Refreshing Revision

Number Sequences 1

What is the 11th:
a) Odd number; 21
b) Square number; 121
c) Prime number. 31

Factors

Find all the factors of:

35

1, 5, 7, 35.

Multiples

Subtract the 5th from the 10th multiples of:

8

40

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) 20.72; 20.7
b) 342792; 343000
c) 0.009795; 0.00980

Area of a Triangle

Find the area of a triangle that has a base of 5cm and a height of 10cm.

25cm2

Area of a Trapezium

Find the area of a trapezium that has a base of 9cm, a height of 6cm and a top (parallel to base) of 3cm. 36cm2

Fractions (Adding)

Evaluate:

\( \frac{4}{6} + \frac{8}{10}\) \(= 1\frac{7}{15}\)

Fractions (Multiplying)

Evaluate:

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

Fractions (Dividing)

Evaluate:

\( \frac{3}{4} ÷ \frac{6}{5}\) \(= \frac{5}{8}\)

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.

\( \frac{5}{9}\) \(= 55.6\)%

Circle Area

Find the area of a circle that has a radius of 12cm. Give your answer to three significant figures.

452cm2

Circle Circumference

Find the circumference of a circle that has a radius of 8cm. Give your answer to three significant figures.

50.3cm2

Decimals (Adding)

Calculate the value of:

2.5 + 5.5

= 8

Decimals (Subtracting)

Calculate the value of:

6.2 − 2.6

= 3.6

Decimals (Multiplying)

Calculate the value of:

4.2 × 2.3

= 9.66

Decimals (Dividing)

Calculate the value of:

138.6 ÷ 18

= 7.7

Indices (Simple)

What is the value of:

42

= 16

Indices (Advanced)

What is the value of:

20

= 1

Basic Addition

Calculate the value of:

67 + 27

= 94

Basic Subtraction

Calculate the value of:

61 − 27

= 34

Basic Multiplication

Calculate the value of:

68 × 59

= 4012

Basic Division 2

Calculate the value of:

1550 ÷ 25

= 62

Percentage (Of)

Find the value of:

50% of 100

= 50

Standard Form 1

Find the value of:

8.54 × 106

= 8540000

Highest Common Factor

Find the highest common factor of twelve and ten.

= 2

Times Tables (2-5)

9 × 5 = 45

6 × 5 = 30

7 × 5 = 35

5 × 5 = 25

4 × 2 = 8

8 × 4 = 32

3 × 5 = 15

2 × 4 = 8

Times Tables (2-12)

3 × 12 = 36

9 × 3 = 27

6 × 4 = 24

5 × 10 = 50

8 × 10 = 80

4 × 4 = 16

7 × 9 = 63

2 × 12 = 24

Times Tables (2)

9 × 2 = 18

5 × 2 = 10

6 × 2 = 12

8 × 2 = 16

4 × 2 = 8

7 × 2 = 14

3 × 2 = 6

2 × 2 = 4

Times Tables (3)

6 × 3 = 18

5 × 3 = 15

7 × 3 = 21

8 × 3 = 24

9 × 3 = 27

3 × 3 = 9

4 × 3 = 12

2 × 3 = 6

Times Tables (4)

7 × 4 = 28

4 × 4 = 16

3 × 4 = 12

8 × 4 = 32

6 × 4 = 24

9 × 4 = 36

5 × 4 = 20

2 × 4 = 8

Times Tables (5)

6 × 5 = 30

4 × 5 = 20

3 × 5 = 15

5 × 5 = 25

7 × 5 = 35

9 × 5 = 45

8 × 5 = 40

2 × 5 = 10

Times Tables (6)

7 × 6 = 42

3 × 6 = 18

6 × 6 = 36

9 × 6 = 54

4 × 6 = 24

5 × 6 = 30

8 × 6 = 48

2 × 6 = 12

Times Tables (7)

8 × 7 = 56

7 × 7 = 49

9 × 7 = 63

5 × 7 = 35

4 × 7 = 28

3 × 7 = 21

6 × 7 = 42

2 × 7 = 14

Times Tables (8)

5 × 8 = 40

3 × 8 = 24

9 × 8 = 72

4 × 8 = 32

7 × 8 = 56

8 × 8 = 64

6 × 8 = 48

2 × 8 = 16

Times Tables (9)

8 × 9 = 72

3 × 9 = 27

4 × 9 = 36

6 × 9 = 54

5 × 9 = 45

9 × 9 = 81

7 × 9 = 63

2 × 9 = 18

Times Tables (12)

3 × 12 = 36

5 × 12 = 60

6 × 12 = 72

9 × 12 = 108

7 × 12 = 84

4 × 12 = 48

8 × 12 = 96

2 × 12 = 24

Fractions (Equivalent)

Write this fraction in its simplest form:

\( \frac{7}{21}\) \(= \frac{1}{3}\)

Fractions (Mixed)

Evaluate:

\( 3\frac{2}{3} − \frac{5}{6}\) \(= 2\frac{5}{6}\)

Pythagoras

Find BC if AB = 4.8m and AC = 6.6m. 8.16m

Trigonometry (Angle)

Find angle BCA if AC = 5.4m and BC = 6.8m. 37.4o

Trigonometry (Side)

Find AC if angle ABC = 51o and BC = 3.9m. 3.03m

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 to 3 significant figures.

\( \frac{3}{7}\) \(= 0.429\)

Decimal to Fraction

Convert this decimal to a fraction.

