GANSBAAI ACADEMIA
TEST
August 2014
Total: 50
Time: 1 hour
MATHEMATICS
Grade 11
EXAMINATOR
MODERATOR
L. Havenga
A. van Wyk / L. Mostert
INSTRUCTIONS
1. Answer on the folio paper.
2. Write in blue or black ink.
3. Round off answers to 2 decimal places where necessary.
4. Neat and legible work will count in your favour.
FORMULAS
Surface area = 2 rh
Volume =
2
Surface area = 4 r
1
 lb  H
3
Volume = lbH
In ΔABC:
In ΔABC:
a
b
c


SinA SinB SinC
a 2  b 2  c 2  2bc.CosA
Area ΔABC:
1
ab.SinC
2
QUESTION 1
Given f  x   2sin x and g  x   tan x for x  [90;180] .
1.1
Write down :
1.1.1 the period of f and g .
(2)
1.1.2 the amplitude of f .
(1)
1.2
Draw the graphs of f and g , and indicate all interceptions with axes and asymptotes.
(6)
1.3
Show with calculations that f and g intercept at x  60; 0; 60 and 180 for
x  [90;180] .
1.4
(7)
With reference to the graphs, write the values of x for which:
1.4.1
1.4.2
1.4.3
f ( x)  g ( x)
g is undefined
f ( x  45)  2
(2)
(2)
(2)
[22]
1
QUESTION 2
2.1
2.2
A sail boat has sails consisting of two triangles joined together by mast AB, as shown in the
diagram.
2.1.1 Calculate the height of the mast AB.
(3)
2.1.2 Calculate the area of ΔAEB.
(3)
A soccer player aims towards a goal post which is 15 meters from the back line CH on a soccer
field. The angle from the left goal post, FG, to the soccer player, S, is 116⁰. The goal posts are
7,32 m wire.
The diagram below represents the above situation.
Calculate:
2.2.1 How far the soccer player is from the left goal post FG.
(3)
2.2.2 How far the soccer player is from the right goal post EH.
(3)
2.2.3 The approximate size of GŜH, the angle within which the soccer player could possibly
score a goal.
(4)
[16]
2
QUESTION 3
3.1
The picture below shows a storage tank in which a farmer stores his grain. The tank is made
up of right cylinder with a hemisphere on top. The perpendicular height of the tank to the top
is 75 m and the radius of the tank is 10 m.
Calculate the total exterior surface area of the tank.
(6)
3.2
Two identical cement pillars are placed at the entrance of a building. They are made up of a
rectangular prism and a right pyramid placed on it. The rectangular prism is 2 m high, 0,6 m
long and 0,5 m wide. The perpendicular height of the pyramid is 0,8 m.
Determine the volume of cement needed to make up the two pillars.
(6)
[12]
TOTAL: 50
3