Assessment Schedule NCEA Level 2 Mathematics (90287) 2011 — page 1 of 2
Assessment Schedule – 2011
Mathematics: Use coordinate geometry methods (90287)
Evidence Statement
Q
Achievement
Use coordinate geometry methods.
ONE
(a)
Solve problems involving coordinate
geometry methods.
Excellence
Sufficiency
Solve extended problems involving
coordinate geometry methods.
ONLY ONE
grade each
question.
(4,–7)
(b)
20
(c)
3
Grad BD = 4
(d)
Merit
Accept eqns in form
y = (not completely simplified)
ax + by = c
3
x − 10
4
or 3x – 4y – 40 = 0
y=
One aspect found – midpoint, distance Algebraically
or equation.
2
(Note: must be different skill than any " 3x ! 10 + 3% + x ! 4 2 = 102
$# 4
'&
already gaining “a”)
Geometrically – two correctly linked
ideas on track to solve problem.
(
)
Algebraic: Let midpoint be M
Distance BD = AC = 20
Distance BM = 10
Equation BD is
3
y = x − 10
4
At B and D
(y + 7)2 + (x − 4)2 = 10 2
3x
( − 10 + 3)2 + (x − 4)2 = 10 2
4
x 2 − 8x − 48 = 0
x = 12 x = −4
Point D is (−4,−13)
Geometric solution – clear method Accept B (12,–1) or both B and
D.
that leads to full solution.
1A = 1 of a
2A = 2 of a
3A = 3 of a
M = a and m
E = M and e
Assessment Schedule NCEA Level 2 Mathematics (90287) 2011 — page 2 of 2
TWO
(a)
(b)
y= x+5
3
26
y= x+
5
5
Accept eqns in form
y = (not completely simplified)
ax + by = c
1A = 1 of a
2A = 2 of a
3A = 3 of a
or 3x – 5y +26 = 0
3
3
and Grad AC =
2
2
Grad AB =
(c)
M = a and m
Or dist BA + dist AC = dist BC.
Or A is the midpoint of BC.
(d)
k
k
x = 3+ , y = 1+
2
2
Algebraically:
2
2
"
k% "
k%
2
$# 4 ! 3+ 2 '& + $# k ! 1! 2 '& = 2
Algebraically:
If C is closest point on line, Eqn HC
is
y = −x + 4 + k
E = M and e
C is where x − 2 = −x + 4 + k
Geometrically – TWO correctly linked
k
k
ie x = 3 + , y = 1+
ideas on track to solve
2
2
(y − k)2 + (x − 4)2 = 4
k 2 − 4k − 4 = 0
k =2±2 2
k = 4.828 or −0.828
Geometric solution – clear method
that leads to full solution.
BOTH required.
Judgement Statement
Achievement
Achievement with Merit
Achievement with Excellence
1 A(Q1) + 1 A(Q2)
OR
3A
1 M(Q2) + 3 A(Q1)
OR
1 M(Q1) + 2 A(Q2)
OR
1E+1A
1E+1M