10PQ

Practice Questions �1.3 and 1.4

Icons from TheNounProject.com�garethbell.com

y = x²

15 September 2026

1

1.4 Easy Revision

2

2

2

1.2/1.4 Easy Revision - A

15/09/2026

1. Round 3.14159 to 2DP
2. What is 4³
3. Perimeter��
4. Area:��
5. J =

​

6. Expand 4(3x – 1)�
7. Factorise 15x + 10�
8. Expand (x - 1)(x + 2)�
9. Solve for x: (x + 5)(x - 5)�
10. Hypotenuse H =���

�

3cm

2cm

4cm

2cm

40°

J

3.14

4cm

3cm

H

64

=3+2+3+2�= 10cm

=0.5×2×4�= 4cm²

=180 - 40�= 140°

12x - 4

5(3x + 2)

x² + 2x – 1x - 2

x² + x – 2

x = 5, - 5

3

3

1.2/1.4 Easy Revision - B

1. Round 6.283185 to 3SF
2. What is 0.5²
3. Perimeter��
4. Area:��
5. J =

​

5m

3m

4cm

2cm

40°

J

6.28

0.25

= 3 +4 +5�= 12cm

= 2×4�= 8cm²

=180 -40 -90�= 50°

4m

6. Expand x(2x + 5)�
7. Factorise 2x² + x�
8. Expand (x - 3)(x + 4)�
9. Solve for x: (x - 3)(x + 4)�
10. Hypotenuse H =���

�

8cm

6cm

H

2x² +5x

x(2x + 1)

x = 3, -4

15/09/2026

x² + 4x – 3x - 12

x² + x – 12

4

4

1.2/1.4 Easy Revision - C

6. Expand 4x(3x – 5)
7. Factorise 8x – 4
8. Expand (x - 3)(x + 2)��
9. Solve for x: (x + 12)(x - 7)�
10. Solve for x:�4x + 5 = 17

600cm

2m

80°

J

0.03

3

=6+2+6+2�= 16m �(or 1600cm)

=2 × 6�= 12m²

=360 - 120 � - 80 - 90�= 70°

4x = 17 - 5

4x = 12

x = 12 ÷ 3

12x² – 20x

4(2x - 1)

= x² – 3x + 2x – 6

= x² - x - 6

x = -12, 7

600cm

2m

120°

15/09/2026

5

5

1.2/1.4 Easy Revision - D

1. Round 12345 to 0dp
2. What is 3³
3. Perimeter��
4. Volume:��
5. J =

​

5m

3m

2cm

2cm

12345

= 27

= 12m

=2×2×2�= 8cm³

=360 - 40 - 90�= 230°

4m

6. Expand 2x(x + 1)
7. Factorise 14x² + 7
8. Expand (x - 3)(x - 4)��
9. Factorise x² + 7x + 10�
10. Hypotenuse H=���

�

1m

1m

H

=2x² + 2x

=7(2x² + 1)

= x² - 3x - 4x +12

= x² - 7x + 12

(x + 2)(x + 5)

2cm

40°

J

15/09/2026

6

6

1.2/1.4 Easy Revision - E

6. Expand x(2y – 5)
7. Factorise 2x² + 2x
8. Expand (x + 5)(x + 7)��
9. Solve for x: (x + 5)(x + 7)�
10. Solve for x:�4x² + -16 = 0

2cm

J

$2.35

8

=2 × 10 �= 20cm

=0.5×5×3�= 7.5km²

= 79°�(vert opp angles are equal)

=2xy - 5x

2x(x + 1)

= x² + 5x + 7x + 35

= x² +12x + 35

x = -5, -7

5km

3km

79°

15/09/2026

7

7

1.2/1.4 Easy Revision - F

1. Round 3.45 to 1dp
2. What is 4³
3. Area��
4. Volume��
5. J =

​

5m

2m

3cm

2cm

3.5

= 64

=2m² + 4m^2�= 6m²

=2×3×3�= 18cm³

=360 - 222 - 90�= 48°

5m

6. Expand 2x(x - 1)
7. Factorise 5x² + 10
8. Expand (x + 3)(x - 1)��
9. Factorise x² + 7x + 12�
10. Hypotenuse H=���

�

1m

10m

H

=2x² - 2x

=5(x² + 2)

