Memory Aid | Mathematics — Secondary 4 (SN)

Find the result of the following division:

Simplify the following algebraic expression:

|\displaystyle \frac{x-2}{x+5} - \frac{3}{-3x-12}|​

Find the simplified algebraic expression for the following multiplication: ||(7x+4)(2x^2-4x+3)||

Use the information provided in the table below to determine the parabola’s equation in its three different forms.​

For second-degree polynomial functions: |a \ne \dfrac{\Delta y}{\Delta x}|

A grocery store has a new reward program that offers stamps for discounts on certain items.

Customers receive five stamps with a minimum purchase of $5. They receive seven more stamps for every additional $22 they spend.

Using this information, what interval corresponds to a customer's total bill if they receive 47 stamps from their purchase?

Sketch the inverse of the following function:

The inverse of a function is not always a function itself. In the cases studied here, these functions are inverses of each other:

• Exponential and logarithmic functions;

• A linear function with respect to itself;

• A second-degree function (with a restricted domain) and a square root function​.

As an accountant of a large company, you must give a detailed account of the trends in profits over the past year. To help, here is a graph of the last 12 months.

You must perform a complete study of this graph to prepare for your presentation speech and properly support your argument.

To respect the constraints imposed by the city, an entrepreneur must divide his wooded lot into two different rectangular lots.

Given that the area of the lots must be equivalent, determine the possible dimensions, in decametres, of these two lots.

To make the cost of paving his new driveway the same as paving his old one, Julien wants the two driveways to be equivalent.

​​

What should be the width of his new driveway?

A company that works with outdoor gear wants to offer two different tent models. To keep production costs the same, they want these two models to be equivalent.

What must be the height of the second model for the tents to be equivalent?

Using the angle |\theta| as a reference, we have:

|\sin \theta = \dfrac{\text{Measure of the side opposite}\ \theta}{\text{Measure of the hypotenuse}}|

|\cos \theta = \dfrac{\text{Measure of the side adjacent}\ \theta}{\text{Measure of the hypotenuse}}|

|\tan \theta = \dfrac{\text{Measure of the side opposite} \ \theta}{\text{Measure of the side adjacent to} \ \theta}|

A house's roof trusses must have a minimum angle of elevation of |25^\circ| to meet building standards. To ensure that this constraint is respected, a manufacturer decides to establish this angle at |35^\circ.| If we know that the length of the roof truss is 13 metres, what are the measurements of the other two sides?

​

To determine the route a helicopter should take to pick up distressed people in the forest, a map of the region has been triangulated with the current locations of the helicopter, the hospital, and the people in distress.

According to this drawing, what angle of orientation should the helicopter use to reach the people as quickly as possible?

​|\dfrac{a}{\sin A} = \dfrac{b}{\sin B} = \dfrac{c}{\sin C}|

Horse races are sometimes organized during western festivities to liven up the events. During these races, cowboys must ride around each of three barrels, which are arranged in the shape of an isosceles triangle.

Using the measurements provided, what is the distance between each of the barrels?

To ensure maximum aerodynamics, the shape of some racing cars resembles a triangle.

What should the angle closer to the back wheel measure for these proportions to be maintained?

When identifying triangles, it is always essential to identify

​|a^2 = \color{blue}{b}^2 + \color{red}{c}^2 - 2 \color{blue}{b} \color{red}{c} \cos A|

|\color{blue}{b}^2 = a^2 + \color{red}{c}^2 - 2 a \color{red}{c} \cos \color{blue}{B}|

|\color{red}{c}^2 = a^2 + \color{blue}{b}^2 - 2 a \color{blue}{b} \cos \color{red}{C}|

A hunter, who uses a bow, settles in the corner of his land to maximize his chances of hunting a moose. The following triangle shows the range of his arrows:

Based on the information provided, what |\color{red}{\text{distance}}| can the moose walk while staying as far as possible from the hunter?

A bank is installing a rotating surveillance camera in its entrance hall to keep its employees safe. In addition, a security guard is in charge of monitoring the same area, defined by the following triangle:

What should the camera's rotation angle measure to ensure that there are no blind spots?

Find the area of the following triangle:

Due to machinery problems, construction workers need to complete the construction of a house by assembling the triangular-shaped roof trusses themselves. All of the trusses must be identical.

With the information provided above, demonstrate that these two constructions are congruent.

The city is organizing a family run as part of a fundraiser for a community organization. They want the adults to take a path similar to that of the children.

Taking into account the information provided, demonstrate that the two paths are similar.

To stand out from other contractors, a construction company suggests houses with roofs of different shapes. Among these choices, we have the following shape:

To estimate production costs, the company needs the two missing outer measurements of triangle |(\overline {AB}, \overline {BC}).| Help determine them.

|\text{Distance} = \sqrt{(y_2 - y_1)^2 + (x_2 - x_1)^2}|

where

|(x_1, y_1):| Coordinates of the starting point of the segment

|(x_2, y_2):| Coordinates of the ending point of the segment

To determine the amount of gasoline an airplane needs to complete a Montreal-Paris flight, the cities are represented on a Cartesian plane (graduated in kilometres).

What is the distance between these two cities (in kilometres)?

What is the equation of the line parallel to that identified in the Cartesian plane below and which passes through point C?

What is the equation of the line perpendicular to that in the Cartesian plane below and which passes through point C?​

A new company has increased its profits for five years and seeks to expand its production centre. However, the owners want to ensure that their company’s economic growth is positive and strong. To break it all down, here's a count of business income for the past 30 weeks.

In your opinion, is the economic growth of the company positive and strong?

To understand the success of students who enroll in adult education, an administration team is interested in the correlation between absenteeism (in hours) and final grades (in %). They grouped the data into a scatter plot to properly analyze the situation:

​

What is the correlation coefficient of this study?

Before a new condo tower is built and the landscaping is done, the height of the neighbouring trees is measured so they do not obscure the view for the next 20 years. The following table of values is used to estimate the height of the trees:

Using this information, determine how high the first balconies need to be for the view to remain unobstructed.

Although the situation and data are the same, it is normal that the final answer varies depending on the method used (Median-Median method or Mayer method).

Since these methods are used to estimate and not to predict outcomes with certainty, there may be a difference between the two outcomes.

Before a new condo tower is built and the landscaping is done, the height of the neighbouring trees are measured so they do not obscure the view for at least 20 years. The following table of values is used to estimate the height of the trees:

Using this information, determine how high the first balconies need to be for the view to remain unobstructed.

Although the situation and data are the same, it is normal that the final answer varies depending on the approach used (Median-Median method or Mayer method).

Since these methods are used to estimate and not to predict outcomes with certainty, there may be a difference between the two outcomes.