### 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:

46

1, 2, 23, 46.

### Multiples

Subtract the 6th from the 9th multiples of:

11

33

### Polygons

What are the names of regular polygons with:
a) four sides;
b) five sides;
c) six sides.

Square, Pentagon and Hexagon (all regular)

### Rounding

Round the following numbers to three significant figures:
a) 64.69; 64.7
b) 204893; 205000
c) 0.008495; 0.00850

### Area of a Triangle

Find the area of a triangle that has a base of 6cm and a height of 10cm.

30cm2

### Area of a Trapezium

Find the area of a trapezium that has a base of 11cm, a height of 9cm and a top (parallel to base) of 5cm. 72cm2

Evaluate:

$$\frac{3}{4} + \frac{7}{8}$$ $$= 1\frac{5}{8}$$

### Fractions (Multiplying)

Evaluate:

$$\frac{3}{4} × \frac{6}{8}$$ $$= \frac{9}{16}$$

### Fractions (Dividing)

Evaluate:

$$\frac{2}{4} ÷ \frac{6}{5}$$ $$= \frac{5}{12}$$

### 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.

$$\frac{5}{6}$$ $$= 83.3$$%

### 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 3cm. Give your answer to three significant figures.

18.8cm2

Calculate the value of:

4.7 + 7.4

= 12.1

### Decimals (Subtracting)

Calculate the value of:

5.3 − 2.7

= 2.6

### Decimals (Multiplying)

Calculate the value of:

5.5 × 7.6

= 41.8

### Decimals (Dividing)

Calculate the value of:

89.7 ÷ 13

= 6.9

### Indices (Simple)

What is the value of:

42

= 16

What is the value of:

1-2

= 1

Calculate the value of:

97 + 94

= 191

### Basic Subtraction

Calculate the value of:

53 − 27

= 26

### Basic Multiplication

Calculate the value of:

37 × 42

= 1554

### Basic Division 2

Calculate the value of:

1305 ÷ 29

= 45

### Percentage (Of)

Find the value of:

95% of 380

= 361

### Standard Form 1

Find the value of:

6.23 × 102

= 623

### Highest Common Factor

Find the highest common factor of twenty four and twelve.

= 12

### Times Tables (2-5)

 5 × 2 = 10 3 × 2 = 6 8 × 5 = 40 4 × 4 = 16 7 × 5 = 35 6 × 5 = 30 9 × 4 = 36 2 × 4 = 8

### Times Tables (2-12)

 8 × 9 = 72 3 × 7 = 21 6 × 7 = 42 9 × 5 = 45 7 × 7 = 49 4 × 12 = 48 5 × 2 = 10 2 × 4 = 8

### Times Tables (2)

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

### Times Tables (3)

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

### Times Tables (4)

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

### Times Tables (5)

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

### Times Tables (6)

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

### Times Tables (7)

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

### Times Tables (8)

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

### Times Tables (9)

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

### Times Tables (12)

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

### Fractions (Equivalent)

Write this fraction in its simplest form:

$$\frac{20}{24}$$ $$= \frac{5}{6}$$

### Fractions (Mixed)

Evaluate:

$$1\frac{1}{2} − \frac{5}{6}$$ $$= \frac{2}{3}$$

### Pythagoras

Find AC if AB = 4.5m and BC = 5.5m. 3.16m

### Trigonometry (Angle)

Find angle ABC if AB = 3.6m and BC = 5m. 43.9o

### Trigonometry (Side)

Find BC if angle BCA = 24o and AB = 5.1m. 12.5m

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.

$$0.59$$ = $$\frac{59}{100}$$

### Percentage (Increase)

Increase £180 by 15%

£207

### Lowest Common Multiple

What is the lowest common multiple of fifteen and thirty five.

= 105

### Sequence (Arithmetic)

3,8,13,18,23...

Find the:
a) next term; 28
b) nth term; 5n - 2
c) term number 49; 243

### Sequence (Geometric)

4,8,16,32,64...

