📚 Subject: Mathematics⏱️ Duration: 2 Hours🏆 Total: 100 Marks
📝 Student Information
⚠️ Please enter your Full Name and School before submitting.
SECTION A — Questions 1–24 (2 marks each = 48 marks)
Choose the ONE correct answer for each question.
1
Calculate: 2,045 + 1,055 + 900
2 pts
2
Write in words: 3,005
2 pts
3
Add: 200 g + 0.04 kg = _____ dag (1 dag = 10 g; 1 kg = 1000 g)
2 pts
4
Two lines intersect. One angle is 110° and another marked angle is 30°. Find the size of angle a. (Angles on a straight line = 180°; vertically opposite angles are equal.)
2 pts
5
Calculate: 0.84 × 25
2 pts
6
Simplify completely: (3/7) ÷ (9/14)
2 pts
7
Find the value of m in the equation: 3m − 4 = 5
2 pts
8
Write the next TWO numbers in the sequence: 1, 4, 9, ___, ___ (Square numbers: 1², 2², 3², …)
2 pts
9
Divide 10,000 Rwf in the ratio 3 : 7. What are the two shares?
2 pts
10
Decrease 200 kg by 20%.
2 pts
11
The perimeter of a rectangle is 40 cm. One side is 12 cm. Find x (the other side length).
2 pts
12
The cost of 2 kg of beans is 620 Rwf. Find the cost of 8 kg of beans.
2 pts
13
A number is increased by 20%. The new number is 2,400. Find the original number.
2 pts
14
Complete the table below. The rule is: Bottom = (Top × 2) + 1. Find the two missing values marked ?
A cube has sides of 5 cm and a mass of 200 g. Find its density. (Density = Mass ÷ Volume; Volume = side³)
2 pts
16
Find the Highest Common Factor (HCF) of 12, 15 and 21.
2 pts
✏️ Q17 — Protractor question (teacher-assessed): Measure angles x and t from the printed triangle using a protractor. Typical values: x ≈ 30°, t ≈ 60°. This question is marked by your teacher and is not included in the auto-score.
18
A man buys a car at 3,000,000 Rwf and sells it at 3,900,000 Rwf. What is the percentage profit?
2 pts
19
Simplify completely: 1¼ × 1¹⁄₁₅
2 pts
20
Find the circumference of a circle with radius 5 cm. (Use π = 3.14)
2 pts
21
If a = −1, b = 2 and c = −3, find the value of: ab + 2ac
2 pts
22
How many lines of symmetry does a square have?
2 pts
23
Calculate: 2 h 12 min − 1 h 50 min
2 pts
24
How many 500 ml bottles can be filled from 2 litres of water?
2 pts
SECTION B — Structured Questions (3–7 marks each)
Show all working where required.
25
Poles are fixed at intervals of 50 m along a road of 4,550 m. How many poles are fixed? (Include the pole at the start.)
3 pts
26
Three consecutive odd numbers add up to 39. What are the three numbers? (Let the numbers be n, n+2, n+4)
3 pts
27
Calculate and express the answer in base ten: 111₂ + 102₃
Six men complete a piece of work in 4 days. How many days will 8 men take to complete the same work? (Inverse proportion)
3 pts
29
Arrange the following fractions in ascending order (smallest to largest): 3/7, 5/14, 13/28
3 pts
🔣 Q30 Venn Diagram: Set E = {2, 3, 4, 6, 7} and Set F = {1, 3, 5, 7, 8}
30a
Which numbers are in Set E ONLY (not in F)? — select all that apply
2 pts
30b
Which numbers are in BOTH Set E and Set F (the intersection)? — select all that apply
2 pts
30c
Which numbers are in Set F ONLY (not in E)? — select all that apply
2 pts
31a
Solve: (2x/4) − (x+1)/3 = 2 Find x.
4 pts
31b
The three angles of a triangle are: (x + 40°), x°, and (x − 10°). Find x and state all three angles. (Sum of angles in a triangle = 180°)
3 pts
SECTION C — Longer Structured Questions (Show full working)
32a
Simple interest of 20,000 Rwf was made for 2 years at 10% per year. Find the capital (principal). (SI = PRT/100)
3 pts
32b
8 kg of beans costing 250 Rwf/kg are mixed with 12 kg of another type. The mixture costs 280 Rwf/kg. Find the cost per kg of the second type.
4 pts
🚗 Q33: Town A & B are 300 km apart. Car leaves A at 8:00 am at 90 km/h. Bus leaves B at 8:00 am at 60 km/h.
33a
At what distance from town A will the car meet the bus? (Combined speed = 90 + 60 = 150 km/h; time = 300÷150 = 2 h; distance from A = 90×2)
3 pts
33b
At what time do the two vehicles meet?
2 pts
📈 Q34 — Graph question (partly teacher-assessed): Plot points (0,0), (1,2) and (3,6) on graph paper. The graph is a straight line through the origin with gradient 2 (y = 2x). Q34c is auto-graded below.
34c
The point (x, 3) lies on the line y = 2x. Find the value of x.
2 pts
📊 Q35 Statistics: Ages of 10 people: 35,33,36,42,33,35,40,33,40,33 | Total f=10, Total fx=360
35a
What is the modal age (most frequent)?
2 pts
35b
Calculate the mean age. (Mean = Total fx ÷ Total f = 360 ÷ 10)
2 pts
35c
What is the range of the ages? (Range = highest − lowest = 42 − 33)
2 pts
📋 Your Results
—
'; if(!correct) bd+='
Your answer: '+(got||'(not answered)')+' | Correct: '+DISP[qid]+'
'; bd+=''; }); var pct=Math.round(scored/total*100); var g,gc; if(pct>=80){g='A — Excellent';gc='gA';} else if(pct>=65){g='B — Good';gc='gB';} else if(pct>=50){g='C — Satisfactory';gc='gC';} else if(pct>=40){g='D — Pass';gc='gD';} else{g='F — Below Pass';gc='gF';} var dist=document.getElementById('s-dist').value.trim(); document.getElementById('rn').textContent=nm+(sc?' — '+sc:'')+(dist?', '+dist:''); document.getElementById('rsc').textContent=scored+' / '+total; document.getElementById('rpt').textContent=pct+'% correct'; var gt=document.getElementById('rgr'); gt.textContent=g; gt.className='gtt '+gc; document.getElementById('rbk').innerHTML=bd; var r=document.getElementById('res'); r.style.display='block'; r.scrollIntoView({behavior:'smooth',block:'start'}); }; window.q13retry=function(){ document.querySelectorAll('#q13 input[type=radio]').forEach(function(r){r.checked=false;}); document.querySelectorAll('#q13 input[type=checkbox]').forEach(function(c){c.checked=false;}); document.getElementById('res').style.display='none'; document.getElementById('q13').scrollIntoView({behavior:'smooth',block:'start'}); }; window.q13copy=function(){ var el=document.getElementById('q13'); var st=el.previousElementSibling; var full=(st&&st.tagName==='STYLE'?st.outerHTML+'\n':'')+el.outerHTML; if(navigator.clipboard&&navigator.clipboard.writeText){ navigator.clipboard.writeText(full).then(function(){ var ok=document.getElementById('cok13'); ok.style.display='inline'; setTimeout(function(){ok.style.display='none';},3000); }); } else { var ta=document.createElement('textarea');ta.value=full;ta.style.cssText='position:fixed;opacity:0'; document.body.appendChild(ta);ta.select();document.execCommand('copy');document.body.removeChild(ta); var ok=document.getElementById('cok13'); ok.style.display='inline'; setTimeout(function(){ok.style.display='none';},3000); } }; })();