S.1 – S.
2 END OF YEAR ASSESSEMENT 2025
Theme: PATERNS AND ALGEBRA (GROUP.2)
Time: 30 minutes
Item 1
ASHIM foundation organizes charity fun runs every year. It is observed that the
number of runners increases each day by 5 runners and only 20 runners registered
on the first day. The foundation intends to save at least Ugsh.1.5millions after the
run. It incur certain expenses per day to organize the run, and each runner is to
contribute Ugshs.20, 000.
The foundation planning committee wants to predict the number of participants will
be registered on 30th days and how much should be spent per day in order to meet
the target.
The runners are to go from the start line at (0, 0) to checkpoint A at (3, 4) and from
checkpoint A to finish line at (7, 7), but they are not informed about the displacement
from the checkpoint A to finish line.
The committee is to design a rectangular gold medal for fast runner measuring an
area of 48cm2, whose longest side being 2cm longer than its width.
Task:
You have been selected as the chairperson ASHIM organizing committee;
(a) Determine;
(i) The number of participants will be registered on the 30th day.
(ii) How much to be spent per day.
(b) Determine the displacement from the checkpoint A to finish line.
(c) Calculate the length and width of the rectangular gold medal
BASE OF RESPONSES SCORES
ASSESSMENT
(a)(i) Let the Nth- term in the sequence be Un ,
n- be the number of days, and F=1
Learner’s ability to; d- be the common difference.
No. of 1 2 3 4 n
Identify the pattern. ie, days
the number of runners F= 1
increases by 5 each day. No. of 20 25 30 35 Un
Describe a general rule runner
in the sequence. Nth- 20+5 20+5+5 20+5+5+5
Determine 30th terms in rule 20+5(n-1) M2 = 1
a sequence. Ie, the 20+5×1 20+5×2 20+5×3
number of participants
registered on the 30th The rule general rule for the Nth- term is
day.
Un = 20+5(n-1) F= 1
Use letters to represent
When n = 30,
numbers.
U30 = 20 + 5(30 - 1)
Write statements in M2 = 1
= 20 + 5×29 M2 = 1
algebraic form.
= 165
Evaluate algebraic
expressions by AP2 = 1
There will be 165 participants registered on the 30th day.
substituting numerical
values
(a)(ii) Calculating the total contribution.
Total contribution = No. of participants × Contribution per
Learner’s ability to; participant M2 =1
Identify and use = 165×20000 = 3,300,000 Ugshs. M2 =1
inequality symbols. This is the total from all 30 days.
Solve linear
Determine the target savings.
inequalities in one The target is at least 1,500,000 Ugshs.
unknown.
Let the maximum allowable expenditure be x F= 1
3,300,000 − 𝑥 ≥ 1,500,000 F= 1
𝑥 ≤ 3,300,000 − 1,500,000
𝑥 ≤ 1,800,000 𝑈𝑔𝑠ℎ𝑠. M2 =1
This is the maximum that can be spent over all 30 days.
maximum expenditure per day is;
1,800,000 M2 =1
= 60,000 𝑈𝑔𝑠ℎ𝑠.
30
The foundation therefore should spend no more than AP2 = 1
60,000 Ugshs per day to meet its target.
Determining the displacement from checkpoint A to the
finish line. M2 =1
(b) For
Y-axis
B, Finish line
correct
7
Learner’s ability to;
x-
6
y=3
direction
Define translation
5
A Checkpoint A is at (3, 4)
2 3 4
with a vector. X=4 finish line is at (7, 7) M2 =1
Use vector notation. For
represent vectors correct
1
both single and Start line y-
0 0 1 2 3 4 5 6 7 X-axis direction
combined
geometrically 4
Displacement 𝐴𝐵 = ( ) F= 1
3 Forms a
displace
ment AB
Therefore the displacement from checkpoint A to the
𝟒 AP2 = 1
finish line is ( )
𝟑
(c) Let the width be 'w' cm and F= 1
The length be 'l' cm.
Learner’s ability to;
A= 48cm2 w M2 =1
l = w+2 substitut
es in
𝑙 × 𝑤 = 𝐴 formula
(𝑤 + 2)𝑤 = 48.
This simplifies to; 𝑤² + 4𝑤 − 48 = 0. F= 1
(𝑤 + 8)(𝑤 − 6) = 0. M2 =1 forms a
quadratic
eqtn
Either 𝑤 = −8 or 𝑤 = 6 M2 =1
The required width, w = 6.
The length, 𝑙 = 𝑤 + 2 = 6 + 2 = 8. M2 =1
The width of the rectangular gold medal is 6cm and the AP2 = 1
length is 8cm
TOTAL SCORES 25 scores
