.84 ÷ ) ÷ 0.25 20
1.1 48
20.1

19. Decimals 1.3 5.76 2.346 3.1416 Practice decimals rounding
Round 1.27 to one decimal place
Round to two decimal places
Round to three decimal places
Round to four decimal places
1.3
5.76
2.346
3.1416

20. 10 – 2.20 = 7.80
7.80 ÷ 6 = €1.30
6 apple pies cost : 10 – 2.20 = 7.80
1 pie : 7.80 / 6 = 1.30
1.30

21. Topic: Change between FDP
Fraction to Percentage
Decimal to Percentage
Fraction to Decimal
Percentage to Fraction
Percentage to Decimal
Decimal to Fraction
of 100
x 100
Topic: Change between FDP
Remember what fraction means: num ÷ denom
Use ½ , 50% and 0.5 as an example, they should use it to to help out
Remember what percentage means all over 100
Remember tenths, hundredths, thousandths and simplify

22. Common Fractions

23. Topic: Change between FDP
0.3
30%
9/20
45%
7/25
0.28
0.15
15%

24. Finding Missing Angles using Angle Facts
Which angle facts?
Angles in a triangle add up to 180°
Angles in a quadrilateral add up to 360°
Angles on a straight line add up to 180°
Angles at/around a point add up to 360°
Vertically opposite angles
Finding Missing Angles using Angle Facts

25. Find the missing angles – write the REASONS.
= 210°
x = 360° - 210° = 150°
(Ls around a point)
Find the missing angles – write the REASONS.
y = 85°
(vertically opposite Ls)
z = 180°- 85° = 95°
(Ls on a straight line)

26. Number and Patterns Types of Numbers?
Factors (HCF : Highest Common Factor)
Multiples (LCM: Least Common Multiple)
Indices
Primes (product of prime factors)
Square numbers
1, 4, 9, 16, 25, 36, 49, 64, 81, 100
Triangular numbers
1,3,6, 10, 15, 21, 28….
Rectangular numbers
NOT A SEQUENCE – NON PRIME NUMBERS
Number and Patterns

27. 97 10
100
125

28. In index form:
3 x 23 x 7

29. Find the LCM of 12 and 15 Find the HCF of 24 and 36
12: 12, 24, 36, 48, 60, 72
15: 15, 30, 45, 60
Find the HCF of 24 and 36
24: 1,2,3,6,4,8,12,24
36: 1,2,3,4,6,9,12,18,36
LCM: List the multiples, choose the first one that matches HCF: List the factors, choose the last one that matches