= x² + 3x - 1x - 3

= x² +2x -3

(x + 3)(x + 4)

3cm

J°

222°

1m

15/09/2026

8

8

1.3 and 1.2/1.4 Easy Revision

9

9

9

1.3 - Graphs

1. What is the overall trend?
2. How often does the Seasonal trend happen?
3. What is the peak in 2005?
4. Predict July 08
5. If this is a graph of heater sales in NZ, why the big dips?

​

​

1. Solve: x + 3 = 2
2. Expand: (x + 3)(x – 2)��
3. Factorise: 3x – 9�
4. Use trig to find x���
5. Find H(Pythag)�

​

​

​

3m

20°

H

3m

5m

x

= Increasing (Positive)

= Annually

= ~47

= ~62

= No one buys heaters in summer

x = -1

= x² -2x + 3x – 6

x² + x - 6

= 3(x – 3)

1.4 - Algebra

Find x

15 September 2026

Heaters sold

10

1.3 - Graphs

1. What percentage of Juniors bus?
2. What are the main two forms �of transport for seniors?
3. Which transport is most different for seniors and juniors?
4. What area is most similar?
5. Is this claim true: most seniors are too lazy to walk/cycle?

​

​

1. Simplify: 2(3x² + x) + -2x
2. Solve: x² + 5 = 14�
3. Expand: (x + 1)(x – 2)��
4. Factorise: 4x² – 8x �
5. Write perimeter formula��

CQ) If the perimeter is 12, find x

1.4 - Algebra

2x+1

x + 1

x²

= 25%

= Car & Bus

= Car

= Bus

= Yes 68.75%

= 6x²

x² = 9

x = 3

= 4x(x – 2)

= (2x+1) + (x² )+ (x + 1)

= x² + 3x + 2

Junior School Transport

Senior School Transport

=x² – 2x + 1x – 2

=x² – x – 2

Find x

12 = x² + 3x + 2

0 = x² + 3x -10

0 = (x + 5)(x – 2)

x = -5, 2

15 September 2026

A

11

1.3 - Graphs

1. What was Andy’s Game 2 score?
2. What is Brad’s overall trend?
3. Predict Carl’s game 5 score?
4. What real world event might have happened in the third game?�
5. Describe seasonal trend(s)?

​

1. If a=5, what is 2(2a² - 45)
2. Find b when: �3b - 3 = 2(b + 1)
3. Expand: (x + 4)(x + 4)�
4. Factorise: x² + 8x + 12�
5. Write the triangle’s area formula��

CQ) Find hypotenuse?

x + 2

1.4 - Algebra

x + 6

= 110

= Steady

= ~115

= A distraction. E.g. loud music

= There are none.

=2(2×25 - 45)

= 10

3b - 2b = 2 + 3

b = 5

= (x + 2)(x + 6)

Area = ½ (x + 6)(x + 2)

= ½x² + 4x + 6

Bowling Marathon

= x² + 8x + 16

15 September 2026

B

12

1.3 - Graphs

1. How much pocket money �did the triplets each get?
2. Who spent the most on Robux?
3. What % of Coco’s $ was Temu?
4. Do kids follow the save 10% rule?
5. Discuss the claim that �‘kids eat too many snacks’

​

1. If a=5, what is 3(a - 1) + a
2. Find x when: � 10x ÷ 2 = 10
3. Expand: (x - 2)(x + 2)�
4. Factorise: x² + 8x + 7�
5. Write perimeter formula��

CQ) Find X?

1.4 - Algebra

x² - 1

2x

= $10

= Coco

= 10%

They don’t.

$2 to $4 per week on snacks isn’t much.

