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NCEA Level 1 Mathematics and Statistics 91028 (1.3) — page 1 of 3
SAMPLE ASSESSMENT SCHEDULE
Mathematics and Statistics 91028 (1.3): Investigate relationships between tables,
equations or graphs.
Assessment Criteria
Achievement
Merit
Investigate relationships between
tables, equations and graphs.
Excellence
Investigate relationships between
tables, equations and graphs, using
relational thinking.
Investigate relationships between
tables, equations and graphs, using extended abstract thinking.
Evidence Statement
One
Expected
Coverage
Achievement
Merit
Excellence
Investigates relationships
between tables, equations
and graphs by:
Investigates relationships between tables,
equations and graphs,
using relational thinking,
by:
Investigates relationships between tables,
equations and
graphs, using extended abstract thinking, by:
THREE of:
TWO of:
TWO of:
T  4n  1

(ii)
Graph drawn from
equation or table.
 drawing a correct
graph with n as a continuous variable
 drawing a correct
graph with n=1 to 10
as a continuous variable
 drawing a correct
graph up from n=1
to 10 as a discrete
variable with no y
intercept.
(iii)
Rule given
 using the context to
find the solution of 324
 forming a quadratic
model with minor errors.
 forming a correct
generalisation
 forming the correct
symbolic representation of a relationship
 forming and using the
correct symbolic representation of a relationship
 demonstrating an understanding of one important concept (perhaps vaguely expressed).
 demonstrating an
understanding of both
important concepts
but with incomplete
description(s).
(a)(i)
S  2n  3n
2
(b)
(i)
T  5n
(ii)
T (6)  30
(iii)
The gradient is
steeper having increased from 4 to
5,
and both graphs
begin at the point
(1,5)
linking table to equation
 demonstrating an
understanding of
both important
concepts with
clear and complete descriptions.
NCEA Level 1 Mathematics and Statistics 91028 (1.3) — page 2 of 3
Two
(a)
(i)
Expected
coverage
P  20x  50
Or equivalent
Achievement
Merit
Excellence
Investigates relationships
between tables, equations
and graphs by:
Investigates relationships between tables,
equations and graphs,
using relational thinking,
by:
Investigates relationships between tables,
equations and
graphs, using extended abstract thinking, by:
TWO of:
TWO of:
TWO of:
 linking the graph to the
equation correctly or
solving one of the
problems correctly
 linking the graph to
the equation correctly
 linking the graph
to the equation
correctly
 using the graph to
find a solution to one
problem
(ii)
Cost of 2kg bag is
$10 (accept $5 per
kg)
(iii)
$150 profit over 10
kg implies $30 for
2kg bag (accept
$15 per kg)
(iv)
The y intercept becomes -45 instead
of -50.
But gradient remains the same (as
they are sold at the
same price)
 demonstrating an understanding of one important concept (perhaps vaguely expressed)
 demonstrating an
understanding of both
important concepts
but with incomplete
description(s)
 demonstrating an
understanding of
both important
concepts with
clear and complete descriptions
(v)
Gradient is reduced
after 6 kg of sausages have been
sold.
Extra profit per extra kg sold drops
from $20 to $10
Price per kg drops
from$20 to $10
(halves)
Overall profit reduced from $15 per
kg at original price
to $11 per kg now.
($110÷10, per kg)
 demonstrating an understanding of the
change gradient (perhaps vaguely expressed).
 demonstrating an
understanding of the
change in gradient
with specific values
quoted but not connected to the context.
 demonstrating an
understanding of
the change gradient with specific
values quoted and
clearly connected
to the context.
 using the graph to
find solutions to
both problems
NCEA Level 1 Mathematics and Statistics 91028 (1.3) — page 3 of 3
Three
(a)
(i)
Expected
coverage
x intercepts 1
and -2
y intercept 2
(ii)
y = -(x-1)(x+2)
y = -(x+0.5)2+2.25
y = -x2 – x + 2
(iii)
y = -x2 + 5x + 1
y = -(x+2.5)2+7.25
new y-intercept
=1
Achievement
Merit
Excellence
Investigates relationships between tables,
equations and graphs
by:
Investigates relationships
between tables, equations
and graphs, using relational thinking, by:
Investigates relationships between tables,
equations and graphs,
using extended abstract thinking, by:
THREE of:
TWO of:
TWO of:
 giving either the intercepts or the equation.
 giving a complete solution
 sketching the new
graph and quoting
the new y-intercept
correctly
 developing the equation of the new graph
but not giving the yintercept
 sketching the graph to
give the correct shape,
with the vertex clearly
shown to reach above
6
(b)
(i)
Correct graph
drawn with
smooth curves
 sketching the graph
to give the correct
shape, even if the
vertex is not clearly
shown to reach
above 6
(ii)
For maximum
value x = 2.5
y = 6.25
 quoting a maximum
value consistent with
the graph drawn
above
4   x  x  5
 stating the length of
the support as 3m,
with no algebraic or
graphical justification.
(iii)
x2  5x  4  0
x  1 or 4
length of support
=3
 stating and solving
either consistently an
incorrect equation (of
comparable complexity), or incorrectly solving the correct equation.
 developing the
equation of the new
graph and giving
the y-intercept as 1
 stating and solving
completely the
equation connecting the y-value of 4
with the length of
the support being
3m.
Judgement Statement
Achievement
Achievement with Merit
Achievement with Excellence
Minimum of:
2A
Minimum of:
2M
Minimum of:
2E