Name:
Exam Style Questions
Surds
Equipment needed: Pen
Guidance
1. Read each question carefully before you begin answering it.
2. Check your answers seem right.
3. Always show your workings
Video Tutorial
www.corbettmaths.com/contents
Videos 305, 306, 307, 308
Answers and Video Solutions
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1. Evaluate the following
(a) 3× 7
.........................
(1)
(b) 24 ÷ 6
.........................
(2)
(c) 2 3×3 5
.........................
(2)
(d) 10 8 ÷ 2 2
.........................
(2)
Simplify ( 3)
2
2.
.........................
(1)
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Work out the exact value of ( 2)
4
3.
.........................
(1)
4. (a) Express 75 in its simplest form.
.........................
(1)
(b) Express 32 in its simplest form.
.........................
(1)
(c) Express 8 in its simplest form.
.........................
(1)
(d) Express 200 in its simplest form.
.........................
(1)
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5. Simplify 5× 10
.........................
(2)
6. Simplify fully
(a) 50 + 32
.........................
(2)
(b) 80 + 20
.........................
(2)
(c) 200 − 72
.........................
(2)
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(d) 3 12 + 75
.........................
(3)
7. Tilly has been asked to work out 2+ 8
Tilly says the answer is 10 as 2 + 8 = 10
Is Tilly correct?
Explain your answer.
……………………………………………………………………………………………
……………………………………………………………………………………………
……………………………………………………………………………………………
(2)
8. Express 2+ 98 in the form a 2 where a is an integer.
.........................
(2)
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9. Write 150 + 24 in the form k 6
.........................
(2)
10. Shown below is a rectangle.
5 2 cm
2 cm
(a) Find the perimeter of the rectangle.
.........................cm
(2)
(b) Find the area of the rectangle.
.........................cm²
(2)
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11. Write each of these in the form a 3 , where a is an integer.
(a) 6× 8
.........................
(2)
(b) 27 + 75
.........................
(2)
15
12. Rationalise the denominator of
5
.........................
(2)
13. Simplify fully 600 + 24
.........................
(2)
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12
14. (a) Rationalise the denominator of
3
.........................
(2)
(b) Evaluate 2× 32
.........................
(2)
( 3+ 5)
2
(c) Expand and simplify
.........................
(2)
(d) Evaluate (5 + 2 )(5 − 2)
.........................
(2)
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15. (a) Simplify fully 3 ( 27 − 3)
.........................
(2)
(b) Given that a = 2 b= 15 c = 30
work out the value of
b
ac
write your answer in its simplest form
.........................
(3)
16. Rationalise the denominator of
12
7 3
.........................
(2)
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17. Given that a = 3 and b = 48
(a) nd the value of a 2
.........................
(1)
(b) show that (a + b)2 = 75
.........................
(3)
18. Expand and simplify (3 + 8 )(4 + 2)
Give your answer in the form a + b 2 where a and b are integers.
.........................
(4)
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fi
19. Simplify 5 8+ 18
.........................
(2)
20. Rationalise the denominator of
8
2
.........................
(2)
( 7− 3)
2
21. Expand and simplify
.........................
(2)
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22. Write 11 + 99 in the form a b where a and b are integers.
.........................
(2)
Expand (8 − 3 ) giving your answer in form a + b 3
2
23.
.........................
(2)
( 2 + 3 8 ) = 98
2
24. Show that
.........................
(3)
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25. The midpoints of the sides of a square of side 10cm are joined to form another
square.
This process is then repeated to create the shaded square.
Find the area of the shaded square.
.........................cm²
(4)
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10
26. Simplify 80 −
5
.........................
(3)
27. Given that
10 − 32
=a+b 2
2
where a and b are integer.
Find the values of a and b.
a = .........................
b = .........................
(4)
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28. A shed has dimensions, in metres, of
9
Height = 5 Width = 6 Length =
2
Find the volume of the shed.
Give your answer in the form a 15 , where a is an integer.
.........................m³
(3)
29. (a) Simplify 2y+ 2y+ 2y
.........................
(1)
(b) Simplify fully 2y× 2y× 2y
.........................
(2)
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9 4
30. c= d=
2 y y
Work out cd
.........................
(3)
4 10
31. y=
5
Work out the value of y3
.........................
(3)
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(3 + c 5 ) = d + 24 5
2
32.
Work out the values of c and d.
c = .........................
d = .........................
(4)
33. 300 − 2 x = 4 3
Work out the value of x
.........................
(3)
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34. Given that
2 a 3
1 + 12 =
25 b
Work out the values of a and b
.........................
(3)
35. Write
4 2
− 2 in the form a 5
5 9
.........................
(4)
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6
36. Write in the form a 2
1
+ 2
2
.........................
(4)
16
37. Show that can be written in the form a + b 11
11 − 3
.........................
(4)
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6
38. Show that can be written in the form a+b 3
2− 3
.........................
(4)
4 2 6 a 2−b
39. Write + in the form
3+ 2 2 c
.........................
(4)
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2−2
40. Write in the form a + b 2 , where a and b are integers.
3 2+4
.........................
(4)
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