# ### Number Sequences 1

What is the 5th:
a) Odd number; 9
b) Square number; 25
c) Prime number. 11

### Factors

Find all the factors of:

26

1, 2, 13, 26.

### Multiples

Subtract the 7th from the 11th multiples of:

12

48

### Polygons

What are the names of regular polygons with:
a) eight sides;
b) nine sides;
c) ten sides.

Octagon, Nonagon and Decagon (all regular)

### Rounding

Round the following numbers to three significant figures:
a) 45.19; 45.2
b) 593904; 594000
c) 0.009195; 0.00920

### Area of a Triangle

Find the area of a triangle that has a base of 4cm and a height of 7cm.

14cm2

### Area of a Trapezium

Find the area of a trapezium that has a base of 16cm, a height of 5cm and a top (parallel to base) of 6cm. 55cm2

Evaluate:

$$\frac{4}{5} + \frac{8}{10}$$ $$= 1\frac{3}{5}$$

### Fractions (Multiplying)

Evaluate:

$$\frac{3}{4} × \frac{5}{7}$$ $$= \frac{15}{28}$$

### Fractions (Dividing)

Evaluate:

$$\frac{1}{2} ÷ \frac{5}{4}$$ $$= \frac{2}{5}$$

### Circle (Vocabulary)

Name the red part.  ### Venn Diagrams

Describe the red region.  ### Shape Formulas

What is the formula?  What is it?  ### Fraction to Percentage

Convert this fraction to a percentage to 3 significant figures.

$$\frac{4}{9}$$ $$= 44.4$$%

### Circle Area

Find the area of a circle that has a radius of 1cm. Give your answer to three significant figures.

3.14cm2

### Circle Circumference

Find the circumference of a circle that has a radius of 3cm. Give your answer to three significant figures.

18.8cm

Calculate the value of:

5.5 + 2.7

= 8.2

### Decimals (Subtracting)

Calculate the value of:

8.4 − 2.7

= 5.7

### Decimals (Multiplying)

Calculate the value of:

4.3 × 2.4

= 10.32

### Decimals (Dividing)

Calculate the value of:

182.4 ÷ 19

= 9.6

### Indices (Simple)

What is the value of:

53

= 125

What is the value of:

$$3^{-2}$$

$$= \frac{1}{9}$$

Calculate the value of:

77 + 25

= 102

### Basic Subtraction

Calculate the value of:

71 − 29

= 42

### Basic Multiplication

Calculate the value of:

22 × 28

= 616

### Basic Division 2

Calculate the value of:

1564 ÷ 23

= 68

### Percentage (Of)

Find the value of:

50% of 280

= 140

### Standard Form 1

Find the value of:

6.96 × 102

= 696

### Highest Common Factor

Find the highest common factor of thirty and twenty five.

= 5

### Times Tables (2-5)

 7 × 4 = 28 5 × 5 = 25 9 × 3 = 27 3 × 4 = 12 8 × 4 = 32 4 × 5 = 20 6 × 2 = 12 2 × 3 = 6

### Times Tables (2-12)

 7 × 5 = 35 6 × 4 = 24 3 × 6 = 18 9 × 8 = 72 4 × 2 = 8 8 × 2 = 16 5 × 2 = 10 2 × 9 = 18

### Times Tables (2)

 9 × 2 = 18 6 × 2 = 12 7 × 2 = 14 3 × 2 = 6 4 × 2 = 8 5 × 2 = 10 8 × 2 = 16 2 × 2 = 4

### Times Tables (3)

 3 × 3 = 9 7 × 3 = 21 4 × 3 = 12 5 × 3 = 15 8 × 3 = 24 6 × 3 = 18 9 × 3 = 27 2 × 3 = 6

### Times Tables (4)

 8 × 4 = 32 3 × 4 = 12 7 × 4 = 28 4 × 4 = 16 6 × 4 = 24 5 × 4 = 20 9 × 4 = 36 2 × 4 = 8

