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:

26

1, 2, 13, 26.

Multiples

Subtract the 7th from the 12th multiples of:

10

50

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) 46.07; 46.1
b) 781676; 782000
c) 0.006395; 0.00640

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 9cm, a height of 8cm and a top (parallel to base) of 3cm. 48cm2

Fractions (Adding)

Evaluate:

\( \frac{2}{4} + \frac{7}{10}\) \(= 1\frac{1}{5}\)

Fractions (Multiplying)

Evaluate:

\( \frac{3}{5} × \frac{6}{8}\) \(= \frac{9}{20}\)

Fractions (Dividing)

Evaluate:

\( \frac{3}{5} ÷ \frac{7}{6}\) \(= \frac{18}{35}\)

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.

\( \frac{2}{4}\) \(= 50\)%

Circle Area

Find the area of a circle that has a radius of 2cm. Give your answer to three significant figures.

12.6cm2

Circle Circumference

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

75.4cm2

Decimals (Adding)

Calculate the value of:

9.5 + 4.9

= 14.4

Decimals (Subtracting)

Calculate the value of:

7.4 − 2.6

= 4.8

Decimals (Multiplying)

Calculate the value of:

3.2 × 8.4

= 26.88

Decimals (Dividing)

Calculate the value of:

139.5 ÷ 15

= 9.3

Indices (Simple)

What is the value of:

23

= 8

Indices (Advanced)

What is the value of:

10

= 1

Basic Addition

Calculate the value of:

68 + 99

= 167

Basic Subtraction

Calculate the value of:

94 − 26

= 68

Basic Multiplication

Calculate the value of:

36 × 22

= 792

Basic Division 2

Calculate the value of:

1184 ÷ 16

= 74

Percentage (Of)

Find the value of:

20% of 240

= 48

Standard Form 1

Find the value of:

6.75 × 104

= 67500

Highest Common Factor

Find the highest common factor of thirty two and twenty.

= 4

Times Tables (2-5)

8 × 2 = 16

9 × 4 = 36

3 × 2 = 6

6 × 2 = 12

5 × 2 = 10

4 × 4 = 16

7 × 5 = 35

2 × 3 = 6

Times Tables (2-12)

9 × 2 = 18

7 × 4 = 28

4 × 5 = 20

5 × 6 = 30

6 × 10 = 60

3 × 12 = 36

8 × 5 = 40

2 × 8 = 16

Times Tables (2)

7 × 2 = 14

6 × 2 = 12

5 × 2 = 10

3 × 2 = 6

8 × 2 = 16

4 × 2 = 8

9 × 2 = 18

2 × 2 = 4

Times Tables (3)

5 × 3 = 15

4 × 3 = 12

6 × 3 = 18

8 × 3 = 24

9 × 3 = 27

7 × 3 = 21

3 × 3 = 9

2 × 3 = 6

Times Tables (4)

3 × 4 = 12

5 × 4 = 20

9 × 4 = 36

8 × 4 = 32

7 × 4 = 28

4 × 4 = 16

6 × 4 = 24

2 × 4 = 8

Times Tables (5)

9 × 5 = 45

4 × 5 = 20

8 × 5 = 40

5 × 5 = 25

6 × 5 = 30

7 × 5 = 35

3 × 5 = 15

2 × 5 = 10

Times Tables (6)

6 × 6 = 36

9 × 6 = 54

8 × 6 = 48

3 × 6 = 18

5 × 6 = 30

7 × 6 = 42

4 × 6 = 24

2 × 6 = 12

Times Tables (7)

7 × 7 = 49

4 × 7 = 28

6 × 7 = 42

8 × 7 = 56

5 × 7 = 35

9 × 7 = 63

3 × 7 = 21

2 × 7 = 14

Times Tables (8)

8 × 8 = 64

4 × 8 = 32

9 × 8 = 72

3 × 8 = 24

5 × 8 = 40

6 × 8 = 48

7 × 8 = 56

2 × 8 = 16

Times Tables (9)

3 × 9 = 27

5 × 9 = 45

4 × 9 = 36

6 × 9 = 54

8 × 9 = 72

7 × 9 = 63

9 × 9 = 81

2 × 9 = 18

Times Tables (12)

7 × 12 = 84

9 × 12 = 108

3 × 12 = 36

5 × 12 = 60

4 × 12 = 48

6 × 12 = 72

8 × 12 = 96

2 × 12 = 24

Fractions (Equivalent)

Write this fraction in its simplest form:

\( \frac{24}{32}\) \(= \frac{3}{4}\)

Fractions (Mixed)

Evaluate:

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

Pythagoras

Find AC if AB = 4.2m and BC = 5.7m. 3.85m

Trigonometry (Angle)

Find angle BCA if AC = 4.5m and BC = 6.5m. 46.2o

Trigonometry (Side)

Find AB if angle ABC = 20o and BC = 5.8m. 5.45m

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.

