The RobertSmythSchoolTopic 12
Mathematics FacultySurds
Simplifying Surds and Expanding Brackets
1.(a)Find the value of
(i)
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Answer ……………………………………… (1)
(ii)
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Answer ……………………………………… (2)(Total 3 marks)
2.(a)Simplify
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Answer ...... (2)
(b)Hence simplify
giving your answer in its simplest surd form.
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Answer ...... (3) (Total 5 marks)
3.Show that is an integer.
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(Total 2 marks)
4.Show that
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(Total 3 marks)
5.Find values of a and b such that
(2 + 3)(4 – 3) = a + b3
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Answer a = ...... b = ......
(Total 2 marks)
6.Work out
Give your answer in the form where a and b are integers.
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Answer ......
(Total 3 marks)
7.(a)Simplify
(i)
Answer ......
(1)
(ii)
Answer ......
(1)
(b)Show that simplifies to
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(3) (Total 5 marks)
8.(a)Expand and simplify
(2 + 3)(4–)
Give your answer in the form
a + b+ c+ d
where a, b, c and d are integers.
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Answer ......
(3) (Total 3 marks)
9.Show that (+)2 can be expressed in the form p + q
where p and q are integers to be found.
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Answer ......
(Total 3 marks)
10.(a)You are given that 12 + 27 = a3 where a is an integer.
Find the value of a.
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Answer ......
(2)
(b)Find the value of (m + p)2 when m = 2 and p = 8
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Answer ......
(2)
(Total 4 marks)
11.(a)(i)Show that =
……………...... ……………..……...... ………………………………….
……………...... ……………..……...... ………………………………….
(1)
(ii)Expand and simplify (+)2
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Answer …………………………………..
(2)
(b)Is this triangle right-angled?
You must show your working.
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(3) (Total 6 marks)
Rationalising the Denominator
1.(a)Simplify+
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Answer ......
(2)
(b)Rationalise
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Answer ......
(1)
(Total 3 marks)
2.Rationalise the denominator and simplify fully
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Answer ......
(Total 2 marks)
3.(a)Rationalise the denominator and simplify fully
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Answer ......
(2)
(b)By simplifying,
write
in its simplest form.
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Answer ......
(3) (Total 8 marks)
4.Rationalise the denominator of
Simplify your answer fully.
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Answer ...... (Total 3 marks)
5.(a)Rationalise the denominator of and simplify your answer fully.
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Answer ......
(2)
(Total 2 marks)
6.Simplify fully
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Answer …………………………………...... (Total 4 marks)
7.(a)By rationalising the denominator, simplify
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Answer ......
(2)
(b)Show that
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(2) (Total 4 marks)
8.(a)Write where p is an integer.
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Answer ...... (2)
(b)Hence write in the form .
You may use 338 = 2 × 132
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Answer ......
(2) (Total 4 marks)
9.(a)Rationalise and simplify
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Answer ...... (2)
(b)By simplifying+,
write
in the form where a and b are integers.
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Answer ...... (3)(Total 5 marks)
10.(a)Simplify fully the following expression, leaving your answer in surd form.
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Answer ......
(2)
(b)Given that 135 = 33 5, simplify the expression giving your answer in surd form.
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Answer ......
(3)
(Total 5 marks)
Problem solving using surds
1.(a)Express + in the form p
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Answer ......
(2)
(b)Hence, or otherwise, simplify fully
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Answer ......
(3) (Total 5 marks)
2.(a) Simplify by rationalising the denominator.
Give your answer in its simplest form.
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Answer ………………………………………
(2)
(b)Show that
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(3)
(Total 7 marks)
3.(a)Find the value of m when
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Answer m = ......
(3)
(b)Given that and
(i)Simplify fully,
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Answer ......
(2)
(ii)Show that
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(2)
(Total 7 marks)
4.Two rectangles, A and B, are equal in area.
Calculate the length of rectangle B. Give your Answer in the form .
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Answer ...... cm (Total 4 marks)
5.The area of this rectangle is 30 cm2.
Find the value of x, writing your answer in the form where a and b are integers.
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Answer ...... cm (Total 3 marks)
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