### Times Tables (5)

 9 × 5 = 45 8 × 5 = 40 5 × 5 = 25 6 × 5 = 30 7 × 5 = 35 4 × 5 = 20 3 × 5 = 15 2 × 5 = 10

### Times Tables (6)

 5 × 6 = 30 8 × 6 = 48 7 × 6 = 42 3 × 6 = 18 4 × 6 = 24 9 × 6 = 54 6 × 6 = 36 2 × 6 = 12

### Times Tables (7)

 8 × 7 = 56 3 × 7 = 21 7 × 7 = 49 4 × 7 = 28 5 × 7 = 35 9 × 7 = 63 6 × 7 = 42 2 × 7 = 14

### Times Tables (8)

 6 × 8 = 48 8 × 8 = 64 5 × 8 = 40 3 × 8 = 24 9 × 8 = 72 4 × 8 = 32 7 × 8 = 56 2 × 8 = 16

### Times Tables (9)

 9 × 9 = 81 8 × 9 = 72 4 × 9 = 36 3 × 9 = 27 7 × 9 = 63 5 × 9 = 45 6 × 9 = 54 2 × 9 = 18

### Times Tables (12)

 3 × 12 = 36 5 × 12 = 60 9 × 12 = 108 4 × 12 = 48 8 × 12 = 96 7 × 12 = 84 6 × 12 = 72 2 × 12 = 24

### Fractions (Equivalent)

Write this fraction in its simplest form:

$$\frac{25}{30}$$ $$= \frac{5}{6}$$

### Fractions (Mixed)

Evaluate:

$$1\frac{1}{2} − \frac{4}{5}$$ $$= \frac{7}{10}$$

### Pythagoras

Find AC if AB = 3.5m and BC = 4.6m. 2.98m

### Trigonometry (Angle)

Find angle ABC if AC = 5.8m and BC = 7.5m. 50.7o

### Trigonometry (Side)

Find AC if angle ABC = 24o and BC = 4.7m. 1.91m

2

2

2

### Fraction to Decimal

Convert this fraction to a decimal.

$$\frac{2}{5}$$ $$= 0.4$$

### Decimal to Fraction

Convert this decimal to a fraction.

$$0.07$$ = $$\frac{7}{100}$$

### Percentage (Increase)

Increase £20 by 25%

£25

### Lowest Common Multiple

What is the lowest common multiple of four and twelve.

= 12

### Sequence (Arithmetic)

7,21,35,49,63...

Find the:
a) next term; 77
b) nth term; 14n - 7
c) term number 42; 581

### Sequence (Geometric)

3,6,12,24,48...

Find the:
a) next term; 96
b) nth term; 3 × 2n-1
c) term number 10; 1536

### Interest (Simple)

If £100 is invested for 4 years with a simple interest rate of 2%, find the amount of interest earned. £8.00

### Interest (Compound)

If £220 is invested with an interest rate of 1% compounded annually, find the value of the investment after 5 years. £231.22

### Currency Exchange

If £1 is worth $1.58, convert: a) £180 to dollars;$284.40

b) \$240 to pounds; £151.90

### Coordinates (Midpoint)

What are the coordinates of the midpoint of the line joining:

$$(-5,-7) \text{ and } (5,1)$$

(0,-3)

What is the gradient of the line joining:

$$(6,0) \text{ and } (9,3)$$

1

### Coordinates (Square)

Here are the coordinates of 3 vertices of a square, what are the coordinates of the 4th?

$$(5,3),(9,7),(1,7)$$

(5,11)

### Negative Numbers

a) 10 − 16 = -6
b) 10 × (-8) = -80
c) (9−20)(11−23) = 132
d) 80 ÷ (-8) = -10
e) (-10)2 = 100

