Penabur International School – Junior College Programme
Jln. Banda no 19 – Bandung
NAME/NO :
PM1C1 JC1-2425
1. A curve has equation 𝑦 = 𝑥 2 − 5𝑥 + 7 and a line has equation 𝑦 = 2𝑥 − 3.
a. Find the coordinates of the points of intersection of the line and the curve.
b. Write down the set of values of 𝑥 that satisfy the inequality 𝑥 2 − 5𝑥 + 7 < 2𝑥 − 3.
2. Find the set of values of 𝑘 for which the equation 𝑥 2 + (𝑘 − 2)𝑥 + (2𝑘 − 4) = 0 has real roots.
[3]
[1]
[5]
1
6
3. Use a suitable substitution to solve the equation (3𝑥+1)2 + 5 = 3𝑥+1.
[4]
4. The line 𝑥 + 2𝑦 = 9 intersects the curve 𝑥𝑦 + 18 = 0 at the points 𝐴 and 𝐵.
Find the coordinates of 𝐴 and 𝐵.
[4]
5. It is given that f(𝑥) = 4𝑥 2 + 𝑘𝑥 + 𝑘.
i.
Find the set of values of 𝑘 for which the equation f(𝑥)= 3 has no real roots.
[5]
ii.
In the case where 𝑘 = 10,
Express f(𝑥) in the form (𝑎𝑥 + 𝑏)2 + 𝑐,
[3]
iii.
Find the least value of f(𝑥) and the value of 𝑥 for which this least value occurs.
[2]
6. The equations 𝑦 = (𝑥 − 2)(𝑥 − 3)2 and 𝑦 = 𝑘 have one solution for all 𝑘 < 𝑚.
Find the largest value of 𝑚.
[4]
7. Show that f(𝑥) = 8𝑥 2 − 3𝑘𝑥 + 2𝑘 2 + 1, where 𝑘 is a constant, is positive for all real values of 𝑥.
[4]
si quis autem vestrum indiget sapientiam postulet a Deo qui dat omnibus affluenter et non inproperat et dabitur ei - If any of you lacks
wisdom, let him ask of God, who gives to all liberally and without reproach, and it will be given to him. (James 1 : 5)