=3×(4) +5

= 17

10x = 20

x = 2

= (x + 1)(x + 7)

P = (4x - 2) + 2x + (x² – 1)

= x² + 6x - 3

Pocket Money Spending

= x² + 0x - 4

Sin θ = O / H

H × sin θ = X

5 × sin 30 = X

X = 2.5cm

15 September 2026

Dollars per week

4x - 2

30°

5cm

X

C

13

1.3 - Graphs

1. How many Pinkys in 2024?
2. Describe the Buzz bar trend:
3. How many bars sold 2023?
4. Predict how many Moros �will sell per day in 2026?
5. Discuss the claim that �‘Buzz bars are the best!’

​

1. If x=1, what is (x + 3)(x - 2)
2. Rearrange to find x : �3x² - 9 = 2x²
3. Expand: (x + 7)(x + 1)�
4. Find x�
5. Find A��

CQ) Find area of the flag?

1.4 - Algebra

= 4 bars

= 12

= 8 Moros

They’re not.

They sell 13 Buzz bars over three years compared to 18 Moros

=(4)x(-1)

= -4

x² = 9

x = 3, or -3

= 30°

Cos θ = A/H

H × Cos θ = A

= 1.732m

= x² + 8x + 7

15 September 2026

Average Daily Sales

= Increasing

Have ya seen my ex?

Area = 2A × 2B

Area = 3.464 × 2

Area = 6.93m²

D

bars

14

1.3 - Graphs

1. How long on FB and Insta combined?
2. How many total hours on phone:
3. On Average, how many �chrome hours per day?
4. Which is bigger: Youtube or Chrome?
5. Discuss the claim that �‘I spend over half my �phone time on social �media (tiktok, IG & FB).

​

1. I run 21km in 3 hours. Speed:
2. Solve for x: �2x² + 5 = 7
3. Factorise: 2x² + 6x + 4��
4. Find θ�
5. Find H��

CQ) What is the yellow angle?

1.4 - Algebra

= 11 hours

= 1 hour

= Youtube

Disagree, I don’t.�I only spend 16/36 of my phone time on social media

= 21 ÷ 3

= 7kph

2x² = 2

x = 1 (or -1)

tan θ = O/A

θ = tan^-1 (8/6)

θ = 53.1°

= 2(x² + 3x + 2)

=2(x + 1)(x + 2)

Top ▷ Angle = 36.9° (180 – 53.1 – 90)

Yellow Angle = 323.1° (360 – 36.9)

15 September 2026

My Weekly Phone Hours

= 36 hours

What’s x?

E

15

1.3 - Graphs

1. Total sugar & fat in choc fish?
2. Which has most fat?
3. How many grams of sugar �in 50g of Marshmallows
4. Which is better for you: �Milk choc, or choc fish?
5. Discuss the claim�“Chocolate Chip �Cookies are the �healthiest snack here

1. I run 42m in 6sec. Speed:
2. Solve for x: �5x – 3 = x – 11
3. Expand: (x – 5)(x – 3)��
4. Perimeter of Choc bar�
5. Area of Choc bar�

CQ) If the area is 12cm², how wide?

1.4 - Algebra

=73g

= 29g

= Choc fish: Because 73g of bad stuff vs 85g

Agree because �* Lowest sugar per 100g �* Lowest sugar and fat � combined.

= 42 ÷ 6

= 7ms^-1

4x = -8

x = -2

= (x-1) + (x-1) + (x+3) + (x+3)

= 4x + 4

= (x-1)(x+3) or x² + 2x - 3

= x² – 5x – 3x + 15

= x² – 8x + 15

12 = x² + 2x – 3

0 = x² + 2x – 15

15 September 2026

Sugar and Fat per 100g

= Milk choc

A Chocolate BARRRGH!

x-1

x + 3

0 = (x + 5)(x – 3)

x = -5, 3

Width = 2cm

F

16

1.3 - Graphs

1. What fraction of the day �do pirates ashore drink?
2. How many hours do �pirates at sea sleep?
3. How much more do pirates �repair per day while at ashore
4. Discuss the claim�“Pirates are lazy �when they’re ashore”

1. V = d/t where v = 50kph, t = 4h�Find d:
2. Find x: 5x -15 = 0�
3. Factorise: x² – x – 6�
4. Find angle b�
5. Find length C��

CQ) Area of triangle sail?

