# Grade - examples - page 206

- Curve and line

The equation of a curve C is y=2x² -8x+9 and the equation of a line L is x+ y=3 (1) Find the x co-ordinates of the points of intersection of L and C. (2) Show that one of these points is also the stationary point of C? - Iron density

Calculate the weight of a 2 m long rail pipe with an internal diameter of 10 cm and a wall thickness of 3 mm. The iron density is p = 7.8 g/cm3. - Volume of ball

Find the volume of a volleyball that has a radius of 4 1/2 decimeters. Use 22/7 for π - Train speed

Two guns were fired from the same place at an interval of 10 minutes and 30 seconds, but a person in a train approaching the place hears second shot 10 minutes after the first. The speed of the train (in km/hr), supposing that sound travels at 340 m/s is: - Construct

Construct a triangle ABC inscribed circle has a radius r = 2 cm, the angle alpha = 50 degrees = 8 cm. Make a sketch, analysis, construction and description. - Area of a triangle

What is the area of a triangle that has the base 4 1/4 and the height of 3 3/3? - The length

The length of a rectangle is 6 meters less than twice the width. If the area of the rectangle is 216 meters, find the dimensions of the rectangle. - Winery

The wine processing plant sold 8/15 of its total wine production to the domestic market, 2/7 to the foreign the rest of the wine. How many percents are still in stock? - Circus

On the circus performance was 150 people. Men were 10 less than women and children 50 more than adults. How many children were in the circus? - Equations - simple

Solve system of linear equations: x-2y=6 3x+2y=4 - Evaluation of expressions

If a^{2}-3a+1=0, find (i)a^{2}+1/a^{2}(ii) a^{3}+1/a^{3} - Together

If 8 men, 10 women, 16 children collects ₹1024 in 4 days, how many days will be required for 6 men, 5 women and 4 boys to collect ₹768? (₹ is Indian Rupee) - 12 apples

12 apples and 2 loaves of bread cost 5.76 and 6 apples and 3 loaves of bread cost 7.68. How much is a loaf of bread? - Radioactive material

A radioactive material loses 10% of its mass each year. What proportion will be left there after n=6 years? - Alice

Alice spent 5/11 of her money on a back pack. She has $42 dollars left. How much was her back pack? - Supplementary angles

One of the supplementary angles is larger by 33° than the second one. Calculate the angles size. - Discount sale

At Christmas Sale after a 20% discount cosmetic package was priced at a price of 5 euros and 60 cents; later it went to 3 euros and 80 cents. How much percentage is the total discount? - Account operations

My savings of php 90,000 in a bank earns 6% interest in a year. If i will deposit additional php 10,000 at the end of 6 months, how much money will be left if i withdraw php 25,000 after a year? - Simplify 3

Simplify mixed numerals expression: 8 1/4- 3 2/5 - (2 1/3 - 1/4) Show your solution. - Reducing scale

I am sizing some landscaping and I measured everything for a 20 to 1 scale. I realized when I was done that it was at 30 to 1. How can I convert what I already have to 30 to 1. (Example, grass area is 22,871.6' at 20 to 1, how do you figure it out to be 30

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