- Information
- AI Chat
2019 Year 11 Mathematics Advanced Task 1 with solutions
Maths advanced past paper
Subject
math advanced
513 Documents
Students shared 513 documents in this course
Academic year: 2023/2024
Uploaded by:
0followers
4Uploads
0upvotes
Recommended for you
Preview text
Student’s Name: __________________________ Teacher: Mandile Blair Karagiannis Campain (Circle)
Year 11 Mathematics Advanced
8
th
April 2019
Task 1 - Topic Test
General Instructions
Write using black or blue pen
Graphs can be drawn in pencil
Reading Time 5 minutes
Working time 1 hour
Structure of the Paper
Section
1
/4 Marks Allow about 5
minutes for this
question
Section
2
/62 Marks Allow about 55
minutes for this
question
Total /66 Marks Weighting: 30%
Special Instructions
NESA approved Calculator may be used.
A reference sheet is provided.
Show all relevant mathematical reasoning and/or calculations
Attempt all questions
This examination must not be removed from the Examination Room.
Section I
4 marks
Attempt questions 1 - 4
Allow about 5 minutes for this section
Use the multiple-choice answer sheet for questions 1-
1. A line l has equation 3 y 2x 6 is the gradient of any line parallel to l ?
(A) 2
(B)
2
3
(C)
3
2
(D) 2
2. For y 2x 2 6 x 2 , the minimum value of y is:
(A)
11
2
(B)
7
2
(C)
5
2
(D)
31
2
3. What is the discriminant of 2x 2 3x k 0?
(A) 9 2 k
(B) 9 8 k
(C) 9 12 k
(D) 9 24 k
Section II
62 marks
Attempt all questions
Allow about 55 minutes for this section
Answer the questions in the spaces provided.
Your responses should include relevant mathematical reasoning and/or calculations.
Extra writing space is provided at the back of the examination paper.
Question 5 (4 marks) Marks
Simplify:
(a) 5
( 4x 22
8x
)
2
(b) 2 2 10 9 8 2
Question 6 (2 marks) Marks
Simplify
2 1
x x 1
2
Question 7 (6 marks)
Solve for x :
(a) x 2 4 x 2
(b) x 2 x 1
2
2x 5x
2
(c) | 4x 3| 7 2
Question 11 (3 marks) Marks
Solve the quadratic equation 2x 2 6 x 7 0 by using the quadratic formula, leaving
your answer in simplest surd form.
3
Question 12 (5 marks)
Let
####### 2
f ( x ) 2x 18 and g( x ) x 2.
(a) Find f ( g( x )). 2
(b) Determine the range of f ( g( x )). 1
(c) Solve f ( g( x )) 0. 2
Question 13 (5 marks) Marks
Let f ( x ) p( x 1 )( x 5 ).The following diagram shows part of the graph of f.
The graph has x-intercepts at a and b , and a y-intercept at 10.
(a) (i) Write down the value of a and of b. 2
(ii) Find the value of p. 2
(b) Find the coordinates of the vertex. 1
Question 15 (4 marks) Marks
Consider the function 𝑓ሺ𝑥ሻ ൌ √9 െ 𝑥 ଶ
(a) State the domain and range of 𝑓ሺ𝑥ሻ. 2
(b) State whether the function 𝑓ሺ𝑥ሻ, is odd, even or neither.
You must justify your answer algebraically.
2
Question 16 (3 marks)
The graph of a cubic function has x-axis intercepts 1, 3 and 1 and y-intercept of 3.
Find the rule for this cubic function.
3
Question 17 (8 marks) Marks
A quadrilateral has vertices A(–1, 8), B(7, 12), C(8, 5) and D(2, –3) as shown in the
diagram below.
(a) Find the equation of diagonal BD. 2
(b) The equation of diagonal AC is x 3 y 23 0.
Find the coordinates of E, the point of intersection of the diagonals.
2
Question 17 continues on the next page
Question 18 (5 marks)
Complete the squares in x and y of the relation x 2 2x y 2 4 y 4 and sketch its graph. 5
Question 19 (4 marks) Marks
The graph of y g( x )is given below.
(a) Find g( 2 ). 1
(b) On the same diagram, sketch the graph of y g( x 1 ). 3
End of paper
y g( x )
Section II extra writing space
If you use this space, clearly indicate which question you are answering.
Section II extra writing space
If you use this space, clearly indicate which question you are answering.
Section II extra writing space
If you use this space, clearly indicate which question you are answering.
Was this document helpful?
2019 Year 11 Mathematics Advanced Task 1 with solutions
Subject: math advanced
513 Documents
Students shared 513 documents in this course
Was this document helpful?
Student’sName:__________________________Teacher:MandileBlairKaragiannisCampain(Circle)
Year 11 Mathematics Advanced
8
th
April 2019
Task 1 - Topic Test
GeneralInstructions
Writeusingblackorbluepen
Graphscanbedrawninpencil
ReadingTime
5minutes
Workingtime
1hour
StructureofthePaper
Section
1
/4Marks Allowabout5
minutesforthis
question
Section
2
/62Marks
Allowabout55
minutesforthis
question
Total /66Marks Weighting:30%
SpecialInstructions
NESAapprovedCalculatormaybeused.
Areferencesheetisprovided.
Showallrelevantmathematicalreasoningand/orcalculations
Attemptallquestions
ThisexaminationmustnotberemovedfromtheExaminationRoom.
Discover more from:
- Discover more from:
