Anglo-Chinese School (Barker Road)
Mathematics December 2016 Holiday Homework – Sec 1 Express
Name: ______________________________ (
) Date: ___________ Class: _________
1.
The ratio of the price of a grapefruit to the price of an apple is 2 : 1. A grapefruit can
be bought at 90 cents.. Express the number of apples that can be bought with y dollars.
2.
Given that y 
3.
Given that x = −2, evaluate 5x 2  3x .
4.
Express
5.
Factorize 15a + 3a2 completely.
6.
Factorise 2cv  c  2v  1.
7.
Solve
8.
Solve 5(7m – 3) = 14(2m + 5).
9.
The rectangular plot of land shown below measures (2x + 5) metres by 16 metres.
A path 3 metres wide runs around the edge of the land.
(a)
(b)
(c)
2x  z
, express x in terms of w, y and z.
w
x  2 x 1
as a single fraction in its simplest form.

4
6
1  x 2x  1

1 .
2
5
Show that the area of the garden can be expressed as 10(2x – 1).
Given that the area of the path is 138 square metres, find the value of x.
Hence, find the area of the land.
10.
Write down the nth term of this sequence.
1, 4, 7, 10, 13, 16, 19, …
11.
Solve the inequality 6p −3 ≥ 48 and write down the smallest prime number that satisfy
the inequality.
1
12.
Solve the inequality  18  2 x  14  3(9  5x)  10 .
13.
The diagram shows parallelogram WXYZ where ZY = 15 cm and XY = 9 cm.
If ZX = 12 cm, find the length of ZV.
14.
Convert 5 m3 to cm3.
15.
A metal container shown below is used to make large blocks of ice.
(a)
(b)
Find the amount of water required to fill the container fully.
Assuming that the container has a cover, find the total surface area of the
container.
16. An open cylindrical container has height 50 cm and radius 18 cm. It contains water up
to a depth of 42 cm.
Taking
,
(a) calculate the volume of the water, in litres, in the container, (1 litre = 1000 cm3)
give your answer to the nearest litres,
(b) find the surface area of the container in contact with the water,
give your answer to the nearest cm2.
17.
Write down all the prime numbers considering the following numbers.
3
, 0.25,
11
7 , 29, 12,
169 , 81, 17, 144, 
2
18.
19.
(a)
Using prime factorisation, express 576 as a product of its prime factors. Leave
your answer in index notation.
(b)
Hence, find the value of 576 without the use of calculator.
The numbers A and B, expressed as products of their prime factors are given below.
A  2 2  3 4  5 2  116
B  33  53  116
Find, in index notation
(a)
the LCM of A and B,
(b)
the HCF of A and B,
(c)
the cube root of B.
20.
In a particular town, the temperature at 05 00 was  6C and it rises at a uniform rate
to reach a temperature of 20C at 18 00.
(a) Find the difference in temperature.
(b) Find the time when the temperature was 9C .
21.
Round off 349592.4973 to
(a) 2 significant figures,
(b) 2 decimal places.
22.
A car travels 150 km on 15 litres of petrol. What is the rate of petrol consumption in
(a) km per litre?
(b) litres per km?
23
Convert 7.2m/s to km/h.
24.
A map is drawn to a scale of 1 : 25000.
(a) The distance between two towns on the map is 15 cm. Find the actual distance,
in kilometers, between the two towns.
(b) A lake has an actual area of 3.5 km2. Find the area, in square centimeters, of the
lake on the map.
25.
A car travels at an average speed of 80 km/h for half an hour on an expressway. It rests
for 30 minutes, then it travels at an average speed of 60 km/h for 10 minutes on a road
before arriving at its destination.
(a) Calculate the total distance traveled in km.
(b) Calculate the average speed of the car for the whole journey in km/h.
26
A hawker wants to buy a refrigerator which costs $1 500 on a hire purchase scheme.
1
The deposit is of the price. There is a 4% simple interest charge on the balance
3
amount, which he has to pay in 10 months. Find,
(a) the amount for the deposit,
(b) the monthly installment the hawker has to pay.
3
27.
David invests $20 000 at 3% per annum compound interest compounded halfyearly. How much interest will he receive at the end of 10 years?
28.
In a fund raising, the cost of making a bookmark is $0.50. A total of 600 bookmarks
are made.
(a) Find the total cost of the 600 bookmarks.
(b) 480 of the bookmarks are sold at $0.70 each, 90 of them are sold at the cost price
and the remaining is sold at a discount of 20% of the cost price. Calculate the
overall
(i) profit or loss,
(ii) profit or loss as a percentage of the cost price.
29. The exterior angle of a five-sided polygon are in the ratio of 1 : 2 : 2 : 3 : 4. Find the
size of the smallest interior angle of the polygon.
30.
In a 6-sided polygon, 3 of the interior angles are 105, 99 and 120 . If the size of each
remaining interior angle of the polygon is x ,
(a) calculate the sum of the interior angles of the 6-sided polygon,
(b) calculate the value of x.
[Answer Key]
1.
20
y
9
3.
26
5.
3a(5 + a)
7.
x = −13
9(b) x = 7.4
10. 3n – 2
12.  2  x  3
14.
5 000 000 cm3
16(a) 43 litres
18(a) 576  2 6  32
19(a) 2 2  34  53  116
20(a) 26C
21(a) 350000
23. 25.92 km/h
25(a) 50 km
27. $6937.10
29. 60o
yz  a
2
x4
4.
12
6.
(2v  1)(c  1)
1
8.
12
7
9(c) 316.8 m2
11. p ≥8.5; 11
13. 7.2 cm
15(a) 20 800 cm³
17.
169 , 17, 29
x
2.
2
(b) 5769 cm
(b) 24
(b) 33  5 2  116
(b) 12 30
(b) 349592.50
(b) 42.9 km/h
(c)
3
22(a)
24(a)
26(a)
28(a)
30(a)
(b) 9408 cm²
B  3  5  112
10km/litre
(b) 0.1litre/km
3.75 km
(b) 56 cm2
$500
(b) $103.33
$300
(b) (i) $93
b(ii) 31%
720
(b) 132
4