A Caribbean Algebra II Test: Can American Students Pass It?

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:

p......2........8...........a
--------------------------
q.....6.1.....b..........1.2


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.