Download Exercise 4.1

Pui Ying College
F.1 Mathematics
Chapter Four --- Linear Equations in one unknown
Supplementary Exercise
Name: ______________
Class: __________ ( )
Date: _______________
Exercise 4.1
1.
There are two numbers x and y, x is 25 larger than y. Write an equation to represent the
above information.
2.
The length of a straight line is x cm. The length of another straight line is (2 x  1) cm.
Their total length is 50 cm.
Write an equation to represent the information above.
3.
Susan has x books. Samuel has 7 books more than 3 times those of Susan. They have
totally 75 books. Write an equation to represent the information above.
4.
The sum of three consecutive numbers is 36. Let the smaller number be x. Write an
equation to represent the sum of the three numbers.
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Exercise 4.2
Solve the following equations
1.
9
v
 16
4
2.
v
 13  18
5
3.
2x  3  x  7
4.
52x  7  33x  4
5.
42x  5  3x  10
6.
3x  2x  6  5x  32
7.
7x  1  4x  3  3
8.
22x  1  52  3x  50
9.
8 x  7 3x  8

7
2
10.
x x
x
  9
3 4
6
2
11.
x x5

 x4
3
7
13.
2
3x  8  4
5
15.
5x  4
 10  14
6
17.
62  x  42  x  3x  8
12.
x  11 x  1 x


2
4
3
14.
43x  8  13  17
16.
18.
7
3x  5  6  22
4
32x  57  3x  47  5x  9
3
19.
x  1 x  5 2x  3


3
12
15
20.
2x  3 3 x  3 2x  7
 

6
4
12
15
21. Find the value of the unknown in the formula:
A
1
a  b h , given that a=12, h=15 and A=225.
2
22. Find the value of the unknown in the formula:
S
n
2a  n  1d , given that a=11, n=7 and S=161.
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Exercise 4.3
1. A plant of height 10 cm grows by 3 cm every week. How many weeks later will it be 28
cm tall?
2.
The sum of two consecutive even integers is 54. What are the two numbers?
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3.
A farmer surrounded his farmland using 130 m of wire. 6m of wire was left after he had
surrounded his farmland 4 times. Find the perimeter of his farmland.
4.
A mother is 5 times as old as her daughter. 4 years later, the mother will be 34 years old.
How old is the daughter now?
5.
A father is 4 times as old as his son.
old is the son now?
6.
Raymond bought 20 cans of soft drinks. Some of them cost $3.8 each and the others
cost $3 each. If he paid $62.4 for the soft drink, how many cans of soft drinks of $3 each
did he buy?
7.
The selling price of a computer is $ 13 000. Customers can pay $2 200 as down
payment, and pay the remaining cost in 12 equal instalments. How much is each
instalment?
10 years ago, the sum of their ages was 60. How
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8.
In a mathematics test, Flora got 3 marks less than half of Henry’s mark.
If Flora got 42
marks, how many marks did Henry get?
9.
Mrs. Lee bought 5 cups and 3 plates. The selling price of a plate was $2 higher than that
of a cup. If she spent $86 on them, what was the selling price of a cup?
10. n is the smallest integer among three consecutive integers.
(a) Express the other two integers in terms of n.
(b) Express the sum of these three integers in terms of n.
(c) If the sum of these integers is 87, find the value of n.
11. The three sides of a triangle are 2 x  3 y  cm, 3x  7 cm and 7 y  x  cm respectively.
(a) Express the perimeter of the triangle in terms of x and y.
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(b) If x  4 and y  2 , what is the perimeter of the triangle?
(c) If the perimeter of the triangle is 47 cm and y  3 , find the value of x.
Revision exercise 4
1.
Solve each of the following equations.
a.
2
x  1  27
3
b.
c.
5x  7  2x  11
d.
5  4x
7
3
3x  1  7x  12  12
7
e.
2
2 x  3  x  1
5
f.
3x  4 51  4 x 

4
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2.
A watermelon and 8 apples cost $72.
apple?
If a watermelon costs $32, what is the cost of each
3.
Tony bought 4 exercise books and 3 pens for $18.4.
was the cost of a pen?
4.
A box of candies was divided among 8 children. Each child got 7 candies, and 3 candies
were left in the box. How many candies were there in the box originally?
5.
Write an equation to represent each of the following.
If an exercise book cost $25, what
(a) The weight of oil in a bottle was x g originally. Any used
2
of the oil and 80 g were
3
left.
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(b) The original bus fare was $x. The new fare is
5
of the original fare, and the new
4
fare is $5 higher than the original fare.
6.
Solve each of the following equations.
(a)
x  2 2x  1 5


4
3
2
(c)
1
1
3
(2 x  1)  x  5  2
2
4
8
(e)
342x  1  5x  9  6x  4
(b) 12  3x  2x  4  7  6
(d)
1
1
2 x  7   4 x  11  x  4
6
3
2
9
mv  u 
, find the value of v when m = 3, u = 12, t = 4 and F = 21.
t
7.
Given a formula F 
8.
2
Given a formula V  r 3  r 2 h , find the value of h when   3, r = 2 and V= 76.
3
9.
The total thickness of 5 history books and 8 mathematics books is 47 cm. Suppose a
history book is 3 cm thick.
(a) What is the thickness of a mathematics book?
(b) What is the total thickness of 6 history books and 7 mathematics books?
End
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