1 Mathematics questions arranged by topic

418 Pages·2016·6.84 MB·English

by  Peter Bland

GCSE Mathematics
Questions arranged by topic
In the style of:
1MA1
Pearson Edexcel Level 1/Level 2 GCSE (9 - 1)
by Peter Bland
© Peter Bland
Write your name here
Surname Other names
In the style of:
Centre Number Candidate Number
Pearson Edexcel
Level 1/Level 2 GCSE (9 - 1)
Mathematics
Algebra
Foundation Tier
Paper Reference
GCSE style questions arranged by topic 1MA1/1F
You must have: Ruler graduated in centimetres and millimetres, Total Marks
protractor, pair of compasses, pen, HB pencil, eraser.
Instructions
•
Use black ink or ball-point pen.
•
Fill in the boxes at the top of this page with your name,
centre number and candidate number.
•
Answer all questions.
•
Answer the questions in the spaces provided
–there may be more space than you need.
•
Calculators may not be used.
•
Diagrams are NOT accurately drawn, unless otherwise indicated.
•
You must show all your working out.
Information
•
The total mark for this paper is 80
•
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.
•
Check your answers if you have time at the end.
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© Peter Bland
3 Here are the first six terms of a Fibonacci sequence. 1 Peter thinks of a number.
He multiplies the number by 3
1 1 2 3 5 8 DD A He then adds 2
OO E
The rule to continue a Fibonacci sequence is, N N AR His answer is 20
OO S
TT I (a) What number did Peter think of?
the next term in the sequence is the sum of the two previous terms. W W H
T
RR N
II
TT I
(a) Find the 9th term of this sequence. EE E
I I T
NN I
R
T T W .....................................
HH
II T (2)
SS O
A A N
RERE O Sophie uses the formula P = 2a + b
AA D
to find the perimeter P of this triangle.
a b
.......................................................
(1) (b) Find the value of P when
The first three terms of a different Fibonacci sequence are a = 6 and b = 4
a
a b a + b
DD A
(b) Show that the 6th term of this sequence is 3a + 5b OO E
N N AR
OO S
TT I
W W H
T
RR N P = .....................................
II
TETE E I (2)
I I T
NN I
T T WR (Total for Question 1 is 4 marks)
HH
(2) II T
SS O
A A N 2 (a) Work out the value of
Given that the 3rd term is 7 and the 6th term is 29, RERE O
AA D (i) 42
(c) find the value of a and the value of b.
.....................................
(ii) 64
.....................................
(iii) 3 × 23
DD A
OO E .....................................
N N AR
(3)
OO S
TT I
W W H
T (b) Work out
RR N
....................................................... ITIT I
(3) EE E (i) – 3 + 5
I I T
NN I
R
(Total for Question 3 is 6 marks) TH TH W .....................................
II T
SS O (ii) –2 – 3
A A N
RERE O
AA D .....................................
(2)
(Total for Question 2 is 5 marks)
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3 Here are the first six terms of a Fibonacci sequence. 3 The cost of hiring a car can be worked out using this rule.
1 1 2 3 5 8 DD A
OO E
The rule to continue a Fibonacci sequence is, N N AR Cost = £80 + 50p per mile
OO S
TT I
the next term in the sequence is the sum of the two previous terms. W W H
T
RR N
II
(a) Find the 9th term of this sequence. TETE E I Bill hires a car and drives 90 miles.
I I T
NN I
R
T T W (a) Work out the cost.
HH
II T
SS O
A A N
RERE O
AA D
.......................................................
(1)
The first three terms of a different Fibonacci sequence are
a b a + b
£ .....................................
DD A
(b) Show that the 6th term of this sequence is 3a + 5b OO E (2)
N N AR
OTOT IS The cost of hiring a car and driving m miles is C pounds.
W W H
T
RIRI N (b) Complete the formula for C in terms of m.
TT I
EE E
I I T
NN I
R
T T W
HH
(2) II T
SS O
A A N
Given that the 3rd term is 7 and the 6th term is 29, RERE O
AA D
(c) find the value of a and the value of b.
C = .....................................
(2)
(Total for Question 3 is 4 marks)
DD A
OO E
N N AR
OO S
TT I
W W H
T
RR N
....................................................... ITIT I
(3) EE E
I I T
NN I
R
T T W
(Total for Question 3 is 6 marks) HH
II T
SS O
A A N
RERE O
AA D
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3 Here are the first six terms of a Fibonacci sequence. 4 (a) Complete this table of values for y = 2x – 1
1 1 2 3 5 8 DD A
x –1 0 1 22 3
OO E
The rule to continue a Fibonacci sequence is, N N AR
OO S y –1 3 5
TT I
the next term in the sequence is the sum of the two previous terms. W W H
RR N T (2)
II
TT I
(a) Find the 9th term of this sequence. EE E
I I T
NN I
R
T T W
HH
II T
SS O
A A N y
RERE O
AA D 8
.......................................................
