Original Material © Cambridge University Press 2010

Decide if these statements are true or false.Give some examples if you can.

The last digit of a number formed by squaring a whole number can never be zero.

The last digit of a number formed by squaring a whole number can sometimes be 3.

The last digit of a number formed by cubing a whole number can be any number from 0 to 9.

Squaring and cubing recap

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Use algebra to write expressions for the lengths marked A, B, C, D and E.

Make up some similar puzzles whose answers are:• 2a + 4b• a + b + c 2a Make them as interesting as you can!• 10 + a – b

Simplifying expressions

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What operation or operations are inside each of these function machines?

4 4

115

4

9

59

9

10

6 11

x 2x + 1

A

B

C

D

Function machine re-cap

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Using just 2, 3 and 4 and any maths symbols you know, make as many numbersas you can in 5 minutes.

For example:

Order of operations re-cap

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These three shapes are all made from rectangles. Write an expression for the perimeter of each shape.

Look at the expressions for the perimeters.What do you notice?

(1)

(2)

(3)

Forming and solving equations

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In five minutes make up any many equations as you can with solutions 1, 2, 3 … etc.Try to make them interesting – but be sure you can solve them!

Equations and formulae

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Two friends, Jade and Paul are arguing …

Who is right?

Investigate using the equation

2x – 8 + 2x = 12.

Start by testing Jade’s comment, then test Paul’s.Test it on some other equations. Each time changing what you do to each side.

Solving equations (2)

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Jot down all you can about this sequence of squares.

and so on.

a) How can you tell that there cannot be a pattern consisting of 1000 squares?

b) How many squares are there in the next shape after the one with 1003 squares in it?

c) How many squares are there in the 1000th shape?

Sequences

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The red, blue and green spots continue in the same way.

a) Describe the rule for for placing blue spots.

b) Can there be a point thathas two differentcoloured spots on it?How did you decide?

c) Decide which colour spots, if any,are on these points:

(100, 101), (101, 100)

(101, 103), (100, 100)

(101, 101), (103, 102).

Mappings and straight-line graphs

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a) The equation of thered line is y = 2x + 2.

b) The equation of the greenline is y = 2x.

c) The blue line is parallel to a line with equationy = 2x.

d) The green line will passthrough the point (5, 10).

e) The green line only crosses the other three lines at the points (-2, -4) and (2, 4)and nowhere else.

Straight-line graph re-cap

Are the statements true or false? Explain your answers.