### Substitution

If p = 5, q = 22 and
r = -12 evaluate:

a) 2q − p = 39
b) pq + r = 98
c) p2 − 5q - r = -73

### Equations (Type 1)

Solve:

$$2x = 18$$

$$x = 9$$

### Equations (Type 2)

Solve:

$$3x +5= 23$$

$$x = 6$$

### Equations (Type 3)

Solve:

$$6x -2= 4x + 14$$

$$x = 8$$

### Equations (Type 4)

Solve:

$$4(2x -5)-9= -13$$

$$x = 2$$

### Equations (Type 5)

Solve:

$$4(5x + 5)= 5(3x + 5)$$

$$x = 1$$

### Equations (Simultaneous 1)

Solve:

$$5x-2y = 3$$
$$2x+2y = 18$$

$$x = 3, y = 6$$

### Equations (Simultaneous 2)

Solve:

$$2x+3y = 13$$
$$7x-9y = -13$$

$$x = 2, y = 3$$

### Equations (Simultaneous 3)

Solve:

$$2x+5y = -16$$
$$3x+2y = 9$$

$$x = 7, y = -6$$

### Sets (Union)

Find the union of:

{6,7,8,9,10} and
{2,6,12}

{2,6,7,8,9,10,12}

### Sets (Intersection)

Find the intersection of:

{1,2,3,4,5} and
{2,4,6,8,10}

{2,4}

### Bearings

A plane flies from point A to point B on a bearing of 071o. What bearing would it return on from B to A? 251o

### Probability

A number is picked at random from the set

{1,3,6,10,15}

what is the probability it is even? $$\frac25$$

Evaluate:

32 − 6 × 3 + 2

-7

### Simplify

Simplify the following by collecting like terms:

$$5a−5−4a−5$$

$$a-10$$

### Ratio

Divide 50 in the ratio

3:2

30 and 20

### Graph (Linear)

Draw a rough sketch of the graph of:

$$y=x$$

y intercept 0

### Prime Factors

Express the following number as the product of prime numbers:

180

2 x 2 x 3 x 3 x 5

### Percentage (Reverse)

In a sale an item costs £34 after a 15% reduction. What was the original price?

£40

### Averages

Find the mean, mode, median and range of the following:

5,3,7,5,10

Mean = 6, mode = 5,
median = 5 and range = 7

### Time (Analogue)

What time is this?  ### Time (Digital)

Sketch a clock face:  ### Decimals (Recurring)

Write the following recurring decimal as a fraction in its lowest terms.

0.181818... $$\frac{2}{11}$$

### Percentage (Decrease)

Decrease £140 by 15%

£119

### Brackets (Linear)

Expand:

$$3(3x-2)$$

$$9x-6$$

Expand:

$$(4x+2)(2x-1)$$

$$8x^2-2$$

### Factorise (Linear)

Factorise:

$$6x-9$$

$$3(2x-3)$$

Factorise:

$$x^2+2x-3$$

$$(x+3)(x-1)$$

Factorise:

$$x^2-2x-8$$

$$(x+2)(x-4)$$

### Circle Theorems

Which theorem?  ### Standard Form 2

Find the value of:

2.13 × 10-4

= 0.000213

### Standard Form 3

Write in standard form:

57000

= 5.7 × 104

### Standard Form 4

Write in standard form:

0.000749

= 7.49 × 10-4

Find the nth term:

$$9, 17, 29, 45, 65,$$

$$2n^2+2n+5$$

### Standard Form 5

Multiply 6 × 104
by 4 × 106 and give the answer in standard form.

= 2.4 × 1011

Solve:

$$x^2-x-30= 0$$

$$x = 6$$ and $$-5$$

Solve this equation giving the solutions to 3 significant figures:

$$4x^2-2x-4 = 0$$

$$x = 1.28$$ and $$-0.781$$

### Polygon Angles

What is the size of each interior angle of a regular octagon?

135° ### Change The Subject

Make $$e$$ the subject of the formula
$$f=g(e+h)$$

$$e=\frac{f}{g}-h$$

### Basic Division 1

Calculate the value of:

534 ÷ 2

= 267

### Number Sequences 2

What is the 8th:
a) Cube number; 512
b) Triangular number; 36
c) Fibonacci number. 21

### Square Numbers

What are the next three square numbers after
36

49, 64, 81

### Prime Numbers

What is the 8th prime number?

