Question

TERMEDIATE LEVEL
Number of candidates
1B
Class
1C
1D
Number of
students who
12
score a
20
distinction in
Mathematics
Number of
students who
8
4 Study the table and bar graph.
Class Class Class Class Class
Students who Score a Distinction in
(a) Complete the table and the bar graph.
1A
9
16
12
Mathematics or Science
1B
10
1D
Class
score a
15
an
distinction in
Science
iy
Mathematics
Science
20
6. Th
Numer 8 sem
LO
СС
1A
1E
b) Find the total number of students in the
5 classes who score a distinction in
( Mathematics,
(ii) Science.
(c) Express the number of students who score a
distinction in Mathematics in Class 1D as
a percentage of the total number of students
who score a distinction in Mathematics in the
5 classes.
(d) If there are 40 students in Class 1D, find the
percentage of students in the class who score
a distinction in Science.
(e) Is Jun Wei correct to say that there are
35 students in Class 1E? Explain your answer.
OXFORD
UNIVERSITY PRESS​

Answer 1

Answer:

This implies that

x2+2ax=4x−4a−13

or

x2+2ax−4x+4a+13=0

or

x2+(2a−4)x+(4a+13)=0

Since the equation has just one solution instead of the usual two distinct solutions, then the two solutions must be same i.e. discriminant = 0.

Hence we get that

(2a−4)2=4⋅1⋅(4a+13)

or

4a2−16a+16=16a+52

or

4a2−32a−36=0

or

a2−8a−9=0

or

(a−9)(a+1)=0

So the values of a are −1 and 9.