Mathematics BPM MTH0 Training test
Name: . . . . . . . . . . . . . . . . University number (UˇCO): . . . . . . . . .
Problem 1: Simplyfy and find conditions for:
2x
x + y
+
y
x − y
+
y2
y2 − x2
:
1
x + y
+
x
x2 − y2
.
Problem 2: Solve the equation 4 + 2
√
x − 4 = x.
Problem 3: Solve the inequality x
x−5 > 1
2.
Problem 4: Solve the equation 4x+3
· 8x−3
= 128.
Problem 5: Solve the inequality log5(3x − 1) < 1.
Problem 6: Solve the inequality x2
− 4x − 12 > 0.
Problem 7: Solve the equation |x| − |x − 2| = 2.
Problem 8: Find the inverse of a function y =
√
x − 1.
Problem 9: Find the intersections of the graphs of functions f and
g, where f(x) = x2
− 11x + 20, g(x) = 6 − x2
.
Problem 10: Sketch a graphs of functions h(x) = 2x
, f(x) = 2−x
and g(x) = −2x
into one picture.