🇷🇼 Rwanda National Examinations Council
P6 MATHEMATICS TEST 2012
Revision of Extracted Questions — Primary Leaving Examination 2012
📝 Student Information
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SECTION A — Short Answer Questions (Each question: 2 marks)
Choose the ONE best answer for each question.
1
Find the next two numbers in the sequence: 4, 7, 10, ___, ___
2 pts
2
Calculate: 340 × 4 ÷ 170 × 4
2 pts
3
Find the area of a square whose perimeter is 20 cm.
2 pts
4
Simplify: ¹⁄₃ + ¹⁄₄ + ⁵⁄₁₂
2 pts
5
Share 7,000 frw between two students in the ratio 2 : 5. What does each student receive?
2 pts
6
Express 140 as a product of its prime factors.
2 pts
7
Arrange the following fractions in ascending order: ²⁄₅, ¹⁄₃, ³⁄₇
2 pts
8
Calculate the area of a parallelogram with length 10 cm and height 4 cm.
2 pts
9
The price of petrol was increased by 2% per litre. Find the new price if the old price was 990 frw per litre.
2 pts
10
Solve the equation: 2x + 4 = 8 – 2x
2 pts
11
The perimeter of a rectangle is 36 cm. Find its area if its width is 6 cm.
2 pts
12
Add and give the answer in base two: 1011₂ + 5₁₀
2 pts
🔣 Q13 Set Theory: A = {2, 3, 5, 7, 11} and B = {10, 5, 2, 4}
13a
Find A ∪ B (all elements in A or B)
2 pts
13b
Find A ∩ B (elements common to both A and B)
2 pts
14
Three angles at a point are 3x°, 2x° and 4x°. Find the value of x. (Angles at a point sum to 360°)
2 pts
15
Find the area of a semi-circle whose diameter is 0.14 dm. (π = 22/7)
2 pts
16
A taxi starts from Kigali at 8:05 am and travels at 60 km/hr until 9:00 am. What distance has the taxi travelled?
2 pts
17
Two lines cross. One angle is 150°. Find angles m and n. (Use vertically opposite and supplementary angle rules.)
2 pts
18a
Write a pair of complementary angles. (Two angles that add up to 90°)
2 pts
18b
Write a pair of supplementary angles. (Two angles that add up to 180°)
2 pts
19
There is enough food for 3 people for 12 days. How many days would this food last if there were 9 people?
2 pts
20
The base of a right-angled triangle is 8 cm and the hypotenuse is 10 cm. Find the height of the triangle. (Use Pythagoras: h² = hyp² − base²)
2 pts
21
A triangle has an interior angle of 50° and an exterior angle of 140° at another vertex. Find the third interior angle x. (Exterior angle = sum of two non-adjacent interior angles: 140° = 50° + x)
2 pts
22
To draw an angle of 60° at point A on a line using only a ruler and compasses, which step comes FIRST?
2 pts
SECTION B — Structured Questions (2–3 marks each)
Show all working where necessary.
23
A shirt was sold at 20% loss for 8,000 frw. What was the original cost price?
2 pts
24a
How many lines of symmetry does a RHOMBUS have?
2 pts
24b
How many lines of symmetry does an ISOSCELES TRIANGLE have?
2 pts
25
The cost of a book is 5,000 frw. How many books can be bought with 24,000 frw?
2 pts
26
Given that x = −2 and y = 3, find the value of: 2x² + xy − x
2 pts
27
The perimeter of the base of a cylinder is 31.4 cm. Find the volume if the height is 10 cm. (π = 3.14 — use circumference = 2πr to find r first)
2 pts
28
An interior angle of a regular polygon is 150°. How many sides does the polygon have? (Each exterior angle = 180° − 150° = 30°; no. of sides = 360° ÷ 30°)
2 pts
29
A man spent ¹⁄₈ of his salary on fees and ²⁄₅ on a car loan. He has 380,000 frw remaining. What is his salary?
2 pts
30
A pie chart represents goats, cows and pigs. The angle for pigs is 45°. There are 40 pigs and 120 cows. How many goats are there?
2 pts
💡 Hint: 40 pigs = 45°, so 1° = 40/45 animals. Cows = 120 → angle = 120÷(40/45) = 135°. Goats angle = 360−45−135 = 180°. Goats = 180 × (40/45) = 160.
SECTION C — Long Answer Questions (More marks — show ALL working)
🚗 Q31: Kigali → Rwamagana = 50 km. Car from Kigali at 45 km/hr, Taxi from Rwamagana at 30 km/hr. Both leave at 7:30 am.
31a
Find the distance from Kigali where the two vehicles meet.
3 pts
31b
At what time do the two vehicles meet?
2 pts
🧮 Q32: Quick / Mental Method Calculations
32a
Calculate using a quick method: 642 × 50
2 pts
32b
Calculate using a quick method: 2,224 × 49
2 pts
32c
Calculate using a quick method: 16,999 × 99
2 pts
32d
Calculate using a quick method: 4,444 × 25
2 pts
📊 Q33 Statistics: Football match results — Goals scored: 0,1,2,3,4 | Matches played: 3,2,2,3,0
33a
What is the Total Frequency (Tf)? — sum of all matches played
2 pts
33b
What is the Total fx (Σfx)? — sum of (goals × matches) for each row
2 pts
33c
What is the mean number of goals per match? (Mean = Σfx ÷ Tf)
2 pts
34
90,000 frw is kept at 10% p.a. compound interest. Find the total amount after 3 years.
3 pts
35
Two types of beans are mixed: Type A — 300 kg at 300 frw/kg; Type B — x kg at 400 frw/kg. The mixture costs 340 frw/kg. Find the value of x.
3 pts
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