Find the:
a) next term; 128
b) nth term; 4 × 2n-1
c) term number 9; 1024

### Interest (Simple)

If £220 is invested for 9 years with a simple interest rate of 3%, find the amount of interest earned. £59.40

### Interest (Compound)

If £120 is invested with an interest rate of 4% compounded annually, find the value of the investment after 6 years. £151.84

### Currency Exchange

If £1 is worth $1.46, convert: a) £140 to dollars;$204.40

b) \$160 to pounds; £95.89

### Coordinates (Midpoint)

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

$$(7,-9) \text{ and } (15,3)$$

(11,-3)

What is the gradient of the line joining:

$$(-5,6) \text{ and } (-1,12)$$

$$\frac{3}{2}$$

### Coordinates (Square)

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

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

(1,11)

### Negative Numbers

a) 6 − 17 = -11
b) 6 × (-12) = -72
c) (12−24)(8−18) = 120
d) 72 ÷ (-12) = -6
e) (-5)2 = 25

### Substitution

If p = 6, q = 22 and
r = -12 evaluate:

a) 2q − p = 38
b) pq + r = 120
c) p2 − 5q - r = -62

### Equations (Type 1)

Solve:

$$2x = 10$$

$$x = 5$$

### Equations (Type 2)

Solve:

$$4x +6= 34$$

$$x = 7$$

### Equations (Type 3)

Solve:

$$5x +4= 4x + 11$$

$$x = 7$$

### Equations (Type 4)

Solve:

$$4(2x -4)-12= 4$$

$$x = 4$$

### Equations (Type 5)

Solve:

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

$$x = 3.33 \text{(to 3 sf)}$$

### Equations (Simultaneous 1)

Solve:

$$4x-4y = -16$$
$$2x-4y = -22$$

$$x = 3, y = 7$$

### Equations (Simultaneous 2)

Solve:

$$2x+2y = 8$$
$$2x+8y = 20$$

$$x = 2, y = 2$$

### Equations (Simultaneous 3)

Solve:

$$6x-5y = 60.5$$
$$3x+2y = 5.5$$

$$x = 5.5, y = -5.5$$

### 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:

{1,3,5,7,9} and
{2,6,12}

### Bearings

A plane flies from point A to point B on a bearing of 204o. What bearing would it return on from B to A? 024o

### Probability

A number is picked at random from the set

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

what is the probability it is even? $$\frac12$$

Evaluate:

62 − 5 × 6 + 6

12

### Simplify

Simplify the following by collecting like terms:

$$7d−3e−5d+7e$$

$$4e+2d$$

### Ratio

Divide 195 in the ratio

5:8

75 and 120

### Graph (Linear)

Draw a rough sketch of the graph of:

$$y=x+1$$

y intercept 1

### Prime Factors

Express the following number as the product of prime numbers:

30

2 x 3 x 5

### Percentage (Reverse)

In a sale an item costs £126 after a 10% reduction. What was the original price?

£140

### Averages

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

1,3,1,10,5

Mean = 4, mode = 1,
median = 3 and range = 9

### 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.

0.262626... $$\frac{26}{99}$$

### Percentage (Decrease)

Decrease £120 by 30%

£84

### Brackets (Linear)

Expand:

$$8(6x-9)$$

$$48x-72$$

Expand:

$$(3x+4)(2x-2)$$

$$6x^2+2x-8$$

### Factorise (Linear)

Factorise:

$$4x-36$$

$$4(1x-9)$$

Factorise:

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

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

Factorise:

$$20x^2-7x-3$$

$$(4x+1)(5x-3)$$

Which theorem?

### Standard Form 2

Find the value of:

7.6 × 10-4

= 0.00076

### Standard Form 3

Write in standard form:

80800

= 8.08 × 104

### Standard Form 4

Write in standard form:

0.00558

= 5.58 × 10-3

Find the nth term:

$$15, 24, 37, 54, 75,$$

$$2n^2+3n+10$$

### Standard Form 5

Multiply 7 × 103
by 8 × 103 and give the answer in standard form.

= 5.6 × 107

Solve:

$$x^2+2x-8= 0$$

$$x = 2$$ and $$-4$$

Solve this equation giving the solutions to 3 significant figures:

$$4x^2-x-1 = 0$$

$$x = 0.640$$ and $$-0.390$$

### Polygon Angles

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

51.4°

### 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:

4032 ÷ 7

= 576

### Number Sequences 2

What is the 11th:
a) Cube number; 1331
b) Triangular number; 66
c) Fibonacci number. 89

## 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
• Sunday, October 22, 2017
• Answers for the starter would be great so students can get immediate feedback and become independent learners.

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## Concept Selection

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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...

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...

## 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...

Click the images above to see all the details of these gift ideas and to buy them online.

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