14 questions · 88 marks · ≈ 1 hour · spans 14 of 65 topics
Assembled from the topic question banks — not an official Edexcel paperB
120°
(x + 3) cm
2x cm
A
C
(3x + 1) cm
The diagram shows triangle ABC in which
AB = (x + 3) cm
BC = 2x cm
AC = (3x + 1) cm
∠ABC = 120°
Find the size, in degrees to 3 significant figures, of ∠ACB.
∠ACB = .....................................................................°
Write x2 + 10x - 7 in the form (x + p)2 + q
Hence solve the equation x2 + 10x - 7 = 0
Give your answer in the form a
where a and b are integers.
±
b
Show your working clearly.
Solve the inequality 5(x + 1) < x
Show clear algebraic working.
Solve the simultaneous equations
3x2 + y2 - 7 = 0
y - 3x - 5 = 0
Show clear algebraic working.
Hence find the value of x for which
5(x + 1) < x and 3x2 + y2 - 7 = 0 and y - 3x - 5 = 0
Question 5 continued
A
x°
Diagram NOT
D
accurately drawn
B
110°
40°
E
C
In the diagram, ABC is a triangle with point D on AB and point E on AC such that DE is
parallel to BC.
∠ABC = 40° ∠AED = 110° ∠BAC = x°
Find the value of x.
Give reasons for each stage of your working.
x =
E = {positive integers from 1 to 15 inclusive}
A = {multiples of 3}
B = {even numbers}
Find A ∪ B
Find A ∩ B
Find n([A ∩ B]′)
The set C has 8 elements and B ∩ C = ∅
Write down the elements of set C.
2a cm
b cm
b cm
Figure 3
Figure 3 shows a solid silver paperweight made from a cuboid and a half cylinder.
The cuboid is 2a cm wide, b cm long and b cm high.
The plane face of the half cylinder coincides with the top face of the cuboid.
The total surface area of the paper weight is A cm²
Find an expression for A in terms of , a and b.
Given that a = 6 5 and that the surface area of the paperweight can be written as
(2b2 + 6ab + 60 15) cm²
2a cm
b cm
b cm
Figure 3
Figure 3 shows a solid silver paperweight made from a cuboid and a half cylinder.
The cuboid is 2a cm wide, b cm long and b cm high.
The plane face of the half cylinder coincides with the top face of the cuboid.
The total surface area of the paper weight is A cm²
show that the exact value of b is 10 3 - 6 5
The paperweight is melted down to form a different cuboid.
This second cuboid is 2a cm wide, b cm long and h cm high, as shown in Figure 4.
F
G
h cm
E
H
B
C
b cm
A
2a cm
D
Figure 4
2a cm
b cm
b cm
Figure 3
Figure 3 shows a solid silver paperweight made from a cuboid and a half cylinder.
The cuboid is 2a cm wide, b cm long and b cm high.
The plane face of the half cylinder coincides with the top face of the cuboid.
The total surface area of the paper weight is A cm²
Calculate the size, to the nearest degree, of angle GAC.
Question 12 continued
r h
2
Volume of cylinder
rh
Curved surface area of cylinder 2
Question 12 continued
Question 12 continued
The nth term of a sequence is given by 24 - 5n
Find the sum of the 3rd term and the 10th term of the sequence.
C
B
D
A
E
The diagram shows triangle ACE.
The point B on CA and the point D on CE are such that BD is parallel to AE.
BD FPWRVLJQLILFDQWILJXUHV
AE = 9.3 cm to 2 significant figures.
Area of BCD = 15.4 cm² to 3 significant figures.
Calculate the upper bound, to 3 significant figures, for the area of ACE.
...................................................... cm²
Diagram NOT
accurately drawn
8 cm
C
D
T
O
B
10 cm
A
Figure 1
Figure 1 shows the circle ABCD with centre O and diameter DC.
The point T is such that TCOD is a straight line and TA is the tangent to the circle at A.
AT = 10 cm TC = 8 cm
Calculate the radius, in cm, of the circle.
