Mathematics - ACE HSC
Girraween High School
2016
TRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION
Mathematics General Instructions Total Marks -100 Reading time 5 minutes • Section I Pages 5 - 8 • Working time - 3 hours 10 marks • Write using a black or blue pen • Attempt 1 - JO • Board - approved calculators may be used • Allow about 15 minutes for this section • A laminated reference sheet is provided Answer multiple choice questions on the • Section II Pages 9 - 18 front page • In questions 11 - 16 start all questions on 90 marks • Attempt 11-16 a separate page and show all relevant • Allow about 2 hours and 45 minutes for mathematical. reasoning and/or calculathis section tions
Giii-aween High School Mathematics Trial HSC 2016
Page 3
Section I 10 marks Attempt questions 1 - 10 Allow about 15 minutes for this section Use the multiple-choice answer sheet for Questions 1 - 10. I
Find is the value of loge2016 to three significant figures.
(A) 7.61 (B) 7.60 (C) 7.608 (D) 7.609 2
The graph below shows the maximum stationary point A on the curve y
= f(x).
y
y = f(x) A
X
!--·--------------·----·----
Which of the following is tme at point A? (A) f' (x)
> 0 and f" (x) = 0
(B) f' (x)
< 0 and f" (x) = 0
(C) f' (x)
= 0 and f" (x) > 0
(D) f' (x)
= 0 and f" (x) < 0
Gilrnween High School Mathematics Trial HSC 2016
Pages
3
The equation 2x 2 - 5x - 1 = 0 has roots a and f3. What is the value of~+
t? ·
1
CA)
5
CB) 5
CC) -5 CD)
4
i 5
The coordinates of the focus of the parabola x 2 = 8(y - 3) are: CA) (0, 5) CB) (0, 1)
CC) C5 ,0) CD) (1, 0)
5
1
Ifx=a(b--)then y a
CA) y
= b-x
CB)
Y-
-
CC)
Y-
CD) y
-
a ab-x i
ab-x
= -a - b X
Gllnween High School Mathematics Trial HSC 2016
Page 6
6
Which would give the value of the shaded area? y
y=f(x)
X
2
(A) f0- f(x)dx
7
+ [f01 f(x)dx[
(B)
f~2 f(x)dx + [fo1 f(x)dx[
(C)
[f0- 2 f(x)dx[ + f01 f(x)dx
(D)
[f~
2
f(x)dx[
The solutions to -.ff.sin x
(A)
3
ir
and
4
(B)
3ir
4
+ fo1 f(x)dx
= -1 for O ::; x ::; 2rr are:
sir
4
and
7ir
4
Sir d 7ir (C) -an -
4
4
7ir d 9ir (D) -an -
4
4
Gi.t'raween High School Mathematics Trial HSC 2016
Page 7
8
The solution to the inequality 6 - x - x 2 :5 0 is:
(A) -3 :5 x :5 2 (B) x :5 -3 or x
2016
TRIAL HIGHER SCHOOL CERTIFICATE EXAMINATION
Mathematics General Instructions Total Marks -100 Reading time 5 minutes • Section I Pages 5 - 8 • Working time - 3 hours 10 marks • Write using a black or blue pen • Attempt 1 - JO • Board - approved calculators may be used • Allow about 15 minutes for this section • A laminated reference sheet is provided Answer multiple choice questions on the • Section II Pages 9 - 18 front page • In questions 11 - 16 start all questions on 90 marks • Attempt 11-16 a separate page and show all relevant • Allow about 2 hours and 45 minutes for mathematical. reasoning and/or calculathis section tions
Giii-aween High School Mathematics Trial HSC 2016
Page 3
Section I 10 marks Attempt questions 1 - 10 Allow about 15 minutes for this section Use the multiple-choice answer sheet for Questions 1 - 10. I
Find is the value of loge2016 to three significant figures.
(A) 7.61 (B) 7.60 (C) 7.608 (D) 7.609 2
The graph below shows the maximum stationary point A on the curve y
= f(x).
y
y = f(x) A
X
!--·--------------·----·----
Which of the following is tme at point A? (A) f' (x)
> 0 and f" (x) = 0
(B) f' (x)
< 0 and f" (x) = 0
(C) f' (x)
= 0 and f" (x) > 0
(D) f' (x)
= 0 and f" (x) < 0
Gilrnween High School Mathematics Trial HSC 2016
Pages
3
The equation 2x 2 - 5x - 1 = 0 has roots a and f3. What is the value of~+
t? ·
1
CA)
5
CB) 5
CC) -5 CD)
4
i 5
The coordinates of the focus of the parabola x 2 = 8(y - 3) are: CA) (0, 5) CB) (0, 1)
CC) C5 ,0) CD) (1, 0)
5
1
Ifx=a(b--)then y a
CA) y
= b-x
CB)
Y-
-
CC)
Y-
CD) y
-
a ab-x i
ab-x
= -a - b X
Gllnween High School Mathematics Trial HSC 2016
Page 6
6
Which would give the value of the shaded area? y
y=f(x)
X
2
(A) f0- f(x)dx
7
+ [f01 f(x)dx[
(B)
f~2 f(x)dx + [fo1 f(x)dx[
(C)
[f0- 2 f(x)dx[ + f01 f(x)dx
(D)
[f~
2
f(x)dx[
The solutions to -.ff.sin x
(A)
3
ir
and
4
(B)
3ir
4
+ fo1 f(x)dx
= -1 for O ::; x ::; 2rr are:
sir
4
and
7ir
4
Sir d 7ir (C) -an -
4
4
7ir d 9ir (D) -an -
4
4
Gi.t'raween High School Mathematics Trial HSC 2016
Page 7
8
The solution to the inequality 6 - x - x 2 :5 0 is:
(A) -3 :5 x :5 2 (B) x :5 -3 or x
