Algebra Presentation on Topic Modulus Function and Polynomials Created by: Aisha S. F. & Shearen S. S. Performance Task Binus School Bekasi

1. Solving Questions
on Modulus &
Polynomial
Functions
A i s h a S . F . & S h e a r e n S . S .

2. Question 1:
Modulus
Function
A girl plans to apply for a scholarship at a prestigious
Australian university. The criteria is that all candidates must
have a minimum grade average of 90 on a 100-point scale.
This girl already has a mean score of 89.5 from her past 9
assessments. However, she needs to do one more test to
complete her school report card. The final average will then
be used for her scholarship application.
i. Use the range of acceptable average grade values to
___obtain a modulus expression in the form of | x - a | ≤ b!
ii. Determine the lowest score the girl needs to obtain on
___her last assessment in order to be eligible for the
___scholarship!

3. Solution 1.1The required mean grade should be 90 or
above while the maximum possible value
is 100. We can express this as a range.
Compare the resulting range with the
range from the problem. We now know
that -b + a = 90 and b + a = 100. Subtract one equation from the other to
get the value of b. Then substitute it into
one of the equations to get the value of a.
Inserting these two numbers
into the | x - a | ≤ b form, we
obtain a final expression of
Next, rearrange the basic
inequality by applying one
of the modulus rules.
| x - 95 | ≤ 5

4. Solution 1.2
Find out the sum score of
the girl's previous tests from
her current average.
The girl requires a final average of
at least 90 to qualify for the
scholarship. Express this as an
inequality and utilise it to
determine the minimum score she
needs to earn to be able to apply.
Therefore we know that the
To calculate the new mean, the
girl's score on the last assessment,
x, is added to her total score, and
the result is divided by the number
of completed assessments.
lowest score = 94.5

5. Question 2:
Polynomial
Function
Two polynomials were denoted as f(x) and
g(x). When f(x) - g(x) is divided by x² + x - 2,
the remainder is x. It is also given that
when f(x) + g(x) is divided by x² - 3x + 2, the
remainder is x + 1. Find the remainder when
(f(x))² + (g(x))² is divided by x - 1!

6. Solution 2.0
Identify the given information.
Solve for the x of every factor.
According to the Factor Theorem, we can find
the remainder of a polynomial by inputting the
value of x into the function. From this we obtain
an equation from each given information.

7. Solution 2.0
Identify the asked information.
Solve for the x of the factor
and insert the value into the
function. Our task is to
figure out the remainder of
the polynomial — based on
the Factor Theorem, this
means that we need to find
the sum of (f(1))² + (g(1))².
To do so, square the two
equations we acquired before.
remainder = 5/2
Hence, we are left with
Add them up to eliminate unnecessary variables
and attain an equation for (f(1))² + (g(1))².

8. Hope this
was helpful!