Year 10 Mathematics – Assessment Task 2 Review

Flashcards covering key concepts for Linear Relationships, Financial Mathematics, and Data Analysis in the Year 10 Mathematics Assessment Task 2.

What formula is used to calculate the gradient (slope) of a straight-line interval?

m = (change in y) / (change in x) = rise / run

What is the relationship between the gradients of parallel lines?

Parallel lines have equal gradients (m₁ = m₂).

When are two lines perpendicular?

When the product of their gradients equals –1 (m₁ × m₂ = –1).

What is the midpoint formula for the interval joining (x₁, y₁) and (x₂, y₂)?

Midpoint = ((x₁ + x₂) / 2, (y₁ + y₂) / 2).

How do you calculate the distance between two points (x₁, y₁) and (x₂, y₂)?

Distance = √[(x₂ – x₁)² + (y₂ – y₁)²].

What is the gradient-intercept form of a straight-line equation?

y = mx + c

In y = mx + c, what does the constant c represent?

The y-intercept, where the line crosses the y-axis.

How can you check whether a specific point lies on a given line?

Substitute the point’s x and y into the line’s equation; if the equality holds, the point is on the line.

What are the equations of the coordinate axes?

x-axis: y = 0  y-axis: x = 0

Describe the steps to graph a line using its gradient and y-intercept.

Plot the y-intercept (0, c), then from that point use the gradient m = rise/run to locate a second point and draw the line through both points.

What is meant by a positive gradient?

A gradient where y increases as x increases; the line rises from left to right.

What is the gradient and general equation of a horizontal line?

Gradient 0; equation of the form y = k (k is a constant).

What is the gradient and general equation of a vertical line?

Gradient is undefined; equation of the form x = k (k is a constant).

Give one real-life example that can be modelled by a linear relationship.

Earning wages at a constant hourly rate (wages = rate × hours).

What formula gives the future value earned with annual compound interest?

A = P(1 + r)ᵗ, where P is principal, r is annual interest rate (as a decimal), and t is number of years.

How is compound interest described in terms of percentage change?

It is a repeated percentage increase applied at the end of each compounding period.

What is the formula for reducing-balance depreciation?

V = P(1 – r)ᵗ, where P is initial value, r is depreciation rate per period, and t is number of periods.

What type of data is displayed in a scatter plot?

Bivariate numerical data (pairs of values for two variables).

Which three features summarise the association shown in a scatter plot?

Form (linear/non-linear), strength (strong/moderate/weak), and direction (positive/negative).

How do you draw a line of best fit ‘by eye’?

Sketch a straight line that has roughly equal numbers of points above and below it and follows the overall trend.

Define interpolation in the context of a line of best fit.

Predicting values within the range of observed data using the line of best fit.

Define extrapolation in the context of a line of best fit.

Predicting values outside the range of observed data using the line of best fit.

Name two common sampling methods used in statistical inquiries.

Simple random sampling and stratified sampling.

Why is evaluating a sampling method important in statistics?

Because the reliability and validity of conclusions depend on how representative the sample is of the population.

What equipment must students bring to the open-book class test?

Pens, pencils, eraser, ruler, and a calculator.

What is the restriction on notes allowed during the test?

Students may bring only one A4 sheet of notes (front and back); no other reference materials are permitted.