Having already dealt with many examples from applied Algebra II, those who followed it ought to be easily able to deal with a standard Algebra II test such as administered to Caribbean students by the Caribbean Examinations Council (CXC). Below are sample questions from a particular test. If you try this sample, allot yourself 75 minutes.
1.If (3x + 1)/3 - (x - 3)/2 = 2 + (2x - 3)/3
find the value of x
(b) Factorize completely:
15 x2 y - 20 xy2
2) f and g are functions defined as follows:
f: x -> 3x - 5
g: x -> ½ x
a) Calculate the value of f(-3)
b) Write expressions for (i) f -1 (x) and (ii) g-1 (x)
c) Hence or otherwise, write an expression for: (gf)-1
3) Sketch the graph of the function: x2 + x - 6 for: -4 < x < 3
Given the range of F estimate the interval of the domain for which F(x) < 0
4) Sketch the graph of the curve: y = 2x2 - 3x - 2
a) Using the graph find the gradient of the curve at the point where x = 2.
b) On the same axes, draw the graph of: 5y = 18x + 36
c) Using your graphs find the solutions to the simultaneous equations:
y + 2 = 2x2 - 3x
5y = 18x + 36
5) A car starts from rest and accelerates for 5 seconds to a point P, reaching 30 m/s. It maintains this velocity for 10 seconds.
a) Using 1 cm to represent 2 seconds on the time axis and 1 cm to represent 5 meters per second on the vertical (velocity) axis, draw the velocity-time graph for this part of the car's journey.
b) Using your graph calculate:
i) the velocity of the car after 2 seconds
ii) the car's acceleration in the first 5 seconds
iii) The distance traveled in 15 seconds.
iv) the average speed for the 15 seconds
6) a) Given that q varies directly as p, use the values of q and p in the table below to calculate the values of a and b:
b) 7 pencils and 5 erasers cost $11.60, whereas 5 pencils and 3 erasers cost $7.60. Find the cost of 8 erasers.
c) If S varies directly as (r + 1) and S = 8 when r = 3, calculate the value for r when S = 50.
7) The floor of a room is in the shape of a rectangle. The floor is c meters long. The width of the floor is 2 meters less than its length.
a) State, in terms of c:
i) the width of the floor
ii) the area of the floor
b) If the area of the floor is 15 m2 write down an equation in c to show this information.
(c) Use the equation to determine the width of the floor.