19

### Last Lesson

Write down something you learnt in the previous mathematics lesson.

### Last Week

Write down something you learnt in one of the mathematics lessons last week.

### Angles

Calculate $$x$$.  ### Decimals (Ordering)

Write down these numbers: 9.09, 0.99, 0.9, 9.9, 9.99, 9, 0.09, in ascending order.
0.09, 0.9, 0.99, 9, 9.09, 9.9, 9.99,

### Lengths (Ordering)

Write down these lengths: 107cm, 18mm, 1.08m, 17cm, 1.8m, 1.7cm, in order.
1.7cm, 18mm, 17cm, 107cm, 1.08m, 1.8m,

### Capacities (Ordering)

Write down these capacities: 17cl, 21cl, 18cl, 200ml, 173ml, 18ml, in order.
18ml, 17cl, 173ml, 18cl, 200ml, 21cl,

### Angles with Parallels 1 f = 132

### Angles with Parallels 2 i = 97

## A Mathematics Lesson Starter Of The Day

• Jan, South Canterbury
•
• Thank you for sharing such a great resource. I was about to try and get together a bank of starters but time is always required elsewhere, so thank you.
• Barbara Schindler, Newton Rigg College
•
• I use Refreshing Revision a lot but today all the brackets and fractions keep coming up 'jumbled' . There are curly brackets, part words / 's in odd places and it is impossible to make out the question. It is doing this on 2 computers I have tried. Can you help? thank you.

[Transum: Sorry to hear about this problem Barbara. I have tested it from here and it seems to be working OK. Please take a look at the MathJax FAQ. Many apologies for the inconvenience.]
• Lesley, UK
•
• Answers for the starter would be great so students can get immediate feedback and become independent learners.

[Thanks for your comments Lesley. The answers are only available to signed-in teachers and parents I'm afraid. I you are a subscriber and are projecting this Starter for the whole class to see you can scroll down the page and show the same questions with the answers included in red.]
• Mrs B, Stockport
•
• Refreshing Revision really useful resource, that I have actually used for Ks2 revision as some topics are appropriate. I'd love to see either ks2 version, with purely ks2 SATs level topics or adding them to the current version.

[Transum: Thanks so much for your feedback Mrs B. If you could send me a list of your top ten ideas for topic you would like to see added I will work on it]
• Mark Adams, St Peters RC School Solihull
•
• It would be great if these questions came with answers as well.

[Transum: The answers to Transum activities are available to those signed in to their Transum subscription account. You can sign up for an account here.]

How did you use this starter? Can you suggest how teachers could present or develop this resource? Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for Maths teachers anywhere in the world.

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## Concept Selection

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## GCSE Revision and Practice

Whatever exam board you use for GCSE Mathematics, this book by David Rayner remains an all-round winner. With this latest edition presented in full colour and completely updated for the new GCSE(9-1) specifications, this uniquely effective text continues to increase your chance of obtaining a good grade.

This book is targeted at the Higher tier GCSE, and provides a wealth of practice with careful progression, alongside substantial revision support for the new-style grading and exam questions. With all the new topics included, and a dedicated section on using and applying mathematics, this unique resource can be used either as a course book over two or three years or as a revision text in the run-up to exams. more...  ## Maths T-Shirts Maths T-Shirts on Amazon  Teacher, do your students have access to computers such as tablets, iPads or Laptops?  This page was really designed for projection on a whiteboard but if you really want the students to have access to it here is a concise URL for a version of this page without the comments: Transum.org/go/?Start=April9 However it would be better to assign one of the student interactive activities below. Here is the URL which will take them to a related student activity.

Transum.org/go/?to=topictest Here's a projectable set of randomly-selected revision questions for the end of the lesson.

Transum.org/Intro/?ID=997 Teacher:
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