MCV4U1: Diagnostic Assessment
1. Determine the equation of the line that passes through (2, 1) and (5, –8).
2. Compute 𝑓(3) for each of the given functions.
a) 𝑓(𝑥) = (𝑥 − 1)2 + 2
b) 𝑓(𝑥) =
3. Factor each of the following:
a) 𝑥 4 − 1
c) −8𝑥 3 − 18𝑥 2 − 4𝑥
e) 𝑥 8 − 𝑦 4
g) 𝑥 2𝑎 − 3𝑥 𝑎 − 4
b) 8𝑥 4 − 27𝑥
d) −12𝑥 2 + 27
f) 8𝑥 3 + 1
h) 𝑥 2𝑚 − 36𝑦 2
4. Expand fully
a) (𝑥 + ℎ)3
c) −(3𝑥 − 2𝑦)3
b) (2𝑥 − 1)3
d) −𝑥(𝑥 − 1)2 (𝑥 + 5)
2𝑥+1
𝑥−3
5. State the domain of each of the given functions.
6.
7. Is the following function continuous?
𝑓(𝑥) = { √3 − 𝑥
√3 + 𝑥
𝑥<0
𝑥≥0
8. Solve each polynomial equation.
a) 𝑥 5 − 10𝑥 3 + 9𝑥 = 0
b) 𝑥 5 − 12𝑥 3 + 32𝑥 = 0
c) 𝑥 3 − 2𝑥 2 − 11𝑥 + 12 = 0
d) 𝑥 3 − 𝑥 2 − 8𝑥 + 12 = 0
9. Solve each polynomial inequality.
a) 𝑥 3 + 𝑥 2 − 16𝑥 − 16 ≥ 0
b) 𝑥 4 − 12𝑥 2 + 11 < 0