1.4 - Algebra

= 3 hours

Disagree because

• When ashore, they spend 11 hours pirating or repairing.

Agree because

• They sleep and drink more

4 × 50 = 200km

5x = 15�x = 3

= 25° (alt angles on parallel lines)

= (x – 3) (x + 2)

Height = (cos 25) × 4

Height = 3.625m �

​

15 September 2026

= 8 hours

Area = 0.5 × b × h

A = 3.06m²

Pirates ashore

Pirates at sea

sin θ = O/H

O = sin 25 × 4

O = 1.69m

A

17

1.3 - Graphs

1. Smoking rate in 2018/2019?
2. When were they the same?
3. Predict Smoking in 23/24?
4. What real world event might have happened in 19/20?�
5. Describe overall trend(s)?

​

1. If a=3, what is -3(a² - 8)
2. Find x when: �5x - 6 = 2(11 - x)
3. Expand: (x + 2)(x - 3)�
4. Factorise: x² + x - 6�
5. Write the triangle’s area formula��

CQ) Find hypotenuse?

x + 2

1.4 - Algebra

x + 5

= 12%

= 21/22

= 6%

= Quit smoking for Vaping Adverts

= Smoking decreasing, Vaping increasing

=-3 (9 - 8)

= -3

5x + 2x = 6 + 22

x = 4

= (x + 3)(x - 2)

Area = ½ (x + 5)(x + 2)

= ½x² + 5x + 3.5

NZ Smoking Rate

= x² - x - 6

15 September 2026

NZ Vaping Rate

B

18

1.3 - Graphs

1. How many movies did Andy pirate?
2. How many Games were pirated total?
3. What fraction of Ben’s �pirating was music?
4. Who pirated the most games?
5. Discuss: ‘People mostly �pirate music and movies’

1. If a=7, what is 4(a - 1) + a
2. Find x when: � 5x² ÷ 2 = 10
3. Expand: (x - 5)(x + 7)�
4. Factorise: x² + 7x + 12�
5. Write perimeter formula��

CQ) Perimeter was 12. �How long was x?

1.4 - Algebra

x² - 5

x

= 4

= 6

= 3/8

= Carl.

They don’t. Ben does,

But, On average, 11/24 pirated things were music and movies, so less than half.

=4 × (6) + 7

= 31

5x² = 20

x = 2, -2

= (x + 3)(x + 4)

P = (2x - 1) + x + (x² - 5)

= x² + 3x - 6

Last Eight things Pirated

= x² + 2x - 35

x² + 3x – 6 = 12

X² + 3x - 18 = 0

(x – 3)(x + 6)

x = 3, -6

​

15 September 2026

2x - 1

C

19

1.3 - Graphs

1. How tall are male Moa?
2. Which type of bird is biggest:
3. What is the average Emu height?
4. How much bigger are male �Ostrich than male Emu?
5. Discuss the claim that �“Most Female birds �are bigger!”

​

1. If x=5, what is (x + 1)(x - 2)
2. Rearrange to find x : �√(x-2) = 4
3. Expand: (x - 3)(2x - 3)�
4. Find θ�
5. Find H��

CQ) Find area of the triangle?

1.4 - Algebra

= 2m

= 1.8m

= 0.75m

Yes they are. Because:

Moa Emu females are bigger.

The average female height is bigger.

=(6)x(3)

= 18

x - 2 = 16

x = 18

= 67°

= 2x² -9x + 9

Opp = 2×tan(23)

Opp = 0.849m

​

15 September 2026

Height (metres)

= Moa (females)

Area = ½ B × H

Area = ½ 0.849 × 2

Area = 0.849m2

Big Bird Heights

2m

H

θ

23°

Opp

D

20

1.3 - Graphs

1. How long is Elliott?
2. Which is biggest?
3. Which is bigger Falkor or Toothless?
4. Guess the average length?
5. Discuss the claim that �“Most dragons are �longer than 10m, & �can’t fit on a 747.”

