Indices / surds / irrational numbers



Indices / surds / irrational numbers

You MUST NOT use a calculator for any part of this homework. Show ALL working out.

Year 11 – Weekly revision homework (6) [pic]Score [pic] = %

Topics to revise: (1)

(2)

1. (a) Work out the value of 43

Answer ………………………. (1)

(b) 2n = 8

Work out the value of n.

Answer ……………….……… (1)

(c) Write 43 × 45 as a single power of 4.

Answer ……………………… (1)

(d) Work out 30 000 × 500

Answer ……………………… (1)

(e) Work out

[pic]

Give your answer in standard form.

Answer ……………………… (2)

2. Find the value of

(a) 4–2

Answer ………………………. (1)

(b) 36[pic]

Answer ……………………… (1)

(c) 27[pic]

Answer ……………………. (1)

3. (a) Write down the value of 110

Answer ....................................................

(1)

(b) Find the value of 8[pic]

Answer ....................................................

(2)

(c) Simplify 6–2 × 1440.5

Answer ......................................................

(3)

4. (a) (i) Find the value of x in 4x = [pic]

Answer ....................................................

(1)

(ii) Find the value of y in 8y = 2

Answer ....................................................

(1)

(b) Write down the value of [pic]

Answer ....................................................

(2)

5. (a) Simplify 3a5 × 4a2.

Answer ...........................................

(1)

(b) Work out the value of 21 – 20 + 2–1.

Answer ...........................................

(2)

6. (a) Work out 4 × 107 × 3 × 104

Give your answer in standard form.

Answer ..................................................................

(2)

(b) Work out [pic]

Give your answer in standard form.

Answer ..................................................................

(3)

7. (a) (i) Write down the reciprocal of 3

Answer …………………. (1)

(ii) Write down the reciprocal of [pic]

Answer ………………….. (1)

(b) c and d are positive fractions.

c is greater than d.

Tick the box to show which one of the following three statements is true.

[pic] The reciprocal of c is greater than the reciprocal of d.

[pic] The reciprocal of c is less than the reciprocal of d.

[pic] There is not enough information to know which reciprocal is greater.

(1)

8. Write down the number [pic] as a fraction in its simplest form.

Answer …………………….. (3)

9. (a) (i) Show that [pic]

(1)

(ii) Expand and simplify

[pic]

Answer ………………………… (3)

(b)

[pic]

Is triangle ABC right-angled?

Show your working clearly.

(3)

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