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Artificial Intelligence (AI) technologies such as Generative AI, Image Generators and Large Language Models have had a dramatic impact on teaching, learning and assessment over the past 18 months. The most immediate threat AI posed was to Academic Integrity with Higher Education Institutes (HEIs) focusing their efforts on combating the use of GenAI in assessment. Guidelines were developed for staff and students, policies put in place too. Innovative educators have forged paths in the use of Generative AI for teaching, learning and assessments leading to pockets of transformation springing up across HEIs, often with little or no top-down guidance, support or direction.
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2. QUESTION 1
Find the equation of the circle in general form with
center (7, -4) and radius length 7.
x2 + y2 - 14x + 8y + 16 = 0
3. QUESTION 2
Determine the center and the radius of the circle
x2 + y2 - 6y - 12x = -20.
C(6, 3), r = 5
4. QUESTION 3
Find the equation of a circle in standard form
tangent to the circle x2 + y2 = 4 and with center at
(0, 5).
x2 + (y - 5)2 = 9
5. QUESTION 4
What polynomial will have a quotient of 3x3 -2x2 - 3x + 2
when divided by 2x + 3.
6x4 + 5x3 - 12x2 – 5x + 6
6. QUESTION 5
Find the remainder when 2x300 - 7x201 + 3x105 + 4 is
divided by x + 1.
10
7. QUESTION 6
If x3 + Px2 + Qx -105 is divisible by both x + 5 and
x - 3, find the values of P and Q.
P = 9 and Q = -1
8. QUESTION 8
If x2 – 3x + 1 is divided by x + 2m, the remainder is
-1, what is m?
m = -5/2 and 1
9. QUESTION 9
When 9x3 + Ax2 – 9x + 5 is divided by 3x + 2, the
quotient is 3x2 + Bx – 1 and the remainder is 7. Find
the values of A and B.
A = -3 and B = -3
10. QUESTION 10
Find all the real zeros of P(x) = 2x3 + 3x2 - 8x + 3.
Zeros: {-3, 1, and 1/2}
15. QUESTION 15
Eric invests P2,500 at 10.5% annual interest
compounded monthly. How many years will it take
his money to double in value?
16. QUESTION 16
Under ideal conditions a certain bacteria
population doubles every three hours. Initially
there are 2,000 bacteria in a colony.
a. Find a model for the bacteria population after t hours.
b. How many bacteria are in the colony after 30 hours?
c. When will the bacteria count reach 160,000?