1. Smaug eats 28 people in a week. How many per night?
2. Solve for x: �3x² - 7 = 20
3. Factorise: �x² - 16x + 15
4. Find θ�
5. Find H��

CQ) If the triangle above is a cone, Volume =

1.4 - Algebra

= 15m

= Falkor

= 11m (10-12)

Agree because:

• Average length > 10m
• 4 out of 6 are > 10m
• Only 2 are < 10m

​

28 ÷ 7 = 4 people

x² = 27 ÷ 3

x = 3 (or -3)

=(x - 15)(x - 1)

15 September 2026

Dragon Lengths (m)

= Smaug

4cm

6cm

H

θ

E

21

1.3 - Graphs

1. Who got the most screentime?
2. Who was called on most?
3. How many minutes did �Marshall and Chase get?
4. What portion of the time �did they not call on Skye?
5. Discuss the claim�“Skye is the star �of Paw Patrol.”

1. Chase drives 3km �in 2 mins. Speed:
2. Solve for x: �4x – 3 = x – 6
3. Expand: 2(x – 5)(x + 3)��
4. Perimeter of Rubble’s scoop�
5. Area of Scoop�

CQ) If the area is 10cm², how wide?

1.4 - Algebra

= Skye

= 13.1 min

= 80%

Agree because

• Most minutes in movie.
• Called on second most.

= 1.5k per min

= 90kph

3x = -3

x = -1

= (x+1) + (x+1) + 1 + (2x-1)

= 4x + 2

= box (1(x+1)) + triangle(½x(x+1))

= ½x² + 1.5x + 1

= 2(x² – 5x + 3x – 15)

= 2x² – 4x – 30

10 = ½x² + 1.5x + 1 �0 = ½x² + 1.5x – 9

0 = x² + 3x – 18

15 September 2026

Paw Patrol – who is the star?

= Chase

x+1

0 = (x+6)(x-3)

x = -6, +3

x = 3

100

x + 1

1

2x-1

F

Width = 4cm

22

1.3 - Graphs

1. What % of boys want to be a pirate?
2. How many more boys want �to be athletes than girls?
3. The most popular girl job:
4. Discuss similarities and differences:�

1. I travel at 4ms^-1, for 5 seconds. How far did I go?
2. Find x: 3x² - 5 = 7�
3. Factorise: x² + 5x – 14�
4. Find angle b�
5. Find length B��

CQ) Area of triangle sail?

1.4 - Algebra

= 16%

= Doctor

Similarities:

* Musician about 14-15% for both. * Doctor is 1^st or 2^nd.

Differences:

*Athlete is 1^st for boys, and 4^th for girls, at half the size

* Boys don’t want to teach, whereas 25% of girls do

​

4 × 5 = 20m

x² = 12 ÷ 3�x = 2, -2

= 60° (corresponding � on parallel lines)

= (x + 7)(x - 2)

Width = (cos 60) × 4

Width = 2m �

​

15 September 2026

= 25% - 12% �= 12%

Area = 0.5 × b × h

A = 3.46m²

Boys Dream Jobs

Girl Dream Jobs

sin θ = O/H

O = (sin 60) × 4

O = 3.46m

How far I’ll go?

A

23

1.3 - Graphs

1. Minimum time in exam:
2. Top score:
3. If a person spent two hours, �predict their score:
4. Describe graph features �and their meaning:

​

​

1. If a=9, what is -a(a - 7)
2. Find x when: �x² - 6 + x = x(x + 2)
3. Expand: (3x + 2)(x - 3)�
4. Factorise: x³ + x² - 6x�
5. Write the triangle’s area formula��

CQ) x = 7m. What is H?

x - 2

1.4 - Algebra

x + 5

= 45min

= 21

= ~15

• Positive/Increasing. Meaning the more time the better score.

=-9 (2)

= -18

x² – 6 + x = x² + 2x

x² - x² - 6 = 2x – x

-6 = x

= x(x² + x – 6)

= x(x -2)(x + 3)

Area = ½ (x + 5)(x - 2)

= ½x² + 1.5x - 5

Time spent in exam (min)

= 3x² - 7x - 6

H² = (7 + 5)² + (7 - 2)²

H² = (144) + (25)

√169 = 13m

​

15 September 2026

Exam Score

• Weak relationship: meaning it isn’t a perfect rule.

