Math AA SL
Test on Lines and Quadratics
/50
Date: 12 October 2022
Paper 1
(without GDC)
Name of student: __________________________________________________
1.
[Maximum mark: 9]
(a)
2.
Find the equations of the lines
(i)
L1 passing through A(1,5) and B(7,1).
(ii)
L2 passing through C(1,3) and D(7,3).
(iii)
L3 passing through E(4,-2) and F(4,14).
[6]
(b)
Find the point P of intersection between the lines L2 and L3 .
[1]
(c)
Show that P is the midpoint of the line segment [AB]
[2]
[Maximum mark: 9]
Consider the lines
L1 : 3 x  y  8 .
L2 : 5 x  y  16
The two lines intersect at point P.
3.
(a)
Write down the gradient of the line L2 .
(b)
Find the coordinates of P.
(c)
Find the distance between the y -intercept of L1 and point P in the form a 10 .
[1]
.
[4]
[4]
[Maximum mark: 5]
The line L1 has equation y  3 x  7 .
The line L2 is perpendicular to L1 and passes through the point A(–2,5).
(a)
Write down the gradient of the line L2 .
(b)
Find the equation of the line L2 in the form ax  by  d  0 where a, b, c
are integers.
[1]
[4]
1
4.
[Maximum mark: 10]
The quadratic y  ax 2  bx  c can also be expressed in the form y  a ( x  p )( x  q ) ,
where p and q are positive integers. The following diagram shows its graph, which
passes through the points (–2,0), (3,0) and (0, –12).
(a)
Write down the values of
(iii) c .
[3]
(b)
Write down the equation of the axis of symmetry.
[2]
(c)
Express the quadratic function in the form y  ax 2  bx  c .
[5]
(i)
5.
p
(ii) q
[Maximum mark: 12]
Let f ( x)  2 x 2  8 x  10
(a)
Solve the equation f ( x )  0 .
(b)
For the parabola y  f ( x ) .
(c)
6.
[4]
(i)
Write down the equation of the axis of symmetry.
(ii)
Find the coordinates of the vertex.
[4]
Express f ( x)
(i)
in the form y  a ( x  h) 2  k .
(ii)
in the form y  a ( x  p )( x  q ) .
[Maximum mark: 5]
The line y  mx  1 is tangent to the parabola f ( x)  x 2  5 . Find the possible values
of m .
2
[4]