\(0.96\) = \( \frac{24}{25}\)

Percentage (Increase)


Increase £120 by 25%

£150

Lowest Common Multiple

What is the lowest common multiple of eight and twenty.

= 40

Sequence (Arithmetic)

5,14,23,32,41...

Find the:
a) next term; 50
b) nth term; 9n - 4
c) term number 37; 329

Sequence (Geometric)

5,10,20,40,80...

Find the:
a) next term; 160
b) nth term; 5 × 2n-1
c) term number 10; 2560

Interest (Simple)

If £220 is invested for 7 years with a simple interest rate of 1%, find the amount of interest earned. £15.40

Interest (Compound)

If £160 is invested with an interest rate of 5% compounded annually, find the value of the investment after 5 years. £204.21

Currency Exchange

If £1 is worth $1.59, convert:

a) £100 to dollars; $159.00

b) $180 to pounds; £62.89

Coordinates (Midpoint)

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

\((-8,-5) \text{ and } (-2,5)\)

(-5,0)

Gradient

What is the gradient of the line joining:

\((7,0) \text{ and } (12,6)\)

\(\frac{6}{5}\)

Coordinates (Square)

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

\((5,3),(8,6),(2,6)\)

(5,9)

Negative Numbers

a) 8 − 14 = -6
b) 8 × (-11) = -88
c) (7−18)(10−15) = 55
d) 88 ÷ (-11) = -8
e) (-10)2 = 100

Substitution

If p = 5, q = 19 and
r = -9 evaluate:

a) 2q − p = 33
b) pq + r = 86
c) p2 − 5q - r = -61

Equations (Type 1)

Solve:

\(2x = 18\)

\(x = 9\)

Equations (Type 2)

Solve:

\(3x -5= 10\)

\(x = 5\)

Equations (Type 3)

Solve:

\(9x -6= 4x + 24\)

\(x = 6\)

Equations (Type 4)

Solve:

\(4(4x -3)+7= 123\)

\(x = 8\)

Equations (Type 5)

Solve:

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

\(x = -5\)

Equations (Simultaneous 1)

Solve:

\(4x+4y = 56\)
\(3x-4y = -7\)

\(x = 7, y = 7\)

Equations (Simultaneous 2)

Solve:

\(5x+2y = 39\)
\(4x-8y = 12\)

\(x = 7, y = 2\)

Equations (Simultaneous 3)

Solve:

\(5x+6y = 42.5\)
\(4x-3y = -5\)

\(x = 2.5, y = 5\)

Sets (Union)

Find the union of:

{2,4,6,8,10} and
{5,6,7,8,9,10}

{2,4,5,6,7,8,9,10}

Sets (Intersection)

Find the intersection of:

{1,3,5,7,9} and
{6,7,8,9,10}

{7,9}

Bearings

A plane flies from point A to point B on a bearing of 033o. What bearing would it return on from B to A? 213o

Probability

A number is picked at random from the set

{2,4,6,8,10}

what is the probability it is even? 1

BIDMAS

Evaluate:

24 ÷ 6 × 36 ÷ 4

36

Simplify

Simplify the following by collecting like terms:

\(6m+7+5m+8\)

\(11m+15\)

Ratio

Divide 35 in the ratio

4:3

20 and 15

Graph (Linear)

Draw a rough sketch of the graph of:

\(y=x+1\)

Gradient 1
y intercept 1

Prime Factors

Express the following number as the product of prime numbers:

20

2 x 2 x 5

Percentage (Reverse)

In a sale an item costs £90 after a 25% reduction. What was the original price?

£120

Averages

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

1,2,3,4,5

Mean = 3, no mode,
median = 3 and range = 4

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.

0.474747... \(\frac{47}{99}\)

Percentage (Decrease)


Decrease £140 by 15%

£119

Brackets (Linear)

Expand:

\(5(3x-9)\)

\(15x-45\)

Brackets (Quadratic)

Expand:

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

\(8x^2+8x-6\)

Factorise (Linear)

Factorise:

\(8x-72\)

\(8(1x-9)\)

Factorise (Quadratic 1)

Factorise:

\(x^2+x-12\)

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

Factorise (Quadratic 2)

Factorise:

\(3x^2+8x-3\)

\((x+3)(3x-1)\)

Circle Theorems

Which theorem?

Circle part Circle part

Standard Form 2

Find the value of:

6.81 × 10-4

= 0.000681

Standard Form 3

Write in standard form:

632000

= 6.32 × 105

Standard Form 4

Write in standard form:

0.0173

= 1.73 × 10-2

Sequence (Quadratic)

Find the nth term:

\(-2, 9, 26, 49, 78, \)

\(3n^2+2n-7\)

Standard Form 5

Multiply 9 × 104
by 5 × 104 and give the answer in standard form.

= 4.5 × 109

Equations (Quadratic 1)

Solve:

\(x^2-x-12= 0\)

\(x = 4\) and \(-3\)

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

\(5x^2-4x-5 = 0\)

\(x = 1.48\) and \(-0.677\)

Polygon Angles

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

60°

Interior and Exterior angles

Change The Subject

Make \(h\) the subject of the formula
$$e=\frac{h}{4}-5$$

$$h=4(e+5)$$

Basic Division 1

Calculate the value of:

4266 ÷ 9

= 474

Number Sequences 2

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


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
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  • 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
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  • 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
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  • 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]

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