What grade do Pirates get?

“High Cs”

• Outlier at ~115 minutes, ~4: Long time, still did badly.

B

24

1.3 - Graphs

1. How many ships in 1690?
2. How many Pirate ships in Indian Ocean in 1720?
3. What fraction of 1690s pirates were in Caribbean?
4. Biggest region?
5. Discuss: ‘There were more �pirates everywhere in 1720’

1. If a=3, what is 2(a² - 1)
2. Find x when: � 3x² ÷ 2 = 0
3. Expand: (x - 10)(x - 10)�
4. Factorise: x² - 9�
5. Write perimeter formula��

CQ) Perimeter was 30cm. �How long was x?

1.4 - Algebra

3x

x + 1

= 125

= ~ 60

= 100/125

= Caribbean

Agree because:

* Three regions had an �increase (C, IO, ENA)

* Overall increase (125 → 240)

* However Caribbean decreased (100 → 90)

=2 × (9-1)

= 16

3x² = 0 × 2

x = 0

= (x + 3)(x - 3)

P = (x² - 3) + 3x + (x + 1)

= x² + 4x -2

The Golden Age of Piracy

= x² - 20x + 100

x² + 4x -2 = 30

x² + 4x - 32 = 0

(x – 4)(x + 8)

x = 4, -8 → x = 4cm

​

15 September 2026

x² - 3

Active Pirate Ships

C

25

1.3 - Graphs

1. How many credits do Year 12s �with 75% attendance get?
2. Which year level gets the most?
3. How many more credits does a year 11 earn with 90% attendance vs 70%?
4. Discuss the claim “Credits�aren’t affected by attendance”

​

1. If x=-2, what is (x + 1)(x - 2)
2. Rearrange to find x : �(x-3)² = 4
3. Expand: (x - 1)(2x - 3)�
4. Find θ
5. Find �Adj�

CQ) Find area of �Trapezium:

1.4 - Algebra

= ~45

= ~22

I disagree because

• High attend (>80%) get about 70 creds.
• Low attend (<60%) get about 30 credit.

=(-1)x(-4)

= 4

x - 3 = 2 or -2

x = 5 or 1

= 60°

= 2x² -5x + 3

Area = (a+b) ÷2 × h

Area = (1+5) ÷2 × 6.93

= 20.79m²

​

15 September 2026

Credits that year

= 11

Attendance Rate vs Average Credits

5m

H

θ

30°

Adj

1m

tan θ = O/A

O/tan θ = A

4/tan 30 = 6.93m

D

26

1.3 - Graphs

1. Which is biggest in 2025?
2. Which is smallest in 2000?
3. How much did NZ grow?
4. Overall Trend?
5. Who grow the �most and why?

CQ) Why this �order?

1. Oman has 2.5 births per woman. How many in 17 women?
2. Solve for x: �-2x² + 17 = -15
3. Factorise: �x² - 16x - 17
4. Find θ�
5. Find A��

CQ) 15° is a ladder-safe angle θ. How much higher would this reach?

1.4 - Algebra

= Liberia

= ~1.4mil

= Increase

Most is Oman because:

• Grew by 3.2mil
• Grew 2.5 times bigger
• 2^nd was Liberia @ 2.8mil

17 × 2.5 = 42.5

x² = -32 ÷ -2

x = 4 (or -4)

=(x - 17)(x + 1)

2m x cos(15°) = 1.93m (0.20m higher)

15 September 2026

Population (Millions)

= Oman

1m

2m

θ

= A to Z

A

E

27

1.3 - Graphs

1. Shortest All Black:
2. Heaviest All Black:
3. If a player was 1.9m tall�predict their weight:
4. Describe graph features �and their meaning:

​

​

1. If a=6, what is -a(a - 7)
2. Find x when: �x² - 6 + x = x(x + 2)
3. Expand: (x + 2)(x - 3)�
4. Factorise: x² + 3x² - 6x�
5. What angle θ is this conversion?��

CQ) If a conversion �from 22m travels �in a straight line, goes �through the middle �at a height of 4m, �What diagonal �distance?

