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:

33

1, 3, 11, 33.

Multiples

Subtract the 5th from the 10th multiples of:

10

50

Polygons

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

Hexagon, Heptagon and Octagon (all regular)

Rounding

Round the following numbers to three significant figures:
a) 33.02; 33.0
b) 251009; 251000
c) 0.008195; 0.00820

Area of a Triangle

Find the area of a triangle that has a base of 4cm and a height of 8cm.

16cm2

Area of a Trapezium

Find the area of a trapezium that has a base of 9cm, a height of 5cm and a top (parallel to base) of 3cm. 30cm2

Fractions (Adding)

Evaluate:

\( \frac{4}{6} + \frac{9}{12}\) \(= 1\frac{5}{12}\)

Fractions (Multiplying)

Evaluate:

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

Fractions (Dividing)

Evaluate:

\( \frac{3}{5} ÷ \frac{8}{7}\) \(= \frac{21}{40}\)

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.

\( \frac{4}{7}\) \(= 57.1\)%

Circle Area

Find the area of a circle that has a radius of 5cm. Give your answer to three significant figures.

78.5cm2

Circle Circumference

Find the circumference of a circle that has a radius of 4cm. Give your answer to three significant figures.

25.1cm2

Decimals (Adding)

Calculate the value of:

4.6 + 6.5

= 11.1

Decimals (Subtracting)

Calculate the value of:

9.4 − 1.9

= 7.5

Decimals (Multiplying)

Calculate the value of:

4.5 × 7.2

= 32.4

Decimals (Dividing)

Calculate the value of:

57 ÷ 15

= 3.8

Indices (Simple)

What is the value of:

42

= 16

Indices (Advanced)

What is the value of:

4-3

= 0.015625

Basic Addition

Calculate the value of:

27 + 87

= 114

Basic Subtraction

Calculate the value of:

81 − 29

= 52

Basic Multiplication

Calculate the value of:

96 × 43

= 4128

Basic Division 2

Calculate the value of:

1232 ÷ 14

= 88

Percentage (Of)

Find the value of:

55% of 200

= 110

Standard Form 1

Find the value of:

8.08 × 104

= 80800

Highest Common Factor

Find the highest common factor of twenty four and twelve.

= 12

Times Tables (2-5)

6 × 4 = 24

9 × 4 = 36

7 × 3 = 21

8 × 4 = 32

4 × 5 = 20

5 × 5 = 25

3 × 2 = 6

2 × 5 = 10

Times Tables (2-12)

3 × 8 = 24

7 × 7 = 49

6 × 8 = 48

8 × 8 = 64

4 × 10 = 40

9 × 10 = 90

5 × 9 = 45

2 × 12 = 24

Times Tables (2)

8 × 2 = 16

9 × 2 = 18

5 × 2 = 10

4 × 2 = 8

3 × 2 = 6

6 × 2 = 12

7 × 2 = 14

2 × 2 = 4

Times Tables (3)

6 × 3 = 18

5 × 3 = 15

3 × 3 = 9

4 × 3 = 12

9 × 3 = 27

8 × 3 = 24

7 × 3 = 21

2 × 3 = 6

Times Tables (4)

6 × 4 = 24

5 × 4 = 20

9 × 4 = 36

3 × 4 = 12

7 × 4 = 28

4 × 4 = 16

8 × 4 = 32

2 × 4 = 8

Times Tables (5)

4 × 5 = 20

9 × 5 = 45

6 × 5 = 30

5 × 5 = 25

7 × 5 = 35

3 × 5 = 15

8 × 5 = 40

2 × 5 = 10

Times Tables (6)

8 × 6 = 48

3 × 6 = 18

6 × 6 = 36

4 × 6 = 24

9 × 6 = 54

5 × 6 = 30

7 × 6 = 42

2 × 6 = 12

Times Tables (7)

7 × 7 = 49

6 × 7 = 42

9 × 7 = 63

4 × 7 = 28

3 × 7 = 21

8 × 7 = 56

5 × 7 = 35

2 × 7 = 14

Times Tables (8)

5 × 8 = 40

8 × 8 = 64

6 × 8 = 48

3 × 8 = 24

9 × 8 = 72

7 × 8 = 56

4 × 8 = 32

2 × 8 = 16

Times Tables (9)

9 × 9 = 81

7 × 9 = 63

4 × 9 = 36

3 × 9 = 27

6 × 9 = 54

8 × 9 = 72

5 × 9 = 45

2 × 9 = 18

Times Tables (12)

9 × 12 = 108

4 × 12 = 48

7 × 12 = 84

5 × 12 = 60

6 × 12 = 72

3 × 12 = 36

8 × 12 = 96

2 × 12 = 24

Fractions (Equivalent)

Write this fraction in its simplest form:

\( \frac{40}{48}\) \(= \frac{5}{6}\)

Fractions (Mixed)

Evaluate:

\( 2\frac{3}{4} − \frac{5}{6}\) \(= 1\frac{11}{12}\)

Pythagoras

Find BC if AB = 5.6m and AC = 7.2m. 9.12m

Trigonometry (Angle)

Find angle BCA if AB = 4.2m and AC = 5.7m. 36.4o

Trigonometry (Side)

Find BC if angle BCA = 42o and AB = 3.3m. 4.93m

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.

