Year 12 Summer Quiz

Mechanics

100

State Newton's Second Law

F = ma

200

Which SUVAT equation would be most useful given v, a, s and finding u

v² = u² + 2as

300

A ball is dropped from the top of a building

The ball takes 1.5 seconds to reach the ground

Find the height the ball was dropped from

11m (2sf)

400

A vehicle of mass 2000kg is travelling along a straight horizontal road at 90kmh^-1.

It is brought to rest in a distance of 500m by a force of magnitude P Newtons.

Find P

1250 N

500

A ski slope is modelled as a plane surface inclined at 35^o. Abram (mass 60kg) starts from rest at the top of the slope. 

The coefficient of friction between his skis and the snow is 0.2. The length of the slope is 50 metres

Find his speed when he reaches the bottom of the slope. 

20ms^-1 (2sf)

Pure 1

100

Find the centre and radius of the circle with equation:

x^2+y^2-14x+16y-12=0

Centre (7, -8) 

Radius =  5\sqrt5 

200

Find the remainder when  2x^3-5x^2-16x+10 is divided by  (x-4) 

-6

300

Find the expansion of  (2x-5)^4 in ascending powers of x

 625-1000x+600x^2-160x^3+16x^4 

400

Find the equation of the normal to the curve  y=8-\sqrt 3  at the point where  x=4 

Give your answer in the form ax + by + c = 0

3y-4x+10=0

500

Solve the equation

 3^x=2^(x+1) 

x=1.7095

Pure 2

100

How many radians is equivalent to 180 degrees?

pi

200

Differentiate 

y=2^(3x)

dy/dx=3(2^(3x))ln2

300

Solve 

 4cosec^2 theta-9=cottheta 

theta=38.7^o, 219^o, 135^o,315^o

400

Given that  y=\sqrt(5x^2+1) 

Find  dy/dx when  x=4 

20/9

500

Differentiate 

 y=sinx/e^(2x) 

dy/dx=e^(-2x)(cosx-2sinx)

Maths

100

What character did Mr Tyrrell play in the staff play?

The pilot (liam)

200

What four instruments can Mr Johnson play?

Piano
Saxophone
Steel pans
Recorder

300

What car does Miss Reid drive?

Vauxhall Astra

400

Which two members of the maths department went to school at Trinity?

Mr Jonson

Mr Tomlin

500

Which member of the maths department has the most dogs?

Mr Tyrrell

1% Club

100

Rearrange the words in this calculation to make another calculation with the same answer

TWELVE + ONE

ELEVEN + TWO

200

In this puzzle, what four letter word replaces the missing part of this sentence?

"Mr Owl ate my metal ____"

worm

300

What is the first number in the English language that has its letters in alphabetical order when spelled out?

FORTY

400

These words have all been assigned a two digit number according to a certain rule. What two digit number should go with SEVENTEEN?

ONE = 12
EIGHT = 32
TEN = 21
TWELVE = 42
SEVENTEEN = ??

54

500

Which two letters replace the question marks?

TE times T equals MESSAGE
TO times IN equals POISON
E times ?? equals LEAVE

IT