5.6m

1.4 - Algebra

22m

= 1.76m

= ~144kg

= ~110kg

• Positive/Increasing. Meaning the taller they are the heavier.

= -6×(-1)

= 6

x² – 6 + x = x² + 2x

x² - x² - 6 = 2x – x

-6 = x

= 4x² -6x

= 2x(2x – 3)

Height (m)

= x² - x - 6

a² + b² = c²

22² + 2.8² = 22.18²

Ground = 22.18, Height = 4

Hypotenuse = 22.54m

15 September 2026

Weight (Kg)

• Weak relationship: meaning it isn’t a perfect rule.

• Outlier at 145kg – A big big player (Tamaiti Williams)

θ

F

28

1.3 - Graphs

1. What percentage of boys �play soccer?
2. How many more boys �play rugby than girls?
3. What is most popular �sport overall?
4. Discuss the claim:�“Rugby has twice as �many players as BBall”

1. V = d/t where v = 12m/s, t = 4s�Find d:
2. Find x: 3x + 12 = 0�
3. Factorise: x² – 0x – 16�
4. Find angle b�
5. Find length X���

CQ) Area of triangle?

1.4 - Algebra

= 26%

Rugby �(38% and 20%)

Disagree because

• Average, Rugby (29%) is 3x the size of average BBall (9%)
• In girls it is 5 times as many

​

4 × 12 = 48m

3x = -12�x = -4

= 30° (alt angles on � parallel lines)

= (x – 4)(x + 4)

Y = (sin 60) × 4

Y = 3.464m �

​

15 September 2026

38% - 20% = 18%

Area = 0.5 × X × Y

Area = 3.464m²

Boys’ Sports

Girls’ Sports

cos θ = A/H

A = cos 60 × 4

X = 2m

A

2m

29

1.3 - Graphs

1. How tall was Lia at 11?
2. When did Lia stop growing?
3. Predict Dex’s height at 18?
4. What will be Lia’s height at 18?�
5. Describe overall trend(s)?

​

1. If x=7, what is x(x² - 50)
2. Find x when: �3x - 15 = 2(x - 4)
3. Expand: (x + 7)(x - 7)�
4. Factorise: x² - x - 42�
5. Write the triangle’s area formula��

CQ) Find a positive�integer x?

x + 1

1.4 - Algebra

x + 2

= 145cm

= 15

= ~180cm?

= 162cm

= Both Increasing (No outliers, no seasonal trends)�Lia stopped growing at 162cm�

=7×(49 - 50)

= -7

3x – 15 = 2x - 8 x = 7

= (x - 7)(x + 6)

Area = ½ (x + 1)(x + 2)

= ½x² + 1.5x + 1

Dex’s Height

= x² - 49

x = 2 (3, 4, 5 is a Pythagorean triple)

​

15 September 2026

Lia’s Height

B

x + 3

(cm)

30

1.3 - Graphs

1. Total hours sleep on weekdays?
2. What day has most sleep?
3. What fraction of �weekdays is learning?
4. How are holidays �different to �weekends?

1. If a=5, what is a(a + 3) - 35
2. Find x when: �2x² ÷ 10 = 5
3. Expand: (x + 5)(x + 11)�
4. Factorise: x² - 7x + 12�
5. Write & simplify perimeter��

CQ) Perimeter was 30 �How long was x?

1.4 - Algebra

x + 7cm

5cm

= 8

= Holiday

Holidays have

* More sleep ( 9 → 10 hours)

• Less learning (1 → 0 hours)
• More phone (6 → 8 hours)

Probably because holidays are more chill

=5×(8) - 35

= 5

2(x²) = 5×10

x² = 25

x = 5, -5

= (x - 3)(x - 4)

P = (x² – 12) + (x+7) + 5

P = x² + x _{or P = x(x + 1)}

= x² + 16x + 55

30 = x² + x

0 = x² + x – 30

0 = (x + 6)(x - 5)

X = -6cm, 5cm

​

15 September 2026

x² – 12cm

C

31

1.3 - Graphs

1. How Addictive is alcohol?
2. How harmful are vapes?
3. Which is most harmful?
4. How much more addictive �are Vapes than Ice Cream?
5. Discuss the claim:�“Smokes should be �illegal for all people” �(relate to context)

​

1.4 - Algebra

= 6

= Smokes

9-2 = 7

Agree because: * Most harmful (9)�* Most addictive (9) * There are Less harmful alternatives (ice cream). �In context this means easy to get addicted and do harm, so should be banned. Limit: ‘Scale’ is unclear?

