Refreshing Revision

Number Sequences 1

What is the 12th:
a) Odd number; 23
b) Square number; 144
c) Prime number. 37

Factors

Find all the factors of:

49

1, 7, 49.

Multiples

Subtract the 7th from the 11th multiples of:

7

28

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) 65.55; 65.6
b) 201760; 202000
c) 0.005395; 0.00540

Area of a Triangle

Find the area of a triangle that has a base of 6cm and a height of 11cm.

33cm2

Area of a Trapezium

Find the area of a trapezium that has a base of 15cm, a height of 12cm and a top (parallel to base) of 7cm. 132cm2

Fractions (Adding)

Evaluate:

\( \frac{2}{5} + \frac{7}{10}\) \(= 1\frac{1}{10}\)

Fractions (Multiplying)

Evaluate:

\( \frac{1}{2} × \frac{4}{5}\) \(= \frac{2}{5}\)

Fractions (Dividing)

Evaluate:

\( \frac{3}{5} ÷ \frac{9}{7}\) \(= \frac{7}{15}\)

Circle (Vocabulary)

Name the red part.

Circle part Circle part

Venn Diagrams

Describe the red region.

Circle part Circle part

Shape Formulas

What is the formula?

Circle part Circle part

Formulas (Advanced)

What is it?

Circle part Circle part

Fraction to Percentage

Convert this fraction to a percentage to 3 significant figures.

\( \frac{5}{6}\) \(= 83.3\)%

Circle Area

Find the area of a circle that has a radius of 7cm. Give your answer to three significant figures.

154cm2

Circle Circumference

Find the circumference of a circle that has a radius of 10cm. Give your answer to three significant figures.

62.8cm2

Decimals (Adding)

Calculate the value of:

7.6 + 4.9

= 12.5

Decimals (Subtracting)

Calculate the value of:

9.3 − 3.8

= 5.5

Decimals (Multiplying)

Calculate the value of:

2.4 × 8.4

= 20.16

Decimals (Dividing)

Calculate the value of:

39 ÷ 15

= 2.6

Indices (Simple)

What is the value of:

53

= 125

Indices (Advanced)

What is the value of:

5-1

= 0.2

Basic Addition

Calculate the value of:

79 + 34

= 113

Basic Subtraction

Calculate the value of:

72 − 26

= 46

Basic Multiplication

Calculate the value of:

39 × 73

= 2847

Basic Division 2

Calculate the value of:

1850 ÷ 25

= 74

Percentage (Of)

Find the value of:

10% of 140

= 14

Standard Form 1

Find the value of:

1.37 × 103

= 1370

Highest Common Factor

Find the highest common factor of twenty four and sixteen.

= 8

Times Tables (2-5)

7 × 3 = 21

6 × 2 = 12

5 × 3 = 15

4 × 3 = 12

3 × 2 = 6

9 × 3 = 27

8 × 3 = 24

2 × 2 = 4

Times Tables (2-12)

5 × 3 = 15

7 × 12 = 84

9 × 8 = 72

3 × 5 = 15

4 × 12 = 48

8 × 8 = 64

6 × 10 = 60

2 × 9 = 18

Times Tables (2)

4 × 2 = 8

8 × 2 = 16

3 × 2 = 6

6 × 2 = 12

9 × 2 = 18

7 × 2 = 14

5 × 2 = 10

2 × 2 = 4

Times Tables (3)

3 × 3 = 9

8 × 3 = 24

7 × 3 = 21

5 × 3 = 15

6 × 3 = 18

9 × 3 = 27

4 × 3 = 12

2 × 3 = 6

Times Tables (4)

7 × 4 = 28

6 × 4 = 24

9 × 4 = 36

5 × 4 = 20

4 × 4 = 16

3 × 4 = 12

8 × 4 = 32

2 × 4 = 8

Times Tables (5)

3 × 5 = 15

8 × 5 = 40

9 × 5 = 45

7 × 5 = 35

4 × 5 = 20

6 × 5 = 30

5 × 5 = 25

2 × 5 = 10

Times Tables (6)

