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Gold Level
Model Answers 1
Level IGCSE
Subject Maths
Exam Board Edexcel
DifficultyLevel Gold
Booklet ModelAnswers 1
Time Allowed: 60 minutes
Score: / 50
Percentage: /100
www.igexams.com
1 y = 1.8 correct to 1 decimal place.
Calculate the lower bound for the value of 4y + 1
..............................................
(Total for Question is 2 marks)
www.igexams.com
2
A
A, B, C and D are points on a circle, centre O.
Angle ADB = 57°.
Angle BCD = 106°.
(a) (i) Calculate the size of angle AOB.
.......................................
°
(ii) Give a reason for your answer.
.................................................................................................................................................................................................................................................................................
.................................................................................................................................................................................................................................................................................
(2)
(b) Calculate the size of angle BAD.
.......................................
°
(1)
(Total for Question is 3 marks)
Diagram NOT
accurately drawn
B
C
D
O
57°
106°
www.igexams.com
3 P is directly proportional to the cube of Q.
When Q = 15, P = 1350
(a) Find a formula for P in terms of Q.
P = ....................................
(3)
(b) Calculate the value of P when Q = 20
P = ....................................
(1)
(Total for Question is 4 marks)
4 x = a×10
n
where n is an integer and 10 !a <10
Find, in standard form, an expression for x2
.
Give your expression as simply as possible.
............................................................
(Total for Question is 3 marks)
0.4Q3
www.igexams.com
5
ABCD is a rectangle.
AB = 10 cm.
BC = 8 cm.
,
P Q, R and S are points on the sides of the rectangle.
BP = CQ = DR = AS = x cm.
(a) Show that the area, A cm2
, of the quadrilateral PQRS is given by the formula
A = 2x2
– 18x + 80
Diagram NOT
accurately drawn
A
x cm
S
R
Q
P
D C
B
x cm
x cm
x cm
10 cm
8 cm
(3)
www.igexams.com
(b) For A = 2x2
– 18x + 80
(i) find
d
d
A
x
,
.....................................................
(ii) find the value of x for which A is a minimum.
x = .....................................
(iii) Explain how you know that A is a minimum for this value of x.
.................................................................................................................................................................................................................................................................................
.................................................................................................................................................................................................................................................................................
(5)
(Total for Question is 8 marks)
www.igexams.com
6 Solve the simultaneous equations
=
y x
2 3
−
x y
2 2
+ = 2
...............................................................................................................
(Total for Question is 6 marks)
www.igexams.com
7
The diagram shows a solid cylinder and a solid sphere.
The cylinder has radius r.
The sphere has radius r.
Given that
Total surface area of cylinder
Surface area of sphere
= 2
find the value of
Volume of cylinder
Volume of sphere
.......................................................................................
(Total for Question is 5 marks)
Diagram NOT
accurately drawn
r
r
www.igexams.com
8 The incomplete histogram and table give information about the ages of people living in
a village.
0
Frequency
Density
10 20 30 40 50 60 70 80
Age (x years)
Age (x years) Frequency
0 - x < 10 100
10 - x < 15 60
15 - x < 30
30 - x < 50
50 - x < 75 50
75 - x < 80 20
(i) Use the histogram to complete the table.
(ii) Use the table to complete the histogram.
(Total for Question is 4 marks)
www.igexams.com
9 Alan has to attend a meeting on Monday and on Tuesday.
The probability that he is late for a meeting is
1
8
(a) Complete the probability tree diagram.
(3)
Monday meeting Tuesday meeting
1
8
late
not late
(b) Calculate the probability that Alan is late for at least one of these meetings.
..............................................................
(3)
(Total for Question is 6 marks)
www.igexams.com
10 Show that the recurring decimal 0
44
111
.396 =
(Total for Question is 2 marks)
•
•
www.igexams.com
11 f(x) =
2
x
+
g(x) =
x
x
1
(a) State which value of x cannot be included in the domain of f or g.
..............................................................
(1)
(b) Solve gf(a) = 3
a = ..............................................................
(3)
(c) Express the inverse function g–1
in the form g–1
(x)
g–1
(x) = ..............................................................
