Challenging questions for our school mathematics

Challenging questions for our school mathematics

Made by: Usmonov Risqiboy

8th grade

Ration, proportion and Persentage

200 g of 25% sulphuric acid solution was added to 300 g of 40% sulphuric acid solution. Find the concentration of the acid in the mixture.

Amount of acid in the 1st solution = 0.25 × 200 = 50 g. Amount of acid in the 2nd solution = 0.4 × 300 = 120 g. Total amount of acid = 50 + 120 = 170 g.

∴ Required concentration = 170 / (200 + 300) × 100 = 34%

Speed, distance and time

• On the first part of a journey, a motorcyclist travels for 3 hours at an average speed of 55 miles per hour.
• On the second part of a journey, the same motorcyclist travels for 90 minutes at an average speed of 48 miles per hour.
• How far does the motorcyclist travel in total?

Explanation!!!

Distance =3 hours × 55 mph =165 miles

90 minutes =1 1/2 hours or 1.5 hours

Distance =1.5 hours×48 mph=72 miles

165+72=237 miles

Negative and Positive Numbers

A scuba diver starts at the water’s surface and then descends 40 feet below the surface. Later, the diver ascends 15 feet. What is the diver’s depth relative to the surface?
Descends means swim down.
Ascends means swim up.
Descending 40 feet is represented by – 40, and ascending 15 feet is represented by +15.
To find the diver’s final depth, we add these directed numbers:
-40 + 15 = -40 + (+15) = -25
Explanation!!!

Brackets and simplifying

3(x + 5) − 4(2x + 3)
3(x + 5) − 4(2x + 3)
= 3x + 15 − 8x – 12
= 3 − 5x
Explanation!!!

Linear equations

7-2x=2x-7
7-2x=2x-7
= -4x= -14
x=3.5
Explanation!!!

Linear equations

6x-19 =3x-10
6x - 3x = -10 + 19
3x = 9
x = 3
Explanation!!!

Simutaneous equations

3x + y = 45
z + 3y = −15
3z + x = 6
Find: x+y+z
4x + 4y + 4z = 45 − 15 + 6
4(x + y + z) = 36
x + y + z = 9
Explanation!!!

Problems solved simutaneous equations

Bob bought TV and two phones for 8$. His friend john bought two TV’s and three phones for 14$.
Find the price of TV and phone.
Note: they live on other planet.
x+2y=8 2x+4y=16 y=2
2x+3y=14 2x+3y=14 x=4
Explanation!!!
Price of TV=4$
Price of phone=2$