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Instructions ● Use black ink or ball-point pen. ● Fill in the boxes at the top of this page with your name and teacher ● Circle your teaching group ● Answer all questions. ● Answer the questions in the spaces provided
- there may be more space than you need. ● You must show all your working. ● Diagrams are NOT accurately drawn, unless otherwise indicated. ● Calculators may not be used. Information ● The total mark for this paper is 42. There are 10 questions. ● The marks for each question are shown in brackets - use this as a guide as to how much time to spend on each question. Advice ● Read each question carefully before you start to answer it. ● Keep an eye on the time. ● Try to answer every question.
October 2022
Teacher
11X1 11X2 11X3 11Y1 11Y
● Check your answers if you have time at the end.
Question 1
Simplify fully 7 +√ 5 √^5 −^1 giving your answer in the form a + b (^) √ 5 , where a and b are integers. ……………………………. (Total for question = 4 marks)
Question 3
y is inversely proportional to the square root of x.
y = 7 when x = 25.
Find the value of y when x = 100.
y =¿ ..........................
(Total for question = 3 marks)
Question 4
Solve the inequality x 2 − x − 12 > 0.
……………………………………………................................ (Total for question = 3 marks)
Question 5
a) Write down the letter of the graph which could have the equation
y = 1 − 3 x
.......................... (1 mark) b) Write down the letter of the graph which could have the equation
y =
x
.......................... (1 mark) c) Write down the letter of the graph which could have the equation
y = 2 x
2
+ 7 x + 3
..........................
Question 7
A and B are two similar cylindrical containers. The surface area of container A : the surface area of container B = 4 : 9
The volume of container A is 160 c m 3.
Work out the volume of container B.
.......................... c m
3
(Total for question = 3 marks)
Question 8
Simplify fully 6 + [
( x + 5 ) ÷
x
2
+ 3 x − 10
x − 1 ] giving your answer in the form
ax − b
cx − d
where a , b , c and d are integers.
…………......................... (Total for question = 4 marks)
Question 10
f ( x )=
x
g ( x )=
x + 1
x
a) Work out g (− 2 )
.......................... (2 marks)
b) State which value of x cannot be included in the domain of f or g.
.......................... (1 mark)
c) Express the inverse function g −^1 in the form g −^1 ( x )
g
x )=¿ ..........................
(3 marks)
f ( x )=
x
g ( x )=
x + 1
x
(as before)
d) Solve gf ( a )= 3
.......................... (3 marks) (Total for question = 10 marks)
TOTAL FOR PAPER IS 42 MARKS
Answers
Question 1
3 + (^2) √ 5
Question 2
±
b 2 − b
Question 3
x + 3 y = 17
Question 4
y =
√^7
x +
√^7
Question 5
PQ =√ 40
Question 6
Question 7
Question 8
∠ BDC =¿ 28 º and BD =¿ 10 cm
- Question
- Question - y =¿ 3.
- Question - √
- Question
Question 17
x =
,^ y^ =^
or x = 5 , y =− 3
Question 18
"E"
Question 19
"A"
Question 20
"I"
Question 27
" BC is common", " DEC = AEB (Vertically opposite angles are equal)" and
" EAB = EDC (Angles in the same segment are equal)"
Question 28
a = 7
Question 29
7 x − 13 x − 2
Question 30
Question 31
Question 32
"-5 OR - 5", "3" and "change of sign OR sign change OR change in sign OR change of signs OR change in signs"
