Brain- Buster #2: Math 'MAULERS'

MATH MAULERS:  (Level:  High School)

  

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

find the value of x

(b) Factorize completely:

(i) 15 x²y - 20 xy²

(ii) 3 - 12b²


(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 ^-1x  and (ii) g^-1x

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 between 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