Aitchison College Senior School
Diagnostic Test 2025
Aitchison College Lahore
Senior School
Diagnostic Test 2025
Candidate Name: __________________________ School No: ____________ Section: _____
Date: ___________
Subject: IGCSE Mathematics 0580
Paper: Diagnostic
Time: 50 mins
Marks: 35
Candidates answer on the Question Paper.
WITHOUT CALCULATOR
READ THESE INSTRUCTIONS FIRST
Write your school name and number on all the work you hand in.
Write in dark blue or black pen.
You may use an HB pencil for any diagrams or graphs.
Do not use staples, paper clips, glue or correction fluid.
This test consists of TWO sections: Section I comprises 18 MCQs, and Section II comprises
structured questions.
Answer ALL the questions.
If working is needed for any question in Section 2, it must be shown below that question.
Electronic calculators are NOT allowed.
If the degree of accuracy is not specified in the question, and if the answer is not exact, give the
answer to three significant figures. Give answers in degrees to one decimal place.
For 𝝅, use either your calculator value or 3.142.
At the end of the examination, fasten all your work securely together.
Section
1
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Marks
Section
2
1
2
3
TOTAL
Checker Initials
Marks
This Examination paper consists of 7 pages including 1 blank page and the front page
This paper is approved by HoD of Mathematics.
Page 1 of 7
Aitchison College Senior School
Diagnostic Test 2025
SECTION 1
Attempt ALL the MCQs; each carries 1 mark.
1. The ratio 8:3 can be written in the form of 1:n as
☐ 1 : 2.67
☐ 0.375 : 1
☐ 2.67 : 1
☐ 1 : 0.375
2. Decide whether the statement 82% > 0.8𝟐𝟑̇
☐ True
☐ False
3. 657892 = _______________ to two significant figures
☐ 657992
☐ 657890
☐ 660000
☐ 658000
4. Simplify √𝟕𝟓 + √𝟏𝟐
☐ √87
☐ 5√3 + 2√3
☐ 7√3
☐ 3√7
5. A car is sold for $2280, at a loss of 5% on the cost price. Find the cost price.
☐ $3400
☐ $2400
☐ 2800
☐ $3000
6. The longest side of a right-angled triangle is 10m and one of the shorter sides is 6m. The length of
the other side is
☐ 4m
☐ 16 m
☐ 136 m
☐ 8m
7. The factorized form of 𝒙𝟐 − 𝟏𝟔 is
☐ (x + 4) (x – 4)
☐ (x + 8) (x - 2)
☐ (x – 2) (x + 8)
☐ (x – 4) (x – 4)
☐ (16y+3) (4y+1)
☐ (16y-3) (4y-1)
8. The factorized form of 𝟔𝟒𝒚𝟐 + 𝟒𝒚 − 𝟑 is
☐ (16y-3) (4y+1)
9.
☐ (16y+3) (4y-1)
A movie starts at 10:30 AM and lasts for 2 hours and 45 minutes. What time does the movie end?
☐ 12:45 PM
☐ 1:15 PM
☐ 1:30 PM
☐ 1:45 PM
(−𝟐𝒙)𝟑
10. −𝟐𝒙𝟐 = _______
☐ 4x
☐ x
☐ -x
☐ - 4x
11. A diver is below the surface of the water at -15m. She dives down by 6m, then rises 4m. At what
depth is she now?
☐ - 9m
☐ 9m
☐ -17m
☐ -5m
12. ( 5.2 × 𝟏𝟎−𝟐 ) − ( 𝟐 × 𝟏𝟎−𝟒 ) = ______________________
☐ 5.18 × 10−2
☐ 3.2 × 10−6
☐ 5 × 102
☐ 5.18 × 10−6
13. The simplified form of 𝟓𝒙 − 𝟕𝒙𝟐 − (𝟐𝒙)𝟐 is
☐ 5𝑥 − 5𝑥 2
☐ 5𝑥 − 3𝑥 2
☐ 5𝑥 − 11𝑥 2
Page 2 of 7
☐ 5𝑥 + 11𝑥 2
Aitchison College Senior School
Diagnostic Test 2025
𝟓
14. If 𝟖 of the children in a school are boys, what is the ratio of boys to girls.
☐3:5
☐ 5:3
☐3:8
☐ 5:8
15. The cost of 1km of pipe at 7 cents for every 40 cm.
☐ 170 cents
☐ 172 cents
☐ 174 cents
☒ 175 cents
16. An increase of 30% followed by another increase of 30% is equivalent to a single increase of how
many percent?
☐ 69%
☐ 60%
☐ 169%
☐ 75%
17. The speed of 54 km/h into meter per second is
☐ 90 m/s
☐ 1500 m/s
☐ 15 m/s
☐ 1.5m/s
𝟏
18. Rearrange the formula to make h the subject of the formula 𝑨 = 𝟐 (𝒂 + 𝒃 )𝒉
2𝐴
☐ ℎ = 𝑎+𝑏
☐ ℎ=1
2
☐ ℎ=
𝐴
(𝑎+𝑏)
𝐴(𝑎+𝑏)
2
𝐴
☐ ℎ = 2(𝑎+𝑏)
Page 3 of 7
Aitchison College Senior School
Diagnostic Test 2025
SECTION II
Q1: (a) Simplify
𝟑+ √𝟔
√𝟑
[3]
(b) Express 3.6 kg as a percentage of 9 kg.
[3]
Page 4 of 7
Aitchison College Senior School
Diagnostic Test 2025
Q2: (a) Find a formula for the nth term of the sequence 3, 8, 15, 24, 35, ...
[3]
(b) Solve
𝒙−𝟏
𝟒
−
𝟐𝒙−𝟑
𝟓
𝟏
= 𝟐𝟎
[4]
Page 5 of 7
Aitchison College Senior School
Diagnostic Test 2025
Q3: (a) Solve the simultaneous Equations
𝒚=𝒙+𝟏
𝒚 = 𝒙𝟐 + 𝟑𝒙 − 𝟐
[4]
Page 6 of 7
Aitchison College Senior School
Diagnostic Test 2025
Blank Page
Page 7 of 7