(1)
The first three terms of a different Fibonacci sequence are 6
a b a + b
DD A
(b) Show that the 6th term of this sequence is 3a + 5b OO E
N N AR 4
OO S
TT I
W W H
T
RR N
II
TT I
EE E 2
I I T
NN I
R
T T W
HH
(2) II T
SS O
A A N
Given that the 3rd term is 7 and the 6th term is 29, RERE O –3 –2 –1 O 1 2 3 4 x
AA D
(c) find the value of a and the value of b.
–2
–4
DD A (2)
OO E
N N AR (b) On the grid, draw the graph of y = 2x – 1
OO S
TT I
W W H
T (Total for Question 4 is 4 marks)
RR N
....................................................... ITIT I
(3) EE E
I I T
NN I
R
T T W
(Total for Question 3 is 6 marks) HH
II T
SS O
A A N
RERE O
AA D
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3 Here are the first six terms of a Fibonacci sequence. 5 Work out an estimate for the value of _3_1_ _×_ 4_._9_2_
0.21
1 1 2 3 5 8 DD A
OO E
The rule to continue a Fibonacci sequence is, N N AR
OO S
TT I
the next term in the sequence is the sum of the two previous terms. W W H
T
RR N
II
TT I
(a) Find the 9th term of this sequence. EE E
I I T
NN I
R
T T W
HH
II T
SS O
A A N
RERE O
AA D
....................................................... ......................................
(1)
(Total for Question 5 is 2 marks)
The first three terms of a different Fibonacci sequence are
a b a + b
DD A
(b) Show that the 6th term of this sequence is 3a + 5b OO E 6. (a) Expand y(2y – 3)
N N AR
OO S
TT I
W W H
T
RIRI N ......................................
TT I
EE E (1)
I I T
NN I
R
T T W
HH (b) Factorise x2 – 4x
(2) II T
SS O
A A N
Given that the 3rd term is 7 and the 6th term is 29, RERE O
AA D
(c) find the value of a and the value of b.
......................................
(2)
k is an integer such that –1 (cid:45) k < 3
(c) List all the possible values of k.
DD A
OO E
N N AR
OO S
TT I .....................................................
W W H
T
RR N (2)
....................................................... ITIT I
(3) EE E
I I T
NN I (Total for Question 6 is 5 marks)
R
T T W
(Total for Question 3 is 6 marks) HH
II T
SS O
A A N
RERE O
AA D
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3 Here are the first six terms of a Fibonacci sequence. 7 (a) Factorise x2 – 5x
1 1 2 3 5 8 DD A
OO E
The rule to continue a Fibonacci sequence is, N N AR .....................................
OO S (2)
TT I
the next term in the sequence is the sum of the two previous terms. W W H
T
RR N (b) Expand 3(5x –2)
II
TT I
(a) Find the 9th term of this sequence. EE E
I I T
NN I
R
T T W .....................................
HH
II T (1)
SS O
A A N
RERE O (Total for Question 7 is 3 marks)
AA D
8 A hotel has 64 guests.
.......................................................
(1) 40 of the guests are male.
The first three terms of a different Fibonacci sequence are (a) Work out 40 out of 64 as a percentage.
a b a + b
DD A
(b) Show that the 6th term of this sequence is 3a + 5b OO E
N N AR
OO S
TT I
W W H
T
RR N ..................................... %
II
TT I
EE E (2)
I I T
NN I
R
T T W 40% of the 40 male guests wear glasses.
HH
(2) II T
SS O
A A N (b) Write the number of male guests who wear glasses as a fraction of the 64 guests.
Given that the 3rd term is 7 and the 6th term is 29, RERE O Give your answer in its simplest form.
AA D
(c) find the value of a and the value of b.
.....................................
DD A
OO E
N N AR (2)
OTOT IS (Total for Question 8 is 4 marks)
W W H
T
RR N
....................................................... ITIT I
(3) EE E
I I T
NN I
R
T T W
(Total for Question 3 is 6 marks) HH
II T
SS O
A A N
RERE O
AA D
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3 Here are the first six terms of a Fibonacci sequence. 9 (a) Simplify 8x – 4x
1 1 2 3 5 8 DD A .....................................
