Final test, Mathematics 0 BPM MTH0 autumn 2023
Name: . . . . . . . . . . . . . . . . University number (UˇCO): . . . . . . . . .
Problem 1: Solve the inequality x2
− 5x + 7 ≥ 3x.
Problem 2: Solve the inequality
x − 1
x + 3
≤ 3.
Problem 3: Solve the equation x +
√
x = 2.
Problem 4: Solve the equation 52x+4
= 256x+1
.
Problem 5: Solve the equation log3(log2(x) − 5) = 3.
Problem 6: Sketch the parabola y = x2
− 2x + 3, and find the
coordinates of its vertex.
Problem 7: Sketch the graph of a function y = log10(x + 1) − 2,
and find its intersections with the axes.
Problem 8: Find the inverse of a function y = 3−x
and determine
its domain.
Problem 9: Simplify
1
√
x + 1
−
√
x
x − 1
:
√
1 − x +
1
√
1 − x
.
Problem 10: For a > 0, simplify 3 a·a2
a
1
2
2