Diagram NOT
accurately drawn
8 cm
C
D
T
O
B
10 cm
A
Figure 1
Figure 1 shows the circle ABCD with centre O and diameter DC.
The point T is such that TCOD is a straight line and TA is the tangent to the circle at A.
AT = 10 cm TC = 8 cm
Calculate the length, in cm to 3 significant figures, of the arc ABC.
Question 3 continued
The functions f and g are defined as
fixr3x-5
1
gixre
2x —3
State the value of x that must be excluded from any domain of g.
The functions f and g are defined as
fixr3x-5
1
gixre
2x —3
Find gf
The function h is defined as
h:ixre where x # 3
x
x _
The functions f and g are defined as
fixr3x-5
1
gixre
2x —3
Solve fh(x) = 7
The functions f and g are defined as
fixr3x-5
1
gixre
2x —3
Express the inverse function h™! in the form ht! : x +>...
The functions f and g are defined as
fixr3x-5
1
gixre
2x —3
Solve the equation g(x) + h(x) = 1
Show your working clearly.
Give your solutions in the form a + Vb where a and b are integers.
—b+vVb? - we]
soto of ax? + bx +c = Oarex = 5
................................................................
Express as a single fraction in its simplest form
5
2
−
x
x
−
3
2
2
5
B
H
F
A
C
O
M
N
G
J
D
The diagram shows circle ABCD with centre O, diameter AMONC and radius r.
The diagram also shows circle AFOG, with centre M, and circle OHCJ, with centre N.
Find and simplify an expression, in terms of r and , for the perimeter of the shaded
region in the diagram.
The line FH is the tangent to the circle AFOG at the point F.
The line FH is also the tangent to the circle OHCJ at the point H.
The point P on circle ABCD is such that OFP is a straight line.
The point Q on circle ABCD is such that OHQ is a straight line.
The region FPBQH inside circle ABCD is bounded by the straight line FP, the arc PBQ
of circle ABCD and the two straight lines QH and HF.
B
H
F
A
C
O
M
N
G
J
D
The diagram shows circle ABCD with centre O, diameter AMONC and radius r.
The diagram also shows circle AFOG, with centre M, and circle OHCJ, with centre N.
Find and simplify an expression, in terms of r and , for the area of FPBQH.
−
−
2
2
1
2
The transformation with matrix A is equivalent to the transformation with matrix B
followed by the transformation with matrix C, where C is a 2 × 2 matrix.
Find matrix C.
a
b
d
b
−
1
The inverse of matrix
is
c
d
c
−
ad
bc
a
−
Question 9 continued
Write down all the multiples of 3 lying between 1 and 20
Ahmed and Hani play a game with 20 numbered balls.
The 20 balls are numbered from 1 to 20
1
2
3
20
...
The balls are put in a bag.
Ahmed takes at random a ball from the bag, makes a note of its number and puts the ball
back into the bag.
If the number of the ball is a multiple of 5, Ahmed wins the game.
If Ahmed does not win the game, Hani takes at random a ball from the bag, makes a note
of its number and puts the ball back into the bag.
If the number of the ball is a multiple of 3, Hani wins the game.
If Hani does not win the game, Ahmed takes at random a ball from the bag, makes a note
of its number and puts the ball back into the bag.
If the number of the ball is a multiple of 6, Ahmed wins the game.
If Ahmed does not win the game, Hani takes at random a ball from the bag, makes a note
of its number and puts the ball back into the bag.
If the number of the ball is a multiple of 4, Hani wins the game.
If Hani does not win the game, the game stops and the result is a draw.
The incomplete probability tree diagram for the game is shown below.
Complete the probability tree diagram for Ahmed and Hani’s game.
Determine which player, Ahmed or Hani, is more likely to win the game.
Give a reason for your answer.
Ahmed
wins
Hani
wins
Ahmed
Ahmed
does not
wins
win
Hani
Hani
does not
wins
win
Ahmed
does not
win
Hani
does not
win
Question 7 continued