Cambridge Essentials Mathematics Extension 9 A4 End-of-unit Test
/ A4 End-of-unit Test1 Look at this sequence of patterns made with discs.
Pattern 1 Pattern 2 Pattern 3
Write down an expression for the total number of grey discs in the nth pattern.
………………
1 mark
Write down an expression for the total number of white discs in the nth pattern.
………………
1 mark
How many grey discs are there in the 10th pattern?
………………
How many white discs are there in the 12th pattern?
………………
What is the total number of discs in the 20th pattern?
………………
1 mark
Write down an expression for the total number of discs in the nth pattern.
………………
1 mark
2 The distance–time graph represents the journey of a courier, starting at 10 a.m.
He stopped to deliver an important package, then again for lunch, before returning home at 3 p.m.
a What was the average speed during the first part of the journey?
……………… mph
1 mark
b Between what times did he stop for lunch?
Between ……………… and ………………
1 mark
c How far was the courier from home at 1:30 p.m.?
……………… miles
1 mark
d What was the total length of his journey?
……………… miles
1 mark
3 The sketch shows a right-angled triangleP, Q and R are the midpoints of
the sides of the triangle.
Work out the coordinates of P, Q and R. /
P = (………, ………)
1 mark
Q = (………, ………)
1 mark
R = (………, ………)
1 mark
4 The speed–time graphs show information about four different car journeys.
Write the correct letter of the graph next to the journey descriptions below.
Letter / DescriptionThe car increased its speed at a constant rate.
The car accelerated, braked sharply, then accelerated again.
The car accelerated away to reach a constant speed before coming to a gradual stop.
The car increased its speed before coming to a sudden halt.
2 marks
5 a Show that the points (1, 4), (4, 13) and (7, 22) all lie on the line y = 3x + 1.
1 mark
b A different line goes through the points (0, −1), (3, 5) and (5, 9).
Write down the equation of this straight line.
………………
1 mark
6 a The grid shows a sketch of a straight line.Two of the equations below also describe the straight line.
Draw a circle around each of these equations. /
x = y − 1 y = 2x + 1
x − y = 1 y − x = 1 xy = 1
1 mark
b Write down two coordinates that are on this line.
(………, ………), (………, ………)
2 marks
7 a These are expressions for the nth term of a sequence.
For each expression say whether the series is increasing, decreasing or neither.
increasing decreasing neither
2 marks
b Work out the first four terms for a sequence which has as its nth term the expression .
………………, ………………¸ ………………, ………………
2 marks
c A straight line is parallel with the line y = x + 1.
It passes through the point (0, −2).
What is the equation of this straight line?
………………
1 mark
8 Here are two coordinates.
(2, 1) (4, 3)
Write down the equation of the line that goes through these two points.
………………
1 mark
9 Look at the graph.
At points P and Q, the line y = x − 3 crosses the curve y = x² − 3.
What are the coordinates of P and Q?
P (………, ………)
Q (………, ………)
2 marks
10 Complete this table of values for the graph of y = x² − 2x + 3.
x / −2 / −1 / 0 / 1 / 2 / 3 / 4y
2 marks
Draw the graph of y = x² − 2x + 3.
2 marks
END OF ASSESSMENT
/ A4 End-of-unit Test – Teacher GuidanceUnits covered: A4.1, A4.2, A4.3
Guide to Levels.
Level / Description6 / Deriving the nth term for a simple number sequence
Using and interpreting a time–distance graph
Finding the coordinates of midpoints of lines
Understanding linear graphs of the form y = mx + c
7 / Working with reciprocal number sequences
Working with straight lines and gradient
8 / Sketching and interpreting graphs of quadratic and linear functions
Answers
Question / Level / Mark / Answer / Notes1 / 6
6
6
6 / 1
1
1
1 / n + 1
2n
11
24
61
3n + 1 / 1 mark
1 mark
1 mark for all three
1 mark
2 a
b
c
d / 6
6
6
6 / 1
1
1
1 / 60
12 noon, 12:30 p.m.
26
120 / 1 mark
1 mark
1 mark
1 mark
3 / 6 / 3 / (18, 24)
(36, 12)
(18, 12) / 1 mark
1 mark
1 mark
4 / 6 / 2 / BDAC / 2 marks for all correct, or 1 mark for three correct.
5 a
b / 7
7 / 1
1 / Shown
y = 2x − 1 / 1 mark for working (e.g. substitution of the points into the equation)
1 mark
6 a
b / 7
7 / 1
2 / x = y − 1,
y − x = 1
Coordinates / 1 mark for both and no others
1 mark for first coordinate, 1 mark for second coordinate
7 a
b
c / 7
7
8 / 2
2
1 / I, D, N, D
1/9,1/16, 1/25,1/36
y = x − 2 / 1 mark for 3 correct
1 mark for 3 correct or correct substitution of 1, 2, 3, 4
1 mark
8 / 7 / 1 / y = x − 1 / 1 mark
9 / 8 / 2 / P(0, −3)
Q(1, −2) / 1 mark
1 mark
10 / 8 / 2
2 / 11, 6, 3, 1, 3, 6, 11
Graph / 1 mark for at least 4 correct
1 mark for approximate parabola with some errors
NB: Levels are approximate only.
Suggested guidance on overall level based on performance:
Level 6 / Level 7 / Level 8 / Total7 marks / 17 marks / 24 marks / 30 marks
NB: Levels are approximate only.
Original material © Cambridge University Press 2010 / 8