9 × 6 = 54

5 × 6 = 30

8 × 6 = 48

4 × 6 = 24

3 × 6 = 18

6 × 6 = 36

7 × 6 = 42

2 × 6 = 12

Times Tables (7)

3 × 7 = 21

5 × 7 = 35

7 × 7 = 49

8 × 7 = 56

6 × 7 = 42

9 × 7 = 63

4 × 7 = 28

2 × 7 = 14

Times Tables (8)

7 × 8 = 56

6 × 8 = 48

9 × 8 = 72

8 × 8 = 64

5 × 8 = 40

3 × 8 = 24

4 × 8 = 32

2 × 8 = 16

Times Tables (9)

5 × 9 = 45

8 × 9 = 72

9 × 9 = 81

6 × 9 = 54

7 × 9 = 63

4 × 9 = 36

3 × 9 = 27

2 × 9 = 18

Times Tables (12)

9 × 12 = 108

3 × 12 = 36

4 × 12 = 48

8 × 12 = 96

6 × 12 = 72

5 × 12 = 60

7 × 12 = 84

2 × 12 = 24

Fractions (Equivalent)

Write this fraction in its simplest form:

\( \frac{27}{45}\) \(= \frac{3}{5}\)

Fractions (Mixed)

Evaluate:

\( 3\frac{4}{5} − \frac{6}{7}\) \(= 2\frac{33}{35}\)

Pythagoras

Find BC if AB = 5.1m and AC = 7m. 8.66m

Trigonometry (Angle)

Find angle ABC if AC = 4m and AB = 5.6m. 35.5o

Trigonometry (Side)

Find AC if angle BCA = 32o and AB = 3.7m. 5.92m

Roman Numerals (1-12)

Give your answer in Roman numerals.

2

Roman Numerals (60-100)

Give your answer in Roman numerals.

2

Roman Numerals (Large)

Give your answer in Roman numerals.

2

Fraction to Decimal

Convert this fraction to a decimal.

\( \frac{3}{5}\) \(= 0.6\)

Decimal to Fraction

Convert this decimal to a fraction.

\(0.82\) = \( \frac{41}{50}\)

Percentage (Increase)


Increase £80 by 25%

£100

Lowest Common Multiple

What is the lowest common multiple of twelve and eighteen.

= 36

Sequence (Arithmetic)

6,18,30,42,54...

Find the:
a) next term; 66
b) nth term; 12n - 6
c) term number 43; 510

Sequence (Geometric)

6,18,54,162,486...

Find the:
a) next term; 1458
b) nth term; 6 × 3n-1
c) term number 11; 354294

Interest (Simple)

If £140 is invested for 9 years with a simple interest rate of 3%, find the amount of interest earned. £37.80

Interest (Compound)

If £220 is invested with an interest rate of 5% compounded annually, find the value of the investment after 4 years. £267.41

Currency Exchange

If £1 is worth $1.47, convert:

a) £220 to dollars; $323.40

b) $180 to pounds; £149.66

Coordinates (Midpoint)

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

\((9,-8) \text{ and } (15,2)\)

(12,-3)

Gradient

What is the gradient of the line joining:

\((-5,1) \text{ and } (-1,4)\)

\(\frac{3}{4}\)

Coordinates (Square)

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

\((3,5),(7,11),(-3,9)\)

(1,15)

Negative Numbers

a) 6 − 13 = -7
b) 6 × (-7) = -42
c) (5−14)(12−23) = 99
d) 42 ÷ (-7) = -6
e) (-7)2 = 49

Substitution

If p = 6, q = 18 and
r = -11 evaluate:

a) 2q − p = 30
b) pq + r = 97
c) p2 − 5q - r = -43

Equations (Type 1)

Solve:

\(2x = 8\)

\(x = 4\)

Equations (Type 2)

Solve:

\(3x -5= 13\)

\(x = 6\)

Equations (Type 3)

Solve:

\(9x +5= 5x + 37\)

\(x = 8\)

