“WTF was that exam,” was the resounding sentiment of HSC students in New South Wales after Monday’s mathematics papers.
More than 60,000 students sat exams across Mathematics Standard 1 and 2, Mathematics Advanced and Mathematics Extension 2. Mathematics Extension 1 students have to wait another week to sit their exam.
“The paper just kept getting worse,” one student posted to a Facebook discussion group after the Advanced paper.
“I was holding in tears.”
The Standard 2 exam, sat by more than half of all HSC maths students, received particular spite.
“After that Math Standard exam I’m officially marrying a rich man,” one student posted to a Facebook group.
Another wrote: “Was that … exam written by the CEO of… Westpac? WHY WAS THERE SO MUCH FINANCE”.
“What the actual hell,” another student said, discussing the paper on TikTok. “That was quite difficult, and I also didn’t finish. But whatever … no more maths!”
An ominous question about a wombat was a crowd favourite to hate. “Chat I got 1350 seconds for the Wombat question, am I cooked,” one student mused on Facebook.
And now you can give it a try.
Here are some questions pulled from the HSC maths exams so far. Calculators approved by the NSW Education Standards Authority were permitted for all three exams.
How many can you answer?
Mathematics Standard 1
Question 5 (one mark):
A car is valued at $25,000 when new. Its value depreciates by 25% per annum.
Which of the following best describes the change in value of the car after one year?
A. Decrease of $1,000
B. Increase of $1,000
C. Decrease of $6,250
D. Increase of $6,250
Question 9 (one mark):
An equilateral triangle and an isosceles triangle are shown.
The triangles have the same perimeter.
What is the value of x ?
A. 8
B. 9
C. 11
D. 12
Question 24 (3 marks):
Students in two classes, Class A and Class B, recorded the number of text messages they sent in a day. Each class has 18 students.
The results are shown in the dot plots.
Compare the two datasets by examining the skewness, median and spread of the distributions.
Mathematics Standard 2
Question 1 (one mark):
If x = -2.531, what is the value of x^2 rounded to 2 decimal places?
A. -6.41
B. -6.40
C. 6.40
D. 6.41
Question 7 (one mark):
Three years ago, the price of a uniform was $180.
Due to inflation, the price increased annually by 2.5%.
What is the price of this uniform now?
A. $180.14
B. $181.35
C. $193.50
D. $193.84
Question 29 (four marks):
The graph shows the decreasing value of an asset.
For the first 4 years, the value of the asset depreciated by $1,500 per year, using a straight-line method of depreciation.
After the end of the 4th year, the method of depreciation changed to the declining-balance method at the rate of 35% per annum.
What is the total depreciation at the end of 10 years?
Question 33 (three marks):
Wombats can run at a speed of 40 km/h over short distances.
At this speed, how many seconds would it take a wombat to run 150 metres?
Mathematics Advanced
Question 1 (one mark):
Consider the function shown.
Which of the following could be the equation of this function?
A. y = 2x + 3
B. y = 2x - 3
C. y = –2x + 3
D. y = -2x - 3
Question 11 (3 marks):
The graph of the function g(x) is shown.
Using the graph, complete the table with the words positive, zero or negative as appropriate.
Question 19 (5 marks):
Sketch the curve y = x^4 - 2x^3 + 2 by first finding all stationary points, checking their nature, and finding the points of inflection.
Question 31 (6 marks):
Two circles have the same centre O. The smaller circle has radius 1 cm, while the larger circle has radius (1 + x) cm. The circles enclose a region QRST, which is subtended by an angle θ at O, as shaded.
The area of QRST is A cm^2, where A is a constant and A > 0.
Let P cm be the perimeter of QRST.
(a) By finding expressions for the area and perimeter of QRST, show that P(x) = 2 x + 2A / x
(b) Show that if the perimeter, P(x), is minimised, then θ must be less than 2.
