smc-985-40-Simultaneous Equations

Functions, 2ADV F1 2020 HSC 11

There are two tanks on a property, Tank and Tank . Initially, Tank holds 1000 litres of water and Tank B is empty.

Tank begins to lose water at a constant rate of 20 litres per minute. The volume of water in Tank is modelled by where is the volume in litres and is the time in minutes from when the tank begins to lose water. (1 mark)

On the grid below, draw the graph of this model and label it as Tank .
Tank remains empty until when water is added to it at a constant rate of 30 litres per minute.

By drawing a line on the grid (above), or otherwise, find the value of when the two tanks contain the same volume of water. (2 marks)
Using the graphs drawn, or otherwise, find the value of (where ) when the total volume of water in the two tanks is 1000 litres. (1 mark)

--- 2 WORK AREA LINES (style=lined) ---

Show Answers Only

Show Worked Solution

Functions, 2ADV F1 EQ-Bank 12

Two archers play a game where each can aim for a large target or a small target.

If an arrow hits the large target it scores points, and if it hits the small target, it scores points.

The results of a game are shown in the table below.

By forming a pair of simultaneous equations, or otherwise, find the value of and . (3 marks)

--- 8 WORK AREA LINES (style=lined) ---

Show Answers Only

Show Worked Solution

Algebra, STD2 A2 2019 HSC 14 MC

Last Saturday, Luke had 165 followers on social media. Rhys had 537 followers. On average, Luke gains another 3 followers per day and Rhys loses 2 followers per day.

If represents the number of days since last Saturday and represents the number of followers, which pair of equations model this situation?

A.
B.
C.
D.

Show Answers Only

Show Worked Solution

Algebra, STD2 A4 SM-Bank 6 MC

A computer application was used to draw the graphs of the equations

and

Part of the screen is shown.

What is the solution when the equations are solved simultaneously?

Show Answers Only

Show Worked Solution