Application of Linear Equations and Graphs
The gradient of a line is 5.
What does the gradient tell us?
The rate of change (increase of 5 units for every 1 unit across).
In a right-angled triangle, the side opposite the angle is 8 and the hypotenuse is 10.
Which trigonometric ratio should be used?
Sine
Data set: 5, 7, 9, 10, 14
Find the median.
Answer: 9
Which trig ratio uses opposite and adjacent sides?
Tangent
What does "interpret" mean in an exam question?
Explain the meaning of the result in context.
A taxi charges $4 flagfall plus $2.50 per kilometre.
Write a linear equation representing the cost.
C=2.5x + 4
A ladder leans against a wall making an angle of 60° with the ground. The ladder is 5 m long.
How high up the wall does it reach?
4.33m
Data set: 3, 4, 7, 8, 13
Find the mean.
Answer: 7
A right triangle has adjacent side 12 cm and hypotenuse 20 cm.
Find the angle.
θ≈ 53.10
What units should always be included in a final answer?
The units given in the question.
A business has costs represented by C=1500+20x
What does the 1500 represent?
Fixed/start-up costs.
A tree casts a shadow of 12 m. The angle of elevation to the top is 35°.
Find the height of the tree.
8.4m
Data set: 4, 5, 7, 9, 11, 14, 18
Find the range and IQR.
Answer:
Range = 14
IQR = 9
A data set has Q1 = 12 and Q3 = 24.
Find the IQR.
12
When solving a practical problem involving trigonometry, why should intermediate values not be rounded?
To avoid rounding error.
Two mobile phone plans are:
A=40+5x
B=70+3x
Find the number of units where both plans cost the same.
15 units.
A surveyor stands 40 m from a building. The angle of elevation is 52°.
Determine the building height.
51.2m
Data set:
4, 6, 7, 9, 10, 13, 15, 18, 21
Determine the five-number summary.
Min = 4
Q1 = 6.5
Median = 10
Q3 = 16.5
Max = 21
In a triangle, side a=12cm is opposite angle 35o. Side b is opposite angle 62o.
Find the length of side b.
Answer: 18.518.518.5 cm
A graph shows profit crossing the x-axis.
What does this point represent?
Break-even point.
Revenue is given by R=40x and costs by C=1200+25x.
Determine the break-even point.
Break-even at 80 units.
A triangular block of land has sides 85 m and 120 m with an included angle of 48∘.
Find the length of the third side.
89.4 m
A teacher records the scores of 6 students on a quiz. One score is missing.
The mean score is 18.5.
The 5 known scores are:
18, 17, 20, 19, 16
Determine the missing score.
Answer: 21
A gym offers two membership options.
Write an equation for each plan and determine after how many weeks the total cost will be the same.
Plan A:
C=12x+50
Plan B:
C=15x+20
The plans cost the same after 10 weeks.
Name three statistics commonly included in a five-number summary.