# Assessment Specifications

Level 1 Mathematics and Statistics 2021

## General information

#### Method of assessment

Written examination

## Information relating to all achievement standards

Each examination will be made up of three questions, and each question may have only one opportunity for Excellence.

Questions may:

• require candidates to process word problems at all levels of achievement
• have multiple parts.

Opportunities for Merit and Excellence will be spread through the examination. As a result, the parts of a question may not be arranged in increasing order of difficulty.

Teachers should be familiar with the two documents listed below:

#### Special notes

In any of the Level 1 external assessments, candidates may be expected to demonstrate evidence through investigating a situation in order to make a generalisation or provide a proof for a given outcome.

This may involve the investigation of a numerical, algebraic, statistical, or geometric relationship, and begin with a word problem or situation. In the case of numerical situations, candidates will most likely be required to express this algebraically as a generalisation.

Candidates will be expected to demonstrate an understanding of the mathematical concepts, rather than directly transferring results from a graphing calculator. This may involve increased use of unknown constants.

Candidates must choose their method when solving a problem. This must be consistent with the title of the achievement standard and at curriculum level 6. The grade awarded may be affected by the level of thinking applied in solving the problem.

Guess-and-check methods are unlikely to show the required thinking beyond possibly Achievement, and the opportunity to use this as evidence may be limited within any assessment. As good mathematical practice, candidates should show intermediate steps in a logical manner and clearly communicate what is being calculated. By giving only the answer, candidates may lose the opportunity to provide evidence for grades or to have minor errors ignored.

The answer from one part of a question may be required in answering subsequent parts. In this case, consistency of response may be assessed as being correct, provided the solution is not an essential component of the standard and providing the incorrect solution does not result in an easier question being solved.

The context needs to be considered when stating final solutions, e.g. the number of rolls of wire that need to be bought to fence an area (6 rolls not 5.42 rolls), or restrictions on a variable to ensure area has a positive value.

In algebra standards, answers should be expressed in their simplest algebraic form.

Standards require a range of methods / procedures that may be assessed. A combination of methods / procedures may be required in any part of a question and for the award of any level of achievement. Evidence of relational and abstract thinking may be demonstrated by the linking of these, leading towards all levels of achievement within part of a question.

#### Equipment

Candidates require a ruler and a calculator for standards 91028, 91031, and 91037. Any approved scientific or graphing calculators may be used, but a graphing calculator is an advantage in 91028.

Note that in the Common Assessment Task for Mathematics 91027 (MCAT), no calculators are allowed.

## Specific information for individual achievement standards

91027

Mathematics

Algebra

#### Title

Apply algebraic procedures in solving problems

4

4

#### Format of the assessment

The MCAT for AS91027 will be delivered on two days in Term 3.

Schools are responsible, through their policies and procedures, for authenticating candidate work. Each school is required to have procedures in place for ensuring the work of each candidate is the candidate’s own. NZQA will require that schools provide notification of any school incidents during the delivery of the MCAT that may affect the authenticity of candidates’ work.

#### Further clarification of the achievement standard

Small numbers are used in problems to compensate for the lack of calculators.

Answers should be expressed in their simplest algebraic form. Except where the numbers are small, it is expected that answers will be left in fractional form and may contain π.

An understanding of the meaning of mathematical language is expected.

Contexts from other strands of mathematics may be used, e.g. angles of simple geometric shapes, or Pythagoras. Linking graphing and algebra is often required. Knowledge of aspects of measurement in common geometrical shapes, e.g. triangles, rectangles, will be assumed. For more complex shapes, a formula may be given.

Candidates will not be directed to solve factorised quadratics, factorise, expand, write or solve a linear equation, or simplify an expression involving the collection of like terms. Questions directing a candidate to perform a specific procedure will require an intermediary procedure from the standard in order to answer the question (e.g. solve a quadratic in expanded form will require factorising).

Given a word problem, candidates are required to write equation(s) representing the situation presented and demonstrate consistent use of these in solving a problem.

Candidates will be expected to have a basic understanding of the relationship between a quadratic function and the associated graph.

91028

Mathematics

Algebra

#### Title

Investigate relationships between tables, equations and graphs

3

#### Number of credits

4

A grid without axes may be provided for some questions.

Investigating relationships may involve writing equations for data provided in a table of values or from a graph.

Candidates are expected to demonstrate the drawing of graphs, construction of tables, and / or forming equations when investigating a situation.

Candidates may be expected to choose the representation to use in the solving of a problem.

Candidates may be required to:

• construct graphs, tables, or equations to represent a practical situation that has been given in word form
• understand the difference between graphs representing situations involving continuous data, and graphs representing situations involving discrete data and piecewise functions
• demonstrate an understanding of the nature of the data when discrete or continuous information is involved.

91031

Mathematics

Geometry

#### Title

Apply geometric reasoning in solving problems

4

#### Number of credits

4

Rounding of bearing answers will not be required to any specified level of accuracy or with an expected number of figures in front of any decimal point.

Solutions to questions involving the use of Pythagoras’ theorem may be left in surd form.

Candidates are expected to be able to work with variables.

Completion of proofs will be required. The use of clearly defined variables or the addition of lines to a diagram by the candidates is to be encouraged in formulating a proof.

Some examples of acceptable geometric reasons are:

• Alt angles
• Corr angles
• Co-int angles
• (Vertically) opp angles
• ∠  (on) line
• Isosc Δ
• Angles (in) △
• Similar Δ
• Angle at C or O.

Terms such as Z or FUZ angles will not be accepted.

Questions may require the use of trigonometric and geometric relationships.

Questions may involve the use of bearings, or solution of problems in two dimensions set in three-dimensional contexts.

91037

#### Subfield

Statistics and Probability

Statistics

#### Title

Demonstrate understanding of chance and data

4

#### Number of credits

4

Candidates will be provided with a Question and Answer booklet, and there may be a separate Resource Sheet.

Essay-style answers are not required. Bulleted responses are acceptable.

Candidates may be expected to find conditional probabilities using an informal approach.

The use of probability trees will not be required; however, candidates may find the use of these helpful in identifying the sample space. The use of probability trees will be accepted but not expected.

Within reading and interpreting statistical representations or analysing statistical investigations, candidates may be required to comment on the appropriate and / or misleading aspects of graphical displays of data.

Knowledge and experience with probability experiments may be helpful in answering questions relating to probability.

Questions will not require the use of ratios to calculate probabilities. However, an answer written correctly as a ratio will be accepted.

Mathematics and Statistics subject page

Examination timetable