\(0.5\) = \( \frac{1}{2}\)

Percentage (Increase)


Increase £100 by 40%

£140

Lowest Common Multiple

What is the lowest common multiple of twelve and twenty four.

= 24

Sequence (Arithmetic)

3,13,23,33,43...

Find the:
a) next term; 53
b) nth term; 10n - 7
c) term number 40; 393

Sequence (Geometric)

7,28,112,448,1792...

Find the:
a) next term; 7168
b) nth term; 7 × 4n-1
c) term number 8; 114688

Interest (Simple)

If £120 is invested for 5 years with a simple interest rate of 2%, find the amount of interest earned. £12.00

Interest (Compound)

If £140 is invested with an interest rate of 4% compounded annually, find the value of the investment after 7 years. £184.23

Currency Exchange

If £1 is worth $1.58, convert:

a) £120 to dollars; $189.60

b) $240 to pounds; £75.95

Coordinates (Midpoint)

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

\((5,4) \text{ and } (17,12)\)

(11,8)

Gradient

What is the gradient of the line joining:

\((-6,3) \text{ and } (0,6)\)

\(\frac{1}{2}\)

Coordinates (Square)

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

\((5,1),(10,4),(2,6)\)

(7,9)

Negative Numbers

a) 6 − 13 = -7
b) 6 × (-5) = -30
c) (8−20)(12−22) = 120
d) 30 ÷ (-5) = -6
e) (-6)2 = 36

Substitution

If p = 5, q = 19 and
r = -12 evaluate:

a) 2q − p = 33
b) pq + r = 83
c) p2 − 5q - r = -58

Equations (Type 1)

Solve:

\(2x = 16\)

\(x = 8\)

Equations (Type 2)

Solve:

\(5x +7= 42\)

\(x = 7\)

Equations (Type 3)

Solve:

\(3x -6= 2x + 1\)

\(x = 7\)

Equations (Type 4)

Solve:

\(5(3x +3)-8= 97\)

\(x = 6\)

Equations (Type 5)

Solve:

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

\(x = 1.6\)

Equations (Simultaneous 1)

Solve:

\(5x-2y = 6\)
\(4x+2y = 12\)

\(x = 2, y = 2\)

Equations (Simultaneous 2)

Solve:

\(4x+4y = 44\)
\(5x+8y = 73\)

\(x = 5, y = 6\)

Equations (Simultaneous 3)

Solve:

\(3x-7y = 51\)
\(2x-7y = 44.5\)

\(x = 6.5, y = -4.5\)

Sets (Union)

Find the union of:

{2,4,6,8,10} and
{1,3,5,7,9}

{1,2,3,4,5,6,7,8,9,10}

Sets (Intersection)

Find the intersection of:

{1,2,3,4,5} and
{5,6,7,8,9,10}

{5}

Bearings

A plane flies from point A to point B on a bearing of 298o. What bearing would it return on from B to A? 118o

Probability

A number is picked at random from the set

{3,6,9,12,15}

what is the probability it is even? \(\frac25\)

BIDMAS

Evaluate:

4 + (4 × 62 − 8)

140

Simplify

Simplify the following by collecting like terms:

\(5a−5−4a−5\)

\(a-10\)

Ratio

Divide 91 in the ratio

3:4

39 and 52

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:

29

29

Percentage (Reverse)

In a sale an item costs £102 after a 15% reduction. What was the original price?

£120

Averages

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

6,7,8,9,10

Mean = 8, no mode,
median = 8 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.

0.838383... \(\frac{83}{99}\)

Percentage (Decrease)


Decrease £120 by 25%

£90

Brackets (Linear)

Expand:

\(5(4x-9)\)

\(20x-45\)

Brackets (Quadratic)

Expand:

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

\(6x^2+3x-9\)

Factorise (Linear)

Factorise:

\(18x-16\)

\(2(9x-8)\)

Factorise (Quadratic 1)

Factorise:

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

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

Factorise (Quadratic 2)

Factorise:

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

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

Circle Theorems

Which theorem?

Circle part Circle part

Standard Form 2

Find the value of:

8.14 × 10-4

= 0.000814

Standard Form 3

Write in standard form:

8820000

= 8.82 × 106

Standard Form 4

Write in standard form:

0.0142

= 1.42 × 10-2

Sequence (Quadratic)

Find the nth term:

\(2, 14, 30, 50, 74, \)

\(2n^2+6n-6\)

Standard Form 5

Multiply 4 × 106
by 4 × 105 and give the answer in standard form.

= 1.6 × 1012

Equations (Quadratic 1)

Solve:

\(x^2+x-6= 0\)

\(x = 2\) and \(-3\)

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

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

\(x = 0.554\) and \(-1.80\)

Polygon Angles

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

120°

Interior and Exterior angles

Change The Subject

Make \(a\) the subject of the formula
$$b=2a-3$$

$$a=\frac{b+3}{2}$$

Basic Division 1

Calculate the value of:

3962 ÷ 7

= 566

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
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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.]

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