10PQ
Practice Questions �1.3 and 1.2/1.4
Icons from TheNounProject.com�garethbell.com
y = x2
28 July 2026
1
1.4 Easy Revision
2
2
2
1.2/1.4 Easy Revision - A
28/07/2026
�
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
5m
3m
4cm
2cm
40°
J
6.28
0.25
= 3 +4 +5�= 12cm
= 2×4�= 8cm2
=180 -40 -90�= 50°
4m
�
8cm
6cm
H
2x2 +5x
x(2x + 1)
x = 3, -4
28/07/2026
x2 + 4x – 3x - 12
x2 + x – 12
4
4
1.2/1.4 Easy Revision - C
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°
28/07/2026
5
5
1.2/1.4 Easy Revision - D
5m
3m
2cm
2cm
12345
= 27
= 12m
=2×2×2�= 8cm3
=360 - 40 - 90�= 230°
4m
�
1m
1m
H
=2x2 + 2x
=7(2x2 + 1)
= x2 - 3x - 4x +12
= x2 - 7x + 12
(x + 2)(x + 5)
2cm
40°
J
28/07/2026
6
6
1.2/1.4 Easy Revision - E
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°
28/07/2026
7
7
1.2/1.4 Easy Revision - F
5m
2m
3cm
2cm
3.5
= 64
=2m2 + 4m2�= 6m2
=2×3×3�= 18cm3
=360 - 222 - 90�= 48°
5m
�
1m
10m
H
=2x2 - 2x
=5(x2 + 2)
= x2 + 3x - 1x - 3
= x2 +2x -3
(x + 3)(x + 4)
3cm
J°
222°
1m
28/07/2026
8
8
1.3 and 1.2/1.4 Easy Revision
9
9
9
1.3 - Graphs
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)
sin θ = O/H
H = 3 ÷ sin 20°
H = 8.8m
32 + 52 = H2
34 = H2
H= √34
H= 5.8m
1.4 - Algebra
Find x
28 July 2026
10
1.3 - Graphs
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
28 July 2026
A
11
1.3 - Graphs
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
H2 = (x+6)2 + (x + 2)2
H2 = (x2 + 12x + 36) + (x2 + 4x + 4)
H = √(2x2 + 16x + 40) - as far as we can go
28 July 2026
B
12
1.3 - Graphs
CQ) Find X?
1.4 - Algebra
x2 - 1
2x
= $10
= Coco
= 10%
= 2/3 do.
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
28 July 2026
Dollars per week
4x - 2
30°
5cm
X
C
13
1.3 - Graphs
CQ) Find area of the flag?
1.4 - Algebra
= 4
= 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
= 30°
Cos θ = A/H
H × Cos θ = A
= 1.732m
= x2 + 8x + 7
B = √(22 – 1.7322)
B = √(4 – 3)
B = 1
28 July 2026
Average Daily Sales
= Increasing
Have ya seen my ex?
30°
x
x
2m
A
B
Area = 2A × 2B
Area = 3.464 × 2
Area = 6.93m2
D
14
1.3 - Graphs
CQ) What is the yellow angle?
1.4 - Algebra
= 11 hours
= 1 hour
= Youtube
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)
28 July 2026
My Weekly Phone Hours
= 36 hours
What’s x?
6m
8m
H
θ
E
15
1.3 - Graphs
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
28 July 2026
Sugar and Fat per 100g
= Milk choc
A Chocolate BARRRGH!
x-1
x + 3
| Marsh�mallow | Milk Choc | Choc chip cookie | Choc Fish |
Sugar | 58 | 52 | 32 | 63 |
Fat | 0 | 33 | 25 | 10 |
0 = (x + 5)(x – 3)
x = -5, 3
Width = 2cm
F
16
1.3 - Graphs
b
25°
4m
C
CQ) Area of triangle sail?