Equations (Type 4)

Solve:

\(4(5x -4)-5= 79\)

\(x = 5\)

Equations (Type 5)

Solve:

\(2(3x + 5)= 4(3x + 5)\)

\(x = -1.67 \text{(to 3 sf)}\)

Equations (Simultaneous 1)

Solve:

\(3x-4y = 5\)
\(2x+4y = 30\)

\(x = 7, y = 4\)

Equations (Simultaneous 2)

Solve:

\(4x-3y = -9\)
\(2x+12y = 90\)

\(x = 3, y = 7\)

Equations (Simultaneous 3)

Solve:

\(6x+6y = 45\)
\(4x-7y = 8\)

\(x = 5.5, y = 2\)

Sets (Union)

Find the union of:

{5,6,7,8,9,10} and
{2,6,12}

{2,5,6,7,8,9,10,12}

Sets (Intersection)

Find the intersection of:

{1,3,5,7,9} and
{1,3,6,10,15}

{1,3}

Bearings

A plane flies from point A to point B on a bearing of 316o. What bearing would it return on from B to A? 136o

Probability

A number is picked at random from the set

{6,7,8,9,10}

what is the probability it is even? \(\frac35\)

BIDMAS

Evaluate:

35 ÷ 5 × 40 ÷ 8

35

Simplify

Simplify the following by collecting like terms:

\(3b+5c+8b+4c\)

\(11b+9c\)

Ratio

Divide 99 in the ratio

3:8

27 and 72

Graph (Linear)

Draw a rough sketch of the graph of:

\(y=x-2\)

Gradient 1
y intercept -2

Prime Factors

Express the following number as the product of prime numbers:

23

23

Percentage (Reverse)

In a sale an item costs £39 after a 35% reduction. What was the original price?

£60

Averages

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

5,8,8,6,7,8

Mean = 7, mode = 8,
median = 7.5 and range = 3

Time (Analogue)

What time is this?

Circle part Circle part

Time (Digital)

Sketch a clock face:

Circle part Circle part

Decimals (Recurring)

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

0.484848... \(\frac{16}{33}\)

Percentage (Decrease)


Decrease £140 by 15%

£119

Brackets (Linear)

Expand:

\(2(8x-7)\)

\(16x-14\)

Brackets (Quadratic)

Expand:

\((4x+4)(x-1)\)

\(4x^2-4\)

Factorise (Linear)

Factorise:

\(9x-27\)

\(9(1x-3)\)

Factorise (Quadratic 1)

Factorise:

\(x^2-3x-4\)

\((x+1)(x-4)\)

Factorise (Quadratic 2)

Factorise:

\(12x^2+7x-12\)

\((3x+4)(4x-3)\)

Circle Theorems

Which theorem?

Circle part Circle part

Standard Form 2

Find the value of:

9.22 × 10-4

= 0.000922

Standard Form 3

Write in standard form:

41000

= 4.1 × 104

Standard Form 4

Write in standard form:

0.000067

= 6.7 × 10-5

Sequence (Quadratic)

Find the nth term:

\(15, 23, 33, 45, 59, \)

\(n^2+5n+9\)

Standard Form 5

Multiply 4 × 104
by 5 × 103 and give the answer in standard form.

= 2 × 108

Equations (Quadratic 1)

Solve:

\(x^2-x-20= 0\)

\(x = 5\) and \(-4\)

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

\(2x^2+4x-4 = 0\)

\(x = 0.732\) and \(-2.73\)

Polygon Angles

What is the size of each exterior angle of a regular nonagon?

40°

Interior and Exterior angles

Change The Subject

Make \(g\) the subject of the formula
$$e=\frac{g}{h}+d$$

$$g=h(e-d)$$

Basic Division 1

Calculate the value of:

5103 ÷ 9

= 567

Number Sequences 2

What is the 6th:
a) Cube number; 216
b) Triangular number; 21
c) Fibonacci number. 8


A Mathematics Lesson Starter Of The Day


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Topics: Starter | Algebra | Arithmetic | Circles | Coordinates | Fractions | Mental Methods | Mixed | Money | Sets | Simultaneous Equations | Tables | Trigonometry

  • 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
  • Sunday, November 19, 2017
  • 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]

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Christmas Present Ideas

It is often very difficult choosing Christmas presents for family and friends but so here are some seasonal, mathematics-related gifts chosen and recommended by Transum Mathematics.

