## Wednesday, April 20, 2011

### Could U.S. High Schoolers Pass a Basic Caribbean Math Test?

In the 1980s, the notion of Caribbean Medical Schools became a widespread common joke, with its denizens mocked as lame losers, or wannabes that couldn't get anything better. This wasn't necessarily helped by the early 90s ABC comedy Going to Extremes, which depicted such students (in Jamaica, called 'Jantique' in the show) more often lollygagging in the Sun for a tan than studying medicine.

However, regular Caribbean academic schools and universities are another matter. They both maintain very high standards, and their curricula are demanding. At the secondary level, all students are required to attain at least a Grade II(roughly equivalent to an 85%) in order to be judged as qualifying for further recommendations, including for university (University of the West Indies). The tests are designated as "General Proficiency" which means the student must demonstrate a general proficiency in performance over a wide spectrum of questions, problems. No test is perhaps more important than the one for Math, since it impinges on a wide array of qualifications including the much prized offshore banking jobs.

This makes it an interesting proposition to see if U.S. students can stand the competition or have the moxie to even come close to Grade II for some sample math questions extracted from papers over 1997-2000. My bet is not one H.S. student, even those with AP prep, will get anywhere close to Grade II, far less a Grade I (95% or more). But hey, I might be wrong! Could be! Anyway, here are ten select questions-problems and I will allot ten marks to each. I'll give the problem solutions in a few days. In the general rubric, 14 problems are given and to be done in 2 hrs. 40 minutes. I am giving ten, so make the cut down to 2 hours exactly. No cheating and taking any longer. Time yourself like you would a mock SAT exam. Here goes!

Caribbean General Proficiency Math (Time 2 hours: Show ALL working!)

1) (a) If (3x + 1)/3 - (x - 3)/2 = 2 + (2x - 3)/3

find the value of x

(b) Factorize completely:

(i) 15 x^y - 20 xy^2

(ii) 3 - 12b^2

(c) Given that: m = -3, n = 2, p = -1

find the value of:

m(p - n)^2/ 3p + m

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) (a) The coordinates of the points L and N are (5, 6) and (8, -2), respectively.
(i)State the coordinates of the midpoint M of the line, LN.

(ii) Calculate the gradient of the line LN

(iii) Determine the equation of the straight line which is perpendicular to LN and which passes through point M.

(b) An aircraft leaves Jamaica at 13:55 hrs. and travels to Barbados via Antigua. The average speed of the aircraft is 420 km/hr. It arrives in Antigua at 16:45 hrs. local time. Given Antigua is ONE hour AHEAD of Jamaica, compute the distance betwen Jamaica and Antigua.

(4) (a) Calculate the exact values of:

i) (2.8 + 1.36)/ 4 - 2.7

ii) (27/8)^1/3

(b) Calculate 9.72 x 12.05

i) Exactly

ii) Correct to two decimal places

iii) Correct to 2 significant figures
iv) in standard form

5)Using Fig. 1 and the information therein, calculate (giving reasons):
a) Angle MSQ

b)Angle RSP

c)Angle SPN

6) (a) Given that: U = {a, b, c, d, e, f, g} where U is the universal set

L = {a, b, c, d, e}

M= {a, c, e, g}

N = {b, e, f, g}

(i)Draw a Venn diagram showing the sets U, L, M, N and their elements

(ii)List the members of the set represented by the union of N with the intersection of L and M

b) If:

(a)
(b) =

(2...3)(-3)
(-1..2)(1)

determine the values of a and b

c) Given the vector:

A =

(4)
(7)

Calculate:

i) ‖A‖, the length of vector A

ii) the size of the angle made by the vector A and the x-axis.

7) This refers to Fig. 2. (Take the radius of the Earth to be 6400 km, and π = 3.14)

The diagram represents the Earth and shows the equator and the Greenwich meridian. Town I is located at (16 N, 30 W), and Town J is at (16 N, 45 W).

(i) Copy the diagram (or print it out) and show the positions of Towns I, J.

(ii) Calculate the radius of the circle of latitude on which Towns I and J are situated.

(iii) Calculate the shortest distance, measured along the Earth's surface, between the two towns.

8)The matrix R =

(cos(Θ)......-sin(Θ))
(sin (Θ)......cos(Θ))

a) Determine the coordinates of the image (1, 2) under the transformation R when Θ = 90 degrees.

b) If the point (p, 3) is on the line (L)given by: x + 2y = 5, calculate the value of p.

c) Given the point (1,2)is on L, determine the image of L (L') of the line L under the transformation R.

d) Write the matrix equation to represent the pair of simultaneous equations given by L and L'.

9) This refers to Fig. 3. The diagram shows a rectangular sheet of metal ABCD supported by a vertical wall (shaded) at right angles to the level ground OX. AB measures 3 meters and AD measures 10 meters.

a) Calculate the size of the angle ODA.

b) Hence, calculate the size of the angle CDX.

c) If CX represents the length in meters of C above the ground, calculate CX.

10)This refers to the Venn diagram in Fig. 4 and the information therein. Assume the same number, x, play football only and tennis only.

(a) Calculate the number who play football.

(b) State the information represented by the shaded portion of the Venn diagram.

(c)State the relationship between the members of the sets C and F, and between the sets C and T.