Doing Maths # 1

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What is the meaning of y = mx + c?

y is called the dependent variable. It depends on the value of x, the independent variable. Let us take an example. If we are paid a salary depending on the following formula:

What we are paid is $5.00 for each piece of work we produce plus a fixed amount of $15 for our transportation, we can express this as a formula: y = 5x + 15. The y is the $ amount we get paid (the dependent variable) and is always dependent of x (the number of artwork produced - the independent variable).

The line y = 5x + 15 is shown in the graph below:

Question # 1: The hourly rate of pay in a factory is $12 per hour. The factory operates a five working days a week with weekends off. Each working day is eight hours and workers are allowed to work up to three hours overtime a day. Overtime is paid at the rate of one-and-a-half of the normal rate. (a) What is the pay of a worker who has done 45 hours of work this week? (b) Express the formula for calculating the pay of any worker who works in excess of 40 hours in a week. (c) Draw the graph line of the formula written in answer to (b).

Question # 2: The area of a rectangular piece of paper is x2 + 2x -3. [x squared plus 2x minus 3]. If one side of this rectangle is (x + 3) (a) What is the value of the other side in terms of x? (b) If x = 4 cm, what is the area of the rectangle in square cm?

Question # 3: (a) If a sunflower grows 7/8 of a centimeter every day, how much taller will it be after four weeks?

Question # 3 (b) The same sunflower is a meter tall now. In how many days time will it grow to a height of 71 centimetres?

Question # 4: Factorise the following expressions: [Factorise means to find the factors or numbers that will multiply out to the expression given. For instance, what the the factors of the expression [12 + 3]? 12 + 3 = 15, factors of 15 are 1 and 15; and 3 and 5.

Question # 4(a): 6m - 2; # 4(b) 3cd - 6c; # 4(c) x2 - 5x + 6 or [x squared minus 5x plus 6]; # 4(d) 5a2 - 7a - 24 or [5 a squared minus 7a minus 24]; # 4(e) am + mp + an + np.

Question # 5: This lean-to storage shed has a side elevation like the diagram shown here. Its width is 20 meters and its two wall heights are 20 meters and 35 meters respectively.

Question # 5(a) Calculate the area of this end wall.

Question # 5(b) If the storage shed is 40 meters long, calculate the volume of space that this storage shed in cubic meters.

Question # 5(c) If there is a door opening measuring 12 meters wide by 16 meters high and two end windows, each 6 meters wide by 3 meters high, calculate the areas of all the internal walls to be painted.

Question # 5(d) If a 5 litres of paint can cover 10 square meters, calculate how many litres of paint is required to do two coats of the painting of the internal walls.