Intermediate GCSE Mathematics
Chapter 6 - Algebra 2
Time Allowed : 50 mins
Calculators are permitted in this examination
Student Name_______________
Teacher_____________
Test A
1. Here is a sequence of matchstick patterns.
(a) How many matches are in the 5th pattern in the
sequence?
(a)_______________
(b) Write a formula for m (matches) in n (pattern number)
(b)_______________
(4 marks)
2. Here is a sequence of tile patterns.
b=
w=
b=
b=
w=
w=
(a) Complete the number of white and black tiles in each of
the above patterns.
(b) How many of each colour tile are in the next pattern in
the sequence.
(c) Write a formula connecting w (number of white tiles) and
b (number of black tiles)
(7 marks)
(b) b = ____ w = ____
(c)_______________
3. Look at the tables below. In each case find a formula
connecting the two letters
(a)
g
h
1
(b)
j
k
11
1
2
14
3
4
(c)
q
s
2
2
2
2
0
4
10
17
3
-2
5
14
20
4
-4
7
22
(a)_______________
(b)_______________
(c)_______________
(6 marks)
4. In the rectangle below calculate the distance h by trial and improvement. Give your
answer accurate to 1 d. p.
Area = 125cm²
Guess
Area
Too high/low?
h
h+4
Ans________
(4 marks)
5. By trial and improvement find the value of x, accurate to 1 d.p.
that satisfies
x² + x = 46
Ans__________
(4 marks)
6. For each question plot each line and mark the x and y values that solve the equations.
a
10
b
10
9
9
8
8
7
7
6
6
5
5
4
4
3
3
2
2
1
1
0
1
2
3
4
5
6
7
y=x+5
x + y = 12
x = _______
8
9
10
0
1
2
3
4
5
6
7
8
y = ½x + 2
y = 2x - 7
y =________
x = _______
y =________
(8 marks)
7. 3x + 4y = 18
7x + 4y = 26
x = _______
y = _______
(4 marks)
9
10
8. 5x - 2y = -22
3x + 5y = 24
x = _______
y = _______
(4 marks)
9. A bank cashier weighs 2 bags of mixed coins. A bag
containing 20 dinars and 10 francs weighs 500g. The
second bag contains 50 dinars and 20 francs, and
weighs 1150 g. How much does each type of coin weigh?
Dinar weighs ______g
Franc weighs ______g
(5 marks)
10. A bag of 50 mixed 2p and 5p coins has a value of £1.84.
How many of each type of coin are there in the bag?
________ 2p coins
________ 5p coins
(5 marks)
11.
90
80
Distance
(km)
70
60
50
40
30
20
10
8
am
9
am
10
am
11
am
12
1
pm
2
pm
3
pm
4
pm
5
pm
6
pm
Time
The graph above shows a return journey from Grimsby to
York, stopping in Scunthorpe.
(a) How long does the car stop in Scunthorpe?
(a)_______________
(b) How far is it from Scunthorpe to York?
(b)_______________
(c) What was the speed of the car from :(i) Grimsby to Scunthorpe?
(c) (i)_____________
(ii) Scunthorpe to York?
(ii)_____________
(iii) York to Grimsby?
(iii)_____________
(d) A man riding a bicycle at 5 km/hr sets off at 8am. Show
this journey on the graph.
(e) What time does the cyclist meet the car?
(e)_______________
(f) How far away from Grimsby are they when they meet?
(f)________________
(16 marks)
12. A electrician charges a £20 call out fee plus £15 for each hour. Complete the
table below.
Hours worked (h)
0
1
Charge (C)
2
3
4
35
90
80
Charge
70
(£)
60
50
40
30
20
10
0
1
2
3
4
5
6
7
8
9
10
Hours worked
(a) Plot a graph to show the relationship between hours
worked (h) and the Charge (C)
(b) How long did the electrician work if his charge was £70?
(You must show on the graph how you obtained the answer)
(b)_____________
(8 marks)
13. A glass vessel is being filled by a tap flowing at a constant rate. Which of the
following graphs best describes the level of water in the vessel against time.
Graph A
Graph B
Level
Graph C
Level
Time
Graph D
Level
Time
Level
Time
Time
Graph_______
(2 marks)
14. Sketch a graph that best describes the following description of unemployment.
'Two years ago unemployment was rising, but last year it didn't rise at all, and this
year it is rising even more rapidly than 2 years ago'
Unemployment
Time
(3 marks)