Algebra techniques
Expand and simplify: (x + 4)(x − 2)
x² + 2x − 8
The variable plotted on the horizontal axis of a scatterplot — usually the one we control
The independent (explanatory) variable
This value is shown as the line inside the box of a boxplot
The median (Q2)
What is the surface area of a cube with a side length of 4 cm?
96 cm²
What is Australia's national gemstone?
Opal
Factorise: x² − 9
(x + 3)(x − 3)
The term for a scatterplot pattern where points trend upward from left to right
Positive correlation
The name for Q3 − Q1
The interquartile range (IQR)
A circle has a diameter of 14 cm. What is its circumference? Give your answer in terms of pi.
14 pi cm
What animal appears on the Australian 50-cent coin?
Australian Coat of Arms — kangaroo and emu
Solve for x: 3x − 7 = 14
x = 7
This value, between −1 and 1, measures the strength and direction of a linear relationship
The correlation coefficient (r)
This measure describes how spread out the data is from the mean
Standard deviation
Close
A sector has a radius of 6 cm and an angle 60o
What is its area?
6π cm²
Along with the echidna, this animal is one of only two egg-laying mammals
The platypus
Solve simultaneously: x + y = 10 and x − y = 2
x = 6, y = 4
This line is drawn to best fit the data and can be used to make predictions
The line of best fit (regression line)
In a boxplot, a data point beyond 1.5 × IQR from the quartiles is called this
An outlier
The volume of a cone with radius 3 cm and height 10 cm (1 d.p.)
≈ 94.2 cm³ (V = ⅓πr²h)
This massive sandstone landmark in Australia's Northern Territory was formerly known as Ayers Rock.
Uluru
Simplify: (2x³y²)² ÷ (4x²y)
x⁴y³
Using a line of best fit to predict a value outside the range of the original data
Extrapolation
For the data set 2, 4, 4, 4, 5, 5, 7, 9 — this is the standard deviation
2
(mean = 5, variance = 4)
A cylindrical tank has radius 2 m and height 5 m. It is filled to 80% of its capacity. How many cubic metres of water does it contain?
16π m3 ≈ 50.3 m³
Australia is home to the world's longest straight stretch of railway track. Approximately how long is it?
About 478 km — the Nullarbor's straight section