(3)
(Total for Question is 7 marks)
www.igexams.com

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A1-Gold-Level-Model-Answers-IGCSE9-1-MA.pdf

  • 1. Gold Level Model Answers 1 Level IGCSE Subject Maths Exam Board Edexcel DifficultyLevel Gold Booklet ModelAnswers 1 Time Allowed: 60 minutes Score: / 50 Percentage: /100 www.igexams.com
  • 2. 1 y = 1.8 correct to 1 decimal place. Calculate the lower bound for the value of 4y + 1 .............................................. (Total for Question is 2 marks) www.igexams.com
  • 3. 2 A A, B, C and D are points on a circle, centre O. Angle ADB = 57°. Angle BCD = 106°. (a) (i) Calculate the size of angle AOB. ....................................... ° (ii) Give a reason for your answer. ................................................................................................................................................................................................................................................................................. ................................................................................................................................................................................................................................................................................. (2) (b) Calculate the size of angle BAD. ....................................... ° (1) (Total for Question is 3 marks) Diagram NOT accurately drawn B C D O 57° 106° www.igexams.com
  • 4. 3 P is directly proportional to the cube of Q. When Q = 15, P = 1350 (a) Find a formula for P in terms of Q. P = .................................... (3) (b) Calculate the value of P when Q = 20 P = .................................... (1) (Total for Question is 4 marks) 4 x = a×10 n where n is an integer and 10 !a <10 Find, in standard form, an expression for x2 . Give your expression as simply as possible. ............................................................ (Total for Question is 3 marks) 0.4Q3 www.igexams.com
  • 5. 5 ABCD is a rectangle. AB = 10 cm. BC = 8 cm. , P Q, R and S are points on the sides of the rectangle. BP = CQ = DR = AS = x cm. (a) Show that the area, A cm2 , of the quadrilateral PQRS is given by the formula A = 2x2 – 18x + 80 Diagram NOT accurately drawn A x cm S R Q P D C B x cm x cm x cm 10 cm 8 cm (3) www.igexams.com
  • 6. (b) For A = 2x2 – 18x + 80 (i) find d d A x , ..................................................... (ii) find the value of x for which A is a minimum. x = ..................................... (iii) Explain how you know that A is a minimum for this value of x. ................................................................................................................................................................................................................................................................................. ................................................................................................................................................................................................................................................................................. (5) (Total for Question is 8 marks) www.igexams.com
  • 7. 6 Solve the simultaneous equations = y x 2 3 − x y 2 2 + = 2 ............................................................................................................... (Total for Question is 6 marks) www.igexams.com
  • 8. 7 The diagram shows a solid cylinder and a solid sphere. The cylinder has radius r. The sphere has radius r. Given that Total surface area of cylinder Surface area of sphere = 2 find the value of Volume of cylinder Volume of sphere ....................................................................................... (Total for Question is 5 marks) Diagram NOT accurately drawn r r www.igexams.com
  • 9. 8 The incomplete histogram and table give information about the ages of people living in a village. 0 Frequency Density 10 20 30 40 50 60 70 80 Age (x years) Age (x years) Frequency 0 - x < 10 100 10 - x < 15 60 15 - x < 30 30 - x < 50 50 - x < 75 50 75 - x < 80 20 (i) Use the histogram to complete the table. (ii) Use the table to complete the histogram. (Total for Question is 4 marks) www.igexams.com
  • 10. 9 Alan has to attend a meeting on Monday and on Tuesday. The probability that he is late for a meeting is 1 8 (a) Complete the probability tree diagram. (3) Monday meeting Tuesday meeting 1 8 late not late (b) Calculate the probability that Alan is late for at least one of these meetings. .............................................................. (3) (Total for Question is 6 marks) www.igexams.com
  • 11. 10 Show that the recurring decimal 0 44 111 .396 = (Total for Question is 2 marks) • • www.igexams.com
  • 12. 11 f(x) = 2 x + g(x) = x x 1 (a) State which value of x cannot be included in the domain of f or g. .............................................................. (1) (b) Solve gf(a) = 3 a = .............................................................. (3) (c) Express the inverse function g–1 in the form g–1 (x) g–1 (x) = .............................................................. (3) (Total for Question is 7 marks) www.igexams.com