1.4 - Algebra
= 4/24 or 1/6
= 3 hours
Disagree because
Agree because
4 × 50 = 200km
5x = 15�x = 3
= 25° (alt angles on parallel lines)
= (x – 3) (x + 2)
Height = (cos 25) × 4
Height = 3.625m �
28 July 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
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
H2 = (x + 5)2 + (x + 2)2
H2 = (x2 + 10x + 25) + (x2 + 4x + 4)
H = √(2x2 + 14x + 29) - as far as we can go
28 July 2026
NZ Vaping Rate
B
18
1.3 - Graphs
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
28 July 2026
2x - 1
C
19
1.3 - Graphs
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°
Cos θ = A/H
H = 2 / Sin 23
= 2.17m
= 2x2 -9x + 9
Opp = 2×tan(23)
Opp = 0.849m
28 July 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
CQ) If the triangle above is a cone, Volume =
1.4 - Algebra
= 15m
= Falkor
= 11m (10-12)
Agree because:
28 ÷ 7 = 4
x2 = 27 ÷ 3
x = 3 (or -3)
tan θ = O/A
θ = tan-1 (3/4)
θ = 36.9°
=(x - 15)(x - 1)
V = 1/3πr2h
1/3 π × 32 × 4 = 37.7cm3
28 July 2026
Dragon Lengths (m)
= Smaug
4cm
6cm
H
θ
E
21
1.3 - Graphs
CQ) If the area is 10cm2, how wide?
1.4 - Algebra
= Skye
= 13.1 min
= 80%
Agree because
= 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
28 July 2026
Paw Patrol – who is the star?
= Chase
x+1
| Chase | Rubble | Marshall | Skye |
Movie Screen Time | 6.6 | 11.1 | 6.5 | 25.9 |
TV Series �‘Called on’ | 23% | 14% | 16% | 20% |
0 = (x+6)(x-3)
x = -6, +3
x = 3cm
100
x + 1
1
2x-1
F
22
1.3 - Graphs
CQ) Area of triangle sail?
60°
4m
b
B
1.4 - Algebra
= 16%
= Doctor
Similarities:
* Musician about 14-15% for both. * Doctor is 1st or 2nd.
Differences:
*Athlete is 1st for boys, and 4th 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 �
28 July 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
CQ) x = 7m. What is H?
x - 2
1.4 - Algebra
x + 5
= 45min
= 21
= ~15
=-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
28 July 2026
Exam Score
What grade do Pirates get?
“High Cs”
B
24
1.3 - Graphs
CQ) Perimeter was 30cm. �How long was x?
1.4 - Algebra
3x
x + 1
= 125
= ~ 60
= 100/125
= Caribbean
There were:
* 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
28 July 2026
x2 - 3
Active Pirate Ships
C
25
1.3 - Graphs
CQ) Find area of �Trapezium:
1.4 - Algebra
= ~45
= ~22
I disagree because
=(-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
28 July 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
CQ) Why this �order?
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:
17 × 2.5 = 42.5
x2 = -32 ÷ -2
x = 4 (or -4)
sin θ = O/h
θ = sin-1 (1/2)
θ = 30
=(x - 17)(x + 1)
1.93 – 1.73 = 0.20m
28 July 2026
Population (Millions)
= Oman
1m
2m
θ
= A to Z
A
E
27
1.3 - Graphs
CQ) If the ball travels �in a straight line, goes �through the middle �at a height of 4m, �What distance?
5.6m
1.4 - Algebra
22m
= 1.76m
= ~144kg
= ~110kg
=-6 (-1)
= -6
x2 – 6 + x = x2 + 2x
x2 - x2 - 6 = 2x – x
-6 = x
= 2x(2x – 3)
θ = tan-1 (O/A)�= 14.3°
Height (m)
= x2 - x - 6
a2 + b2 = c2
222 + 2.82 = 22.182
Ground = 22.18, Height = 4
Hypotenuse = 22.54m
28 July 2026
Weight (Kg)
θ
F
28
Ideas
4-Sept-25
29