=(-2)x(-5)

= 10

x - 3 = 25

x = 28

= 20°

= 2x² +3x - 9

Opp = 10×tan(20)

Opp = 3.25cm

​

15 September 2026

Scale 1-10

= 6

Area = ½ B × H

Area = ½ 3.25 × 10

Area = 16.25cm²

10cm

H

θ

20°

Opp

D

32

1.3 - Graphs

1. How long is Elliott?
2. Which is biggest?
3. Which is bigger Falkor or Toothless?
4. Guess the average length?
5. Discuss the claim that �“Most dragons are �longer than 10m, & �can’t fit on a 747.”

1. Smaug eats 28 people in a week. How many per night?
2. Solve for x: �3x² - 7 = 20
3. Factorise: �x² - 16x + 15
4. Find θ�
5. Find H��

CQ) If the triangle above is a cone, Volume =

1.4 - Algebra

= 15m

= Falkor

= 11m (10-12)

Agree because:

• Average length > 10m
• 4 out of 6 are > 10m
• Only 2 are < 10m

​

28 ÷ 7 = 4 people

x² = 27 ÷ 3

x = 3 (or -3)

=(x - 15)(x - 1)

15 September 2026

Dragon Lengths (m)

= Smaug

4cm

6cm

H

θ

E

33

1.3 - Graphs

1. Who got the most screentime?
2. Who was called on most?
3. How many minutes did �Marshall and Chase get?
4. What portion of the time �did they not call on Skye?
5. Discuss the claim�“Skye is the star �of Paw Patrol.”

1. Chase drives 3km �in 2 mins. Speed:
2. Solve for x: �4x – 3 = x – 6
3. Expand: 2(x – 5)(x + 3)��
4. Perimeter of Rubble’s scoop�
5. Area of Scoop�

CQ) If the area is 10cm², how wide?

1.4 - Algebra

= Skye

= 13.1 min

= 80%

Agree because

• Most minutes in movie.
• Called on second most.

= 1.5k per min

= 90kph

3x = -3

x = -1

= (x+1) + (x+1) + 1 + (2x-1)

= 4x + 2

= box (1(x+1)) + triangle(½x(x+1))

= ½x² + 1.5x + 1

= 2(x² – 5x + 3x – 15)

= 2x² – 4x – 30

10 = ½x² + 1.5x + 1 �0 = ½x² + 1.5x – 9

0 = x² + 3x – 18

15 September 2026

Paw Patrol – who is the star?

= Chase

x+1

0 = (x+6)(x-3)

x = -6, +3

x = 3

100

x + 1

1

2x-1

F

Width = 4cm

34

1.3 - Graphs

1. What is the overall trend?
2. How often does the Seasonal trend happen?
3. What is the peak in 2005?
4. Predict July 08
5. If this is a graph of heater sales in NZ, why the big dips?

​

​

1. Solve: x + 3 = 2
2. Expand: (x + 3)(x – 2)��
3. Factorise: 3x – 9�
4. Use trig to find x���
5. Find H(Pythag)�

​

​

​

3m

20°

H

3m

5m

x

= Increasing (Positive)

= Annually

= ~47

= ~62

= No one buys heaters in summer

x = -1

= x² -2x + 3x – 6

x² + x - 6

= 3(x – 3)

1.4 - Algebra

Find x

15 September 2026

35

Ideas

• Phone time and sleep
• School attendance and job income
• https://shinycharts.substack.com/p/paw-patrol-the-definitive-guide?utm_source=substack&utm_content=feed%3Arecommended%3Acopy_link

​

4-Sept-25

36