\(0.84\) = \( \frac{21}{25}\)

Percentage (Increase)


Increase £100 by 10%

£110

Lowest Common Multiple

What is the lowest common multiple of twenty and twenty five.

= 100

Sequence (Arithmetic)

6,16,26,36,46...

Find the:
a) next term; 56
b) nth term; 10n - 4
c) term number 52; 516

Sequence (Geometric)

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

Find the:
a) next term; 1458
b) nth term; 6 × 3n-1
c) term number 10; 118098

Interest (Simple)

If £220 is invested for 6 years with a simple interest rate of 1%, find the amount of interest earned. £13.20

Interest (Compound)

If £200 is invested with an interest rate of 1% compounded annually, find the value of the investment after 6 years. £212.30

Currency Exchange

If £1 is worth $1.53, convert:

a) £200 to dollars; $306.00

b) $220 to pounds; £130.72

Coordinates (Midpoint)

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

\((2,8) \text{ and } (10,16)\)

(6,12)

Gradient

What is the gradient of the line joining:

\((6,-6) \text{ and } (9,-3)\)

1

Coordinates (Square)

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

\((1,3),(6,9),(-5,8)\)

(0,14)

Negative Numbers

a) 10 − 20 = -10
b) 10 × (-5) = -50
c) (10−17)(7−15) = 56
d) 50 ÷ (-5) = -10
e) (-11)2 = 121

Substitution

If p = 5, q = 25 and
r = -10 evaluate:

a) 2q − p = 45
b) pq + r = 115
c) p2 − 5q - r = -90

Equations (Type 1)

Solve:

\(2x = 8\)

\(x = 4\)

Equations (Type 2)

Solve:

\(2x -4= 2\)

\(x = 3\)

Equations (Type 3)

Solve:

\(10x -2= 6x + 18\)

\(x = 5\)

Equations (Type 4)

Solve:

\(5(4x +4)-10= 130\)

\(x = 6\)

Equations (Type 5)

Solve:

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

\(x = -1.73 \text{(to 3 sf)}\)

Equations (Simultaneous 1)

Solve:

\(5x+2y = 29\)
\(3x+2y = 19\)

\(x = 5, y = 2\)

Equations (Simultaneous 2)

Solve:

\(5x-3y = 20\)
\(3x+6y = 51\)

\(x = 7, y = 5\)

Equations (Simultaneous 3)

Solve:

\(6x+3y = 49.5\)
\(2x+6y = 49\)

\(x = 5, y = 6.5\)

Sets (Union)

Find the union of:

{6,7,8,9,10} and
{1,3,6,10,15}

{1,3,6,7,8,9,10,15}

Sets (Intersection)

Find the intersection of:

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

{6,7,8,9,10}

Bearings

A plane flies from point A to point B on a bearing of 092o. What bearing would it return on from B to A? 272o

Probability

A number is picked at random from the set

{2,3,5,7,11,13}

what is the probability it is even? \(\frac16\)

BIDMAS

Evaluate:

92 − 9 × 2 + 6

69

Simplify

Simplify the following by collecting like terms:

\(3n+7−2n+8\)

\(n+15\)

Ratio

Divide 72 in the ratio

5:3

45 and 27

Graph (Linear)

Draw a rough sketch of the graph of:

\(y=2x-1\)

Gradient 2
y intercept -1

Prime Factors

Express the following number as the product of prime numbers:

48

2 x 2 x 2 x 2 x 3

Percentage (Reverse)

In a sale an item costs £14 after a 30% reduction. What was the original price?

£20

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?

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.

0.555555... \(\frac{5}{9}\)

Percentage (Decrease)


Decrease £160 by 5%

£152

Brackets (Linear)

Expand:

\(4(8x-6)\)

\(32x-24\)

Brackets (Quadratic)

Expand:

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

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

Factorise (Linear)

Factorise:

\(20x-36\)

\(4(5x-9)\)

Factorise (Quadratic 1)

Factorise:

\(x^2-9\)

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

Factorise (Quadratic 2)

Factorise:

\(4x^2+13x-12\)

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

Circle Theorems

Which theorem?

Circle part Circle part

Standard Form 2

Find the value of:

8.95 × 10-3

= 0.00895

Standard Form 3

Write in standard form:

472000

= 4.72 × 105

Standard Form 4

Write in standard form:

0.0425

= 4.25 × 10-2

Sequence (Quadratic)

Find the nth term:

\(15, 27, 43, 63, 87, \)

\(2n^2+6n+7\)

Standard Form 5

Multiply 7 × 104
by 5 × 103 and give the answer in standard form.

= 3.5 × 108

Equations (Quadratic 1)

Solve:

\(x^2+2x-8= 0\)

\(x = 2\) and \(-4\)

Equations (Quadratic 2)

Solve this equation giving the solutions to 3 significant figures:

\(3x^2+5x-4 = 0\)

\(x = 0.591\) and \(-2.26\)

Polygon Angles

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

51.4°

Interior and Exterior angles

Change The Subject

Make \(j\) the subject of the formula
$$b=\frac{3(j-4)}{c}$$

$$j=\frac{bc}{3}+4$$

Basic Division 1

Calculate the value of:

5472 ÷ 9

= 608

Number Sequences 2

What is the 10th:
a) Cube number; 1000
b) Triangular number; 55
c) Fibonacci number. 55


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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