Primary Leaving National Examination — October 2010
📚 Subject: Mathematics⏱️ Time: 2 Hours🏆 Total Marks: 100
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SECTION A — Answer ALL Questions (65 Marks)
Each question in Section A carries 2 or 3 marks as indicated. Choose ONE answer per question unless stated otherwise.
1
Calculate: 55 × 112 − 12 × 55
2 pts
2
What is the place value of 4 in 85,421?
2 pts
3
Arrange the following numbers from the smallest to the largest: 0, −1, −8, 11, 17
2 pts
4
Calculate 0.031 × 1.1 giving the answer corrected to 2 decimal places.
2 pts
5
Complete: 0.4 litre = __________ cm³
2 pts
6
Write the next two numbers in the sequence: 2, 8, 14, _____, _____
2 pts
7
A car uses 4 litres of petrol to travel 60 km. How many km will it travel if it uses 16 litres?
2 pts
8
Find the Lowest Common Multiple (LCM) of 15, 24 and 40.
2 pts
9
Express 48 as a product of its prime factors.
2 pts
10
Solve the equation: 4(x + 1) = 2x + 7
2 pts
11
Increase 240 kg by 9%.
2 pts
12
Find the perimeter of a square whose area is 625 cm².
2 pts
13a
Complete the table (pattern: bottom = top × 2 + 1). What is the value of x (missing top row number)?
Top
4
6
7
x
Bottom
9
13
15
25
1 pt
13b
Using the same table, what is the value of y (missing bottom row number when top = 7)?
Top
4
6
7
x
Bottom
9
13
y
25
1 pt
14
In a sale, goods are sold for ¾ of the usual price. What is the sale price for shorts whose usual price is 2,000 frw?
2 pts
15
Simplify: 4x⁴y³ × 2x²y²
2 pts
16
To make one cake you use 1.25 kg of flour. How many kg of flour will be used to make 6 cakes?
2 pts
17
Find the circumference of a circle with diameter 30 cm (π = 3.14).
2 pts
18
Decrease 150 m in the ratio 3 : 25.
2 pts
19
Ten men can dig a garden in 4 days. How many days would it take eight men to dig the same garden?
2 pts
20
The angles of a triangle are 80°, 30° and x°. Find the value of x°.
2 pts
21
1,200,000 frw is banked at 8% per year simple interest. Find the interest after 3 years.
2 pts
22
Write 45 in Roman numerals.
2 pts
23
Calculate the area of the rectangle with length 13 cm and width 6 cm.
2 pts
24
Calculate: 45 kg + 65 g + 1000 mg = __________ g
2 pts
25
The base area of a cube is 64 cm². Calculate the volume of that cube.
2 pts
26
If the cost price of a goat is 5,000 frw and the selling price is 6,000 frw, what is the percentage profit?
2 pts
27
If the average of 12, X and 8 is 9, what is the value of X?
2 pts
28
A car travels 45 km in 50 minutes. How many km does it travel in 2 hours?
3 pts
29
Simplify: (√64 − √25) ÷ √9
2 pts
📊 Questions 30a & 30b use this data: Ages of 10 pupils: 11, 12, 12, 13, 11, 14, 15, 11, 12, 11
30a
Find the MODE age.
1 pt
30b
Find the MEAN (average) age.
2 pts
SECTION B — Answer FIVE Questions Only (35 Marks)
Each question carries 7 marks. Sub-questions are shown with their mark breakdown.
🏦 Question 31: A trader banks 1,000,000 frw at compound interest of 6% per year for 3 years.
31a
What is the interest at the END of Year 1?
1 pt
31b
What is the TOTAL AMOUNT at the end of Year 1?
1 pt
31c
What is the interest at the END of Year 2?
1 pt
31d
What is the TOTAL AMOUNT at the end of Year 2?
1 pt
31e
What is the FINAL TOTAL AMOUNT after 3 years?
3 pts
📐 Question 32: Right-angled triangle — Hypotenuse = 10 cm, Base = 6 cm. Find its area.
32a
Using Pythagoras theorem, what is the HEIGHT of the triangle? (Hypotenuse = 10, Base = 6)
2 pts
32b
What is the AREA of the right-angled triangle?
2 pts
📦 Question 33: Triangular prism — triangular base with sides 4 cm and 3 cm. Volume = 48 cm³.
33a
Find the LENGTH (height of the prism) if the volume is 48 cm³.
3 pts
33b
What is the hypotenuse (slant side) of the triangular base? (Base = 4, Height = 3)
1 pt
33c
Calculate the TOTAL SURFACE AREA of the prism (L = 8, base sides: 4, 3, hypotenuse = 5).
3 pts
⚖️ Question 34: Proportion Problems
34a
20 kg of a beans-maize mixture contains 8 kg of beans. How many kg of maize will be found in 35 kg of the mixture?
3 pts
34b
50 children have enough food for 18 days. How long would this food last if the number of children was 30?
3 pts
🔢 Question 35: Algebra Problems
35a
Solve: 2(2x − 1)/3 = 3(x + 3)/2
4 pts
35b
If m = −2, n = 3 and p = 5, find the value of: 2m² − 3n + 2p
3 pts
📏 Question 36: Triangle Construction (Teacher Assessed — 7 marks)
36
For the triangle ABC (AB = 6.2 cm, BC = 5.0 cm, ∠ABC = 60°), which statement about angles is CORRECT?
2 pts
✏️ Note: The full construction question (draw triangle ABC using ruler & compasses only, then measure ∠BCA, ∠BAC and length AC) must be done on paper and assessed by a teacher. This multiple-choice sub-question tests the related theory.