Cambridge Essentials Mathematics Extension 9 A1 End-of-unit Test
A1 End-of-unit Test
1
Write these expressions as simply as possible.
k×k×k =
………………
2p + m² + 3p =
………………
4q + 10 − 8q =
………………
2y × 3y =
………………
4 marks
2
Match the expressions that are equivalent. The first one is done for you.
1
2t ÷ 2t
t
2t
t + 2t
3t
2t − t
4t
t2
2t × t
2t2
3t2
t×t
t3
3 marks
Original material © Cambridge University Press 2010
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Cambridge Essentials Mathematics Extension 9 A1 End-of-unit Test
3
a The number of pens is each box is the same.
Box A
Box B
Work out the value of x.
3x + 2
pens
2x + 4
pens
………………
2 marks
b Box B contains more pens than Box A.
Box A
Box B
What is the largest possible value of y?
5y
pens
y + 18
pens
………………
2 marks
4
Fill in the missing expressions so that each statement is always true.
4x + 2x  ………………
4x × 2x  ………………
5y + ………………  7y
5y × ………………  20y²
……………… + ………………  10z
……………… × ………………  24z²
3 marks
Original material © Cambridge University Press 2010
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Cambridge Essentials Mathematics Extension 9 A1 End-of-unit Test
5
The perimeter of a square is 48x + 36.
a Write an expression for the length of one of the sides.
………………
1 mark
b The perimeter of a different regular shape is 18x − 27.
The length of one of its sides is 2x − 3.
How many sides does the shape have?
………………
1 mark
3x − 4
c Find an expression for the perimeter of this
shape.
Give your answer in its simplest form.
2x + 1
………………
2 marks
6
For each expression below, when x increases by 4, what happens to y?
y=x
When x increases by 4, y increases by
………………
y = 3x
When x increases by 4, y increases by
………………
y = 2x + 1
When x increases by 4, y increases by
………………
2 marks
Original material © Cambridge University Press 2010
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Cambridge Essentials Mathematics Extension 9 A1 End-of-unit Test
Original material © Cambridge University Press 2010
4
Cambridge Essentials Mathematics Extension 9 A1 End-of-unit Test
7
a Parham says
‘If I have any two numbers a and b, (a + b)² gives me the same answer
as a² + b².’
Parham is wrong. Explain why.
2 marks
b Sangita says
‘If I have any two numbers a and b, (a + b)² will never be the same as a² + b².
Sangita is wrong. Explain why.
1 mark
8
Complete this statement by writing a single number in each space.
x² + 5x + ……………… = (x + ………………)( x + ………………)
Now write different numbers to complete the statement.
x² + 5x + ……………… = (x + ………………)( x + ………………)
2 marks
9
c − d is half the value of c + d.
Write c in terms of d.
………………
2 marks
Original material © Cambridge University Press 2010
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Cambridge Essentials Mathematics Extension 9 A1 End-of-unit Test
10 Factorise these expressions
x² + 7x − 18
………………
2 marks
x² − 49
………………
2 marks
END OF ASSESSMENT
Original material © Cambridge University Press 2010
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Cambridge Essentials Mathematics Extension 9 A1 End-of-unit Test
A1 End-of-unit Test – Teacher Guidance
Units covered: A1.1, A1.2
Guide to Levels.
Level Description
Simplifying algebraic expressions with powers
6
Understanding the equivalence between algebraic expressions with powers
Deriving and simplifying formulae
Understanding identity and equivalence in a range of expressions
7
Multiplying and simplifying algebraic terms
Deriving and simplifying formulae
Manipulating algebraic equations and expressions, finding common factors
8
and multiplying two linear expressions
Finding the difference of two squares
Answers
Question
1
2
Level
5
6
6
7
5
Mark
1
1
1
1
3
3a
b
5
7
2
2
4
7
3
5a
b
c
7
7
7
1
1
2
6
8
2
7a
7
2
Answer
k³
5p + m²
10 − 4q
6y²
3t
t
2t²
t²
2
4
6x
8x²
2y
4y
6z, 4z
6z, 4z
12x + 9
9
10x − 6
4
12
8
Reason
Original material © Cambridge University Press 2010
Notes
1 mark
1 mark
1 mark
1 mark
3 marks for all four pairs linked
correctly, or 2 marks for two pairs
linked, or 1 mark for just 1 pair linked
correctly
1 mark for writing a correct equation
1 mark for evidence of a method which
would lead to the answer
3 marks for all correct, or 2 marks for
four correct. or 1 mark for just 2 correct.
1 mark
1 mark
1 mark for attempt to add four correct
terms
2 marks for all 3, or 1 mark for 2 correct
2 marks for expansion and full
explanation; 1 mark for numeric
demonstration or expansion without
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Cambridge Essentials Mathematics Extension 9 A1 End-of-unit Test
b
8
8
1
Reason
8
2
e.g. 6, 2, 3
e.g. 4, 4, 1
c = 3d
(x + 9)(x − 2)
(x − 7)(x + 7)
2
2
2
NB: Levels are approximate only.
9
10
8
8
conclusion
1 mark for demonstration e.g. a = 0, b =
1
2 marks for two sets of correct numbers;
1 mark for 1 set
1 mark for correct initial equation
1 mark for 1 factor identified
1 mark for 1 factor identified.
Suggested guidance on overall level based on performance:
Level 6 Level 7
Level 8
Total
5 marks 16 marks 24 marks 31 marks
NB: Levels are approximate only.
Original material © Cambridge University Press 2010
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