Equate board game

Here's a great board game that will give any family with school-aged kids hours of worthwhile fun. Christmas is a time for board games but this one will still be useful at any time of year. Games can be adapted to suit many levels of Mathematical ability.

For Maths tutors working with just one or small groups of pupils this game has proved to be an excellent activity for a tutorial. Deciding on the best moves can spark pertinent discussions about mathematical concepts.

Equate looks a bit like Scrabble--for aspiring mathematicians, that is. Designed by a real mathematician, it works like this: You put down tiles on a board and make points by correctly completing simple equations. Your nine tiles include both numbers and mathematical symbols; you can add on to previous plays both vertically and horizontally. more...

How Not To Be Wrong

The maths we learn in school can seem like an abstract set of rules, laid down by the ancients and not to be questioned. In fact, Jordan Ellenberg shows us, maths touches on everything we do, and a little mathematical knowledge reveals the hidden structures that lie beneath the world's messy and chaotic surface. In How Not to be Wrong, Ellenberg explores the mathematician's method of analyzing life, from the everyday to the cosmic, showing us which numbers to defend, which ones to ignore, and when to change the equation entirely. Along the way, he explains calculus in a single page, describes Gödel's theorem using only one-syllable words, and reveals how early you actually need to get to the airport.

What more could the inquisitive adult want for Christmas? This book makes a cosy, interesting read in front of the fire on those cold winter evenings. more...

Graphic Display Calculator

This handheld device and companion software are designed to generate opportunities for classroom exploration and to promote greater understanding of core concepts in the mathematics and science classroom. TI-Nspire technology has been developed through sound classroom research which shows that "linked multiple representation are crucial in development of conceptual understanding and it is feasible only through use of a technology such as TI-Nspire, which provides simultaneous, dynamically linked representations of graphs, equations, data, and verbal explanations, such that a change in one representation is immediately reflected in the others.

For the young people in your life it is a great investment. Bought as a Christmas present but useful for many years to come as the young person turns into an A-level candidate then works their way through university. more...

iPad Air

The analytics show that more and more people are accessing Transum Mathematics via an iPad as it is so portable and responsive. The iPad has so many other uses in addition to solving Transum's puzzles and challenges and it would make an excellent Christmas gift for anyone.

You have to hold iPad Air to believe it. It’s just 7.5 millimeters thin and weighs just one pound. The stunning Retina display sits inside thinner bezels, so all you see is your content. And an incredible amount of power lies inside the sleek enclosure. So you can do so much more. With so much less. more...

Before giving an iPad as a Christmas gift you could add a link to iPad Maths to the home screen.

Aristotle's Number Puzzle

It’s a bit of a tradition to give puzzles as Christmas Gifts to nieces and nephews. This puzzle is ideal for the keen puzzle solver who would like a challenge that will continue over the festive period (at least!).

This number puzzle involves nineteen numbers arranged into a hexagon. The goal of the puzzle is to rearrange the numbers so each of the fifteen rows add up to 38. It comes in a wooden style with an antique, aged look.

Keep the Maths in Christmaths with this reasonably priced stocking filler. more...

The Story Of Maths [DVD]

The films in this ambitious series offer clear, accessible explanations of important mathematical ideas but are also packed with engaging anecdotes, fascinating biographical details, and pivotal episodes in the lives of the great mathematicians. Engaging, enlightening and entertaining, the series gives viewers new and often surprising insights into the central importance of mathematics, establishing this discipline to be one of humanity s greatest cultural achievements. This DVD contains all four programmes from the BBC series.

Marcus du Sautoy's wonderful programmes make a perfect Christmas gift more...

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