Elementary Mathematics Revision Worksheet 49
1
a)
Sketch the quadratic graph of y  5  ( x  2) 2 .
b)
Write down the equation of the line of symmetry of the
curve y  5  ( x  2) 2 .
[ x  2 ]
Without solving, explain why there is no solution for the
equation 5  ( x  2) 2  1 .
[the curve will not intersect the line y  1 .]
c)
2
3
4
In the diagram, AB is parallel to DE and AF = DC = 3 cm and BC = 2.5 cm.
i)
Prove that ΔABF is congruent to ΔDEC.
ii)
Given that CF = 1.5 cm, find the length of AB. [5 cm]
iii)
ˆ E in terms of a.
Given that ABˆ F  a , find CD
a)
Solve the equation 5x  3  7  3x .
b)
Simplify
c)
Express as a single fraction in its simplest form
4 y  10
.
2 y 2  y  15
[Hint: AAS]
[ 90  a ]
[ x  5]
[
2
]
y 3
5
2
.

p  2 2p 3
[
8 p  19
]
 p  22 p  3
The population, P, of a certain microorganism present at t hours after initially being observed
is given by
the formula P  250  1.3 .
t
a)
How many microorganisms were there initially?
b)
Find the percentage increase in the population after 2 hours.
[250]
[69%]
240°
5
6
The diagram shows three vertices, P, Q and R of an incomplete polygon. The
reflex angle PQR = 240°. The exterior angles at the other vertices are all equal
to 20° each. How many sides does the polygon have?
[16]
A is the point (12, –2), B is the point (20, 10) and C is the point (4, 6).
i)
Find the equation of the line l which is parallel to AC and passes
through B.
[ y   x  30 ]
ii)
The line l crosses the x-axis at P and the y-axis at Q. Find the area
of triangle OPQ.
[450 units2]
P
Q
R