# maths

1.How many seconds are there in a week?(Leave your answer in scientific notation)

2.After an English test, John and David write an expression on the test paper to display their test marks."@" respresents 1, while "*"represents 0.

John:@*@*@*@

David: @@@@**

(a) How many marks did each get in the test in denary scale?

(b) Who had got the highest mark?

(c) Express twice the difference of their marks in denary scale.

3. If Qwxceeds P by 50% and R exceeds Q by 50%, find P:R.

4.Suppose Amy paid \$x for a camera.

(a) Amy sold it to Peter at a loss of 20%. Express, in trem of x, the amount Peter paid.

(b) Peter sold it to Alice at a gain of 10%. Express, in term of x, the amount Alice paid.

(c)Alice paid \$2640 for it. Find the loss Amy made.

5. Find the marked unknown lengths in each of the following:

Rating

1.

Seconds in a week

=60*60*24*7

=36*24*7*10^2

=6048*10^2

=6.048*10^5

2a.

Marks that John got

=1*2^6+0*2^5+1*2^4+0*2^3+1*2^2+0*2^1+1*2^0

=85marks

Marks that David got

=1*2^5+1*2^4+1*2^3+1*2^2+0*2^1+0*2^0

=60marks

2b.

John got a higher mark.

2c.

Twice the difference of their marks

=2(85-60)

=2(25)

=50

3.

From the question, Q=(1+50%)P and R=(1+50%)Q.

Then Q=1.5P...(1) and R=1.5Q...(2)

Put (1) into (2),

R=1.5(1.5P)

R=2.25P

R: P=9:4

P: R=4:9

4a.

Amount Peter paid

=(1-20%)x

=\$0.8x

4b.

Amount Alice paid

=(1+10%)(0.8x)

=1.1(0.8x)

=\$0.88x

4c.

0.88x=2640

x=3000

=(20%)(3000)

=\$600

5.

Since BC//DE, ∠ABC=∠ADE and ∠ACB=∠AED (corresponding angles, // lines)

Also, ∠BAC=∠DAE (common)

x:12=12:(12+4)

x=9