Level I Skill 4
1
1. Simplify 𝑙𝑜𝑔3 9
√2𝑥𝑦 3
2. Break up the expression: 𝑧
3. Solve: ln(3𝑥) = 22
4. The diagram shows three graphs.
B
y
A
C
x
5.
A is part of the graph of y = x.
B is part of the graph of y = 2x.
C is the reflection of graph B in line A.
Write down
(a) the equation of C in the form y =f(x);
(b) the coordinates of the point where C cuts the x-axis.
5. Use a GDC to solve: 2𝑙𝑜𝑔20 3 = 5𝑥 − 2
6. Given that log5 x = y, express each of the following in terms of y.
(a) log5x2
(b)
log5  1 
 x
(c) log25x
7. You invest $8000 in an account that ha a rate of interest fixed at 4.3% per annum.
How much is your investment worth after 10 years.
8. Consider the following relations between two variables x and y.
A. y = sin x
B. y is directly proportional to x
C. y = 1 + tan x
D. speed y as a function of time x, constant acceleration
E. y = 2x
F. distance y as a function of time x, velocity decreasing
Each sketch below could represent exactly two of the above relations on a certain
interval.
(i)
y
(ii)
(iii)
y
x
y
x
x
Complete the table below, by writing the letter for the two relations that each sketch
could represent.
sketch
relation letters
(i)
(ii)
(iii)
9. The equation 𝑘𝑥 2 + 3𝑥 + 1 = 0 has exactly one solution. Find k.
10. Let f(x) = √𝑥, and g(x) = 2x. Solve the equation: (f –1 o g)(x) = 0.25.
11. The graph of y = x2 may be transformed into the graph of y = 5 – 3(x – 4)2 by these
transformations.
A reflection in the line y = 0
followed by
a vertical stretch with scale factor k followed by
a horizontal translation of p units
followed by
a vertical translation of q units.
Write down the value of
(a) k;
(b) p;
(c) q.