This mock exam is designed to test your mastery of Units 1 and 2 of the QCAA Essential Mathematics syllabus. It covers practical applications in finance, logistics, data analysis, and measurement, focusing on the precision required for high-achieving students.
Mock Exam: Essential Mathematics Units 1 & 2
I have generated 10 comprehensive questions that span the key chapters of Units 1 and 2, focusing on the higher-level applications suitable for an excellent student. Good luck with your preparation—pay close attention to the units and the context of each problem!
1.
A builder measures the length of a room to be 4.50 m. However, the actual length is 4.58 m. Calculate the percentage error of this measurement, rounded to two decimal places.
A. 1.78%
B. 0.08%
C. 1.75%
D. 0.02%
Hint: Start by finding the absolute difference between the measured and actual values.
2.
A water tank is in the shape of a cylinder with a radius of 2 m and a height of 3 m. If the tank is currently half full, how many liters of water are inside? (Use π≈3.14 and recall 1 m3=1000 L)
A. 37,680 L
B. 18,840 L
C. 9,420 L
D. 12,000 L
Hint: Calculate the total volume using the cylinder formula first, then divide by two.
3.
The formula for simple interest is I=Prt. If a student earns $450 in interest over 3 years on an investment of $5,000, what was the annual interest rate (r)?
A. 9%
B. 3%
C. 1.5%
D. 0.03%
Hint: Rearrange the formula to isolate r before substituting the known values.
4.
A dataset of five employees’ weekly wages is: $800,$850,$850,$900,$2,500. Which measure of central tendency would be the most ‘fair’ representation of the typical wage?
A. Total Sum
B. Median
C. Range
D. Mean
Hint: Look at the data for any values that are significantly different from the others.
5.
A flight leaves Brisbane (UTC+10) at 10:00 AM on Monday and arrives in Perth (UTC+8) after a 5.5-hour journey. What is the local time in Perth upon arrival?
A. 11:30 AM Monday
B. 1:30 PM Monday
C. 3:30 PM Monday
D. 12:30 PM Monday
Hint: Convert the departure time to the destination’s time zone before adding the travel time.
6.
A truck has a fuel consumption rate of 12 L/100 km. If diesel costs $1.85 per liter, how much will fuel cost for a 450 km trip?
A. $22.20
B. $120.00
C. $99.90
D. $83.25
Hint: First determine the total liters of fuel needed for the entire distance.
7.
An employee earns $25 per hour for a 38-hour week. Any hours over 38 are paid at ‘time-and-a-half’. If they work 42 hours in one week, what is their gross pay?
A. $1,100
B. $1,050
C. $1,000
D. $1,575
Hint: Calculate the normal pay and the overtime pay separately, then add them together.
8.
A scatter plot shows the relationship between daily temperature and ice cream sales. If the points generally follow a straight line going upwards from left to right, what is the correlation?
A. No Correlation
B. Positive Correlation
C. Inverse Correlation
D. Negative Correlation
Hint: Consider if both variables are moving in the same direction.
9.
Which of the following describes ‘Interpolation’ in the context of a line of best fit?
A. Predicting a value that lies outside the range of the original data points.
B. Identifying an outlier in the dataset.
C. Calculating the average of all data points.
D. Predicting a value that lies within the range of the original data points.
Hint: Think about whether the prediction is inside (‘inter’) or outside (‘extra’) the current data set.
10.
Supplier X sells a 5 kg box of screws for $45. Supplier Y sells a 2 kg box for $20. Which is the better value based on unit price?
A. They are the same value
B. Supplier X is better value
C. Supplier X is more expensive per unit
D. Supplier Y is better value
Hint: Calculate the cost per single kilogram for both suppliers to make a fair comparison.