OO E
The rule to continue a Fibonacci sequence is, N N AR (1)
OO S
the next term in the sequence is the sum of the two previous terms. T WT W HI (b) Simplify y × y × y
T
RR N
II
(a) Find the 9th term of this sequence. TETE E I .....................................
IN IN IT (1)
R
T T W
HH
II T (c) Simplify 5y + 4x – 2x + 5x
SS O
A A N
RERE O
AA D
.......................................................
(1) .....................................
(2)
The first three terms of a different Fibonacci sequence are
(Total for Question 9 is 4 marks)
a b a + b
DD A
(b) Show that the 6th term of this sequence is 3a + 5b OO E
N N AR
OO S
TT I
W W H
T
RR N
II
TT I
EE E
I I T
NN I
R
T T W
HH
(2) II T
SS O
A A N
Given that the 3rd term is 7 and the 6th term is 29, RERE O
AA D
(c) find the value of a and the value of b.
DD A
OO E
N N AR
OO S
TT I
W W H
T
RR N
....................................................... ITIT I
(3) EE E
I I T
NN I
R
T T W
(Total for Question 3 is 6 marks) HH
II T
SS O
A A N
RERE O
AA D
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3 Here are the first six terms of a Fibonacci sequence. 10 The two-way table gives some information about how 100 children travelled to school oneday.
1 1 2 3 5 8 DD A
OO E
The rule to continue a Fibonacci sequence is, N N AR Walk Car (cid:37)(cid:76)(cid:78)(cid:72) Total
OO S
the next term in the sequence is the sum of the two previous terms. T WT W HI Boy 15 14 54
T
RR N
II Girl 8 16
TT I
(a) Find the 9th term of this sequence. EE E
I I T
NN I Total 37 100
R
T T W
HH
II T
S AS A NO (a) Complete the two-way table.
RERE O
AA D (3)
....................................................... One of the children is picked at random.
(1)
(b) Write down the probability that this child walked to school that day.
The first three terms of a different Fibonacci sequence are
a b a + b
DD A
(b) Show that the 6th term of this sequence is 3a + 5b OO E
N N AR .....................................
OO S (1)
TT I
W W H
T
RR N One of the girls is picked at random.
II
TT I
EE E
IN IN IT (c) Work out the probability that this girl did not walk to school that day.
R
T T W
HH
(2) II T
SS O
A A N .....................................
Given that the 3rd term is 7 and the 6th term is 29, RERE O
AA D (2)
(c) find the value of a and the value of b.
(Total for Question 10 is 6 marks)
11 (cid:36)pples cost a pence each
Bananas cost b pence each.
Write down an expression for the total cost, in pence, of 2 apples and 4 bananas.
DD A
OO E
N N AR
OO S
TT I
W W H
T
RR N
....................................................... ITIT I
(3) EE E ........................................ pence
I I T
NN I
R (Total for Question 11 is 2 marks)
T T W
(Total for Question 3 is 6 marks) HH
II T
SS O
A A N
RERE O
AA D
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3 Here are the first six terms of a Fibonacci sequence. 12 Diagram NOT
accurately drawn
1 1 2 3 5 8 DD A 4x + 1
OO E
The rule to continue a Fibonacci sequence is, N N AR
OO S
TT I
the next term in the sequence is the sum of the two previous terms. W W TH x x
RR N
II
TT I
(a) Find the 9th term of this sequence. EE E
I I T
NN I
R
TH TH W 2x + 12
II T
SS O
A A N
RERE O The diagram shows a rectangle.
AA D
All the measurements are in centimetres.
....................................................... (a) Explain why 4x + 1 = 2x + 12
(1)
.......................................................................................................................................
The first three terms of a different Fibonacci sequence are
(1)
a b a + b
DD A (b) Solve 4x + 1 = 2x + 12
(b) Show that the 6th term of this sequence is 3a + 5b OO E
N N AR
OO S
TT I
W W H
T
RR N
II
TT I
EE E
I I T
NN I
R
T T W
HH
(2) II T
SS O
A A N
Given that the 3rd term is 7 and the 6th term is 29, RERE O
AA D
(c) find the value of a and the value of b. x = ........................................
(2)
(c) Use your answer to part (b) to work out the perimeter of the rectangle.
DD A
OO E
N N AR
OO S
TT I
W W H ........................................ cm
T
RR N
....................................................... ITIT I (1)
(3) EE E
I I T
NN I
R
T T W
(Total for Question 3 is 6 marks) HH
II T
SS O
A A N (Total for Question 12 is 5 marks)
RERE O
AA D
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