URGENT! Maths gcse questions

got an exam on monday, need help urgently.

1) Solve the equation y^2 + 5y = 0

2) ABCD is a quadrilateral.
AB = 7 cm, AD = 6 cm and BC = 9 cm.
Angle ABC = 75° and angle ADC = 90°

http://www.aqa.org.uk/qual/gcse/qp-ms/AQA-33005-H2-W-QP-JUN04.PDF (question 15)

3) A water tank is 50 cm long, 34 cm wide and 24 cm high.
It contains water to a depth of 18 cm.
Four identical spheres are placed in the tank and are fully submerged.
The water level rises by 4.5 cm.
Calculate the radius of the spheres.

http://www.aqa.org.uk/qual/gcse/qp-ms/AQA-33005-H2-W-QP-JUN04.PDF
(question 16)

Reply 1

TheTallOne

18

1)
You need to factorise. Try replace y with x and do you recognise it?

[br]y^2 + 5y = 0[br][br]x^2 + 5x = 0

2)
Try to find the length of AC and use Pythagoras to find CD.

3)
How much volume is displaced?
Each sphere has what volume?
What's the equation of the sphere?

Reply 2

eggsandbeans

Bare in mind with the first one that when factorising, variables can be equal to 0.
What one thing to y^2 and 5y have in common?

Take it out of the bracket.

Reply 3

medione

4

y^2 + 5y = 0 is a quadratic equation. You need a 2 numbers that when multipled togther equals 0, but when added eqyal 5. The numbers could be 5 and 0...
(y + 5)(y + 0)
when u multiply out the brackets you will get y^2 +5y. therefore, the answer is
y=5 or 0.

Reply 4

medione

4

2) Imagine the quadrilateral in half, so you have 2 triangles. Triangle ADC and triangle ABC.

For the perimeter, you need to find the length of side DC. To do this we can find the length of AC(b) and then use pythagarus to find the length of DC.

To find the length of AC(b) you can use the cosine formula which is shown on the formula page at the beginning.
a^2= b^ + c^2 -2bc Cos A.

in our case we need to make 'b' da subject.

b^2= a^2 + c^2 -2ac Cos B
= 9^2 + 7^2 - 2 x 9 x 7 x Cos 75 (make sure your calculator is in degrees)
= 130 - 32.61119968
= 97.38880032

remember this is b^2...we can leave this as b^2 because in pythagarus theorum we need the sides sqaured.

now we know the squared length of AC(b)...we can use pythagarus 2 find the length DC....

a^2 + b^2 = c^

making b^2 the subject....

b^2 = c^ - a^
= 97.3888032 - 6^2
= 61.38880032

now we can square root b^2, so we just have b and hence the length of DC...

= 7.83510053
= 7.83cm

lastly, we can now add up all the lengths of the sides to find the perimeter....

7.83 + 6 + 9 +7 = 29.83.

hope this is the correct answer lol

Reply 5

medione

4

This one is a bit difficult.
The qu. said that the water rose by 4.5cm.
You need to find the total VOLUME the water rose by...NOT the height it rose by.

So the volume it rose by would be...
lenght x width x height
= 4.5 x 34 x 50 = 7,650.

Now this is the volume it rose by for FOUR spheres....to find the volume of ONE sphere you need to divide by 4.... = 1912.5

Now you need to use the formula for the volume of a sphere...

Volume of sphere = 4/3 x pi x r^3.

making r^3 the subject....

r^3 = Volume divide by 4/3 and then divide by pi.
= 456.575743

now we need to cube root r^3 to find jus r...

= 7.700240297
= 7.70

I hope this is correct also lol

When you come across the harder questions, they are most likely to involve you using the formulas they provide you. The second you read/see sphere, triangle, the ax^2 + bx + c etc you will DEF have 2 refer 2 the formulas......so jus focus your thoughts on how you could use the formuals to work out the answer, insted of sitting there finkin AHHHHHHH lol

Hope ive helped and GOOD LUCK!
Hope ive helped.

Reply 6

eggsandbeans

f45

3) A water tank is 50 cm long, 34 cm wide and 24 cm high.
It contains water to a depth of 18 cm.
Four identical spheres are placed in the tank and are fully submerged.
The water level rises by 4.5 cm.
Calculate the radius of the spheres.

http://www.aqa.org.uk/qual/gcse/qp-ms/AQA-33005-H2-W-QP-JUN04.PDF
(question 16)

I don't know about anyone else, but I wasn't taught this stuff at school...

Reply 7

f45

OP

2

Thanks guys!

I thought the perimeter was just a variation of trigonometry, although I started using the traingel area formula.

I actually find it easier to understand when someone goes through their method, if I wanted answers I'd have used the mark scheme

Reply 8

A-friend99

medione

y^2 + 5y = 0 is a quadratic equation. You need a 2 numbers that when multipled togther equals 0, but when added eqyal 5. The numbers could be 5 and 0...
(y + 5)(y + 0)
when u multiply out the brackets you will get y^2 +5y. therefore, the answer is
y=5 or 0.

y=-5 or 0 because one of the brackets must equal 0 (because anything multiplied by 0 is 0) therefore y+5=0 or y+0=0 so y=-5 or 0

URGENT! Maths gcse questions

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