New Senior Secondary Mathematics
Advanced Exercise Ch. 08: Advanced Equations
ADVANCED EXERCISE CH. 08: ADVANCED EQUATIONS
[Finish the following questions if you aim at DSE Math Level 4]
Q1 [CE Math 87B 3]
Solve the equation 3
3
Q2 [CE Math 84 6]
Solve the equation
5√
Q3 [CE Math 82 7]
Solve the equation
√
2
0.
6
0.
5.
1
Q4 [CE Math 81 5]
Solve the equation 4
10
Q5 [CE Math 85B 3]
Solve the equation 2
3 2
4
1
4
.
0.
Q6 [CE Math 82A 8]
Figure 3 represents the framework of a cuboid made of iron wire. It has a square base of side x cm and a
height of y cm. The length of the diagonal AB is 9 cm. The total length of wire used for the framework
(including the diagonal AB) is 69 cm.
(a)
(b)
Find all the values of x and y.
Hence calculate ∠
to the nearest degree for the case in which
.
[Finish the following questions if you aim at DSE Math Level 5]
Q7 [CE Math 86B 14]
The figure shows the graph of
.
(a)
Find the value of c and hence the values of a and b.
(b)
Solve the following equations by adding a suitable straight line to the
figure for each case. Give your answer correct to 1 decimal place.
(i)
2
3
1
2
1 0
(ii)
Page 1
(10 marks)
(2 marks)
New Senior Secondary Mathematics
Advanced Exercise Ch. 08: Advanced Equations
Q8 [CE Math 81 9]
Normally, a factory produces 400 radios in x days. If the factory were to produce 20 more radios each day, then it would take 10 days
less to produce 400 radios. Calculate x.
Q9 [CE Math 85B 12]
ABC is an isosceles triangle with ∠ = 90 . PQRS is a rectangle inscribed in Δ
, BC =
16 cm, BQ = x cm.
(a)
Show that the area of
= 2(8 − ) cm2.
(b)
The figure shows the graph of = 8 −
for 0 ≤ ≤ 8. Using the graph,
(i) find the value of x such that the area of PQRS is greatest;
(ii) find the two values of x, correct to 1 decimal place, such that the area of PQRS is 28 cm2.
(c)
(i) If the area of PQRS is greater than four times the area of Δ
by 8 cm2, show that
− 4 + 2 = 0.
(ii) Draw a suitable straight line in the figure and hence find, correct to 1 d.p., the two roots of the equation in (c)(i).
Page 2
New Senior Secondary Mathematics
Advanced Exercise Ch. 08: Advanced Equations
Q10 [CE Math 81 11]
A piece of wire 20 cm long is bent into a rectangle. Let one side of the rectangle be x cm long and the area by y cm2.
(a)
(b)
Show that
10 − .
The figure shows the graph of = 10 −
for 0 ≤ ≤ 10. Using the graph,
(i) find the value of y, correct to 1 d.p., when = 3.4.
(ii) find the values of x, correct to 1 d.p., when the area of the rectangle is 12 cm2.
(iii) find the greatest area of the rectangle.
(iv) find the value of x for which y is three times x, by drawing a suitable line on the graph..
Page 3
New Senior Secondary Mathematics
Advanced Exercise Ch. 08: Advanced Equations
Q11 [CE Math 80 16]
The figure shows the graph of
. By drawing suitable lines in the figure, solve the following:
(a)
2 − 5 = 0.
(b)
− 2 − 5 > 0.
(c)
2 − 2 − 5 = 0.
Answers should be corrected to 1 d.p., all lines should be labelled.
Answer:
1. 0
2. 36
3. 8
4.
$
5. 2
6.(a)
= 6,
= 3 or
= 4,
= 7 (b) 39'
7 (a) = −1, = 1, = 6 (b)(i) -1.8, 2.8 (ii) -0.4, 2.4
8. 20
9. (b)(i) 4 (ii) 2.6, 5.4 (c)(ii) 0.6, 3.4
10(b)(i) 22.4 (ii) 1.4, 8.6 (iii) 25 cm2 (iv) 7.0
11 (a) -1.8, 2.8 (b) > 2.8 )* < −1.8 (c) -1.2 or 2.2
Page 4