Number Sequences 1

What is the 8th:
a) Odd number; 15
b) Square number; 64
c) Prime number. 19

Factors

Find all the factors of:

50

1, 2, 5, 10, 25, 50.

Multiples

Subtract the 6th from the 9th multiples of:

10

30

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) 85.09; 85.1
b) 242477; 242000
c) 0.007795; 0.00780

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 16cm, a height of 5cm and a top (parallel to base) of 6cm. 55cm2

Evaluate:

$$\frac{1}{3} + \frac{6}{8}$$ $$= 1\frac{1}{12}$$

Fractions (Multiplying)

Evaluate:

$$\frac{3}{4} × \frac{5}{6}$$ $$= \frac{5}{8}$$

Fractions (Dividing)

Evaluate:

$$\frac{2}{4} ÷ \frac{7}{6}$$ $$= \frac{3}{7}$$

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.

$$\frac{3}{8}$$ $$= 37.5$$%

Circle Area

Find the area of a circle that has a radius of 9cm. Give your answer to three significant figures.

254cm2

Circle Circumference

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

12.6cm

Calculate the value of:

6.8 + 2.4

= 9.2

Decimals (Subtracting)

Calculate the value of:

8.3 − 2.8

= 5.5

Decimals (Multiplying)

Calculate the value of:

3.8 × 2.9

= 11.02

Decimals (Dividing)

Calculate the value of:

106.2 ÷ 18

= 5.9

Indices (Simple)

What is the value of:

22

= 4

What is the value of:

$$2^{0}$$

$$= 1$$

Calculate the value of:

65 + 29

= 94

Basic Subtraction

Calculate the value of:

82 − 28

= 54

Basic Multiplication

Calculate the value of:

54 × 39

= 2106

Basic Division 2

Calculate the value of:

962 ÷ 13

= 74

Percentage (Of)

Find the value of:

55% of 40

= 22

Standard Form 1

Find the value of:

4.62 × 104

= 46200

Highest Common Factor

Find the highest common factor of twenty four and sixteen.

= 8

Times Tables (2-5)

 4 × 4 = 16 9 × 4 = 36 7 × 4 = 28 6 × 5 = 30 8 × 2 = 16 3 × 4 = 12 5 × 4 = 20 2 × 3 = 6

Times Tables (2-12)

 4 × 10 = 40 5 × 5 = 25 7 × 9 = 63 6 × 8 = 48 9 × 8 = 72 8 × 8 = 64 3 × 5 = 15 2 × 4 = 8

Times Tables (2)

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

Times Tables (3)

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

Times Tables (4)

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

Times Tables (5)

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

Times Tables (6)

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

Times Tables (7)

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

Times Tables (8)

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

Times Tables (9)

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

Times Tables (12)

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

Fractions (Equivalent)

Write this fraction in its simplest form:

$$\frac{6}{12}$$ $$= \frac{1}{2}$$

Fractions (Mixed)

Evaluate:

$$1\frac{4}{5} − \frac{6}{7}$$ $$= \frac{33}{35}$$

Pythagoras

Find AC if AB = 4m and BC = 5.1m. 3.16m

Trigonometry (Angle)

Find angle BCA if AB = 5.2m and BC = 6.4m. 54.3o

Trigonometry (Side)

Find AC if angle ABC = 32o and AB = 3m. 1.87m

2

2

2

Fraction to Decimal

Convert this fraction to a decimal to 3 significant figures.

$$\frac{2}{7}$$ $$= 0.286$$

Decimal to Fraction

Convert this decimal to a fraction.

$$0.17$$ = $$\frac{17}{100}$$

Percentage (Increase)

Increase £60 by 5%

£63

Lowest Common Multiple

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

= 24

Sequence (Arithmetic)

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

Find the:
a) next term; 66
b) nth term; 12n - 6
c) term number 37; 438

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 4 years with a simple interest rate of 4%, find the amount of interest earned. £22.40

Interest (Compound)

If £140 is invested with an interest rate of 2% compounded annually, find the value of the investment after 9 years. £167.31

Currency Exchange

If £1 is worth $1.35, convert: a) £140 to dollars;$189.00

b) \$200 to pounds; £148.15

Coordinates (Midpoint)

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

$$(1,8) \text{ and } (7,14)$$

(4,11)

What is the gradient of the line joining:

$$(-5,-7) \text{ and } (-2,-1)$$

2

Coordinates (Square)

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

$$(4,2),(9,5),(1,7)$$

(6,10)

Negative Numbers

a) 9 − 15 = -6
b) 9 × (-6) = -54
c) (8−20)(5−15) = 120
d) 54 ÷ (-6) = -9
e) (-5)2 = 25

Substitution

If p = 6, q = 20 and
r = -12 evaluate:

a) 2q − p = 34
b) pq + r = 108
c) p2 − 5q - r = -52

Equations (Type 1)

Solve:

$$5x = 25$$

$$x = 5$$

Equations (Type 2)

Solve:

$$5x +3= 38$$

$$x = 7$$

Equations (Type 3)

Solve:

$$9x -6= 5x + 30$$

$$x = 9$$

Equations (Type 4)

Solve:

$$2(5x -2)-8= 78$$

$$x = 9$$

Equations (Type 5)

Solve:

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

$$x = 0.857 \text{(to 3 sf)}$$

Equations (Simultaneous 1)

Solve:

$$3x+5y = 27$$
$$2x-5y = -7$$

$$x = 4, y = 3$$

Equations (Simultaneous 2)

Solve:

$$3x+2y = 15$$
$$6x-6y = 0$$

$$x = 3, y = 3$$

Equations (Simultaneous 3)

Solve:

$$5x+3y = -27.5$$
$$3x+2y = -17$$

$$x = -4, y = -2.5$$

Sets (Union)

Find the union of:

{1,2,3,4,5} and
{1,3,5,7,9}

{1,2,3,4,5,7,9}

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 147o. What bearing would it return on from B to A? 327o

Probability

A number is picked at random from the set

{1,2,3,4,5}

what is the probability it is even? $$\frac25$$

Evaluate:

3 + 2 × 4 − 6

5

Simplify

Simplify the following by collecting like terms:

$$5a−5−4a−5$$

$$a-10$$

Ratio

Divide 100 in the ratio

3:7

30 and 70

Graph (Linear)

Draw a rough sketch of the graph of:

$$y=2x-1$$

y intercept -1

Prime Factors

Express the following number as the product of prime numbers:

180

2 x 2 x 3 x 3 x 5

Percentage (Reverse)

In a sale an item costs £78 after a 35% reduction. What was the original price?

£120

Averages

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

5,3,7,5,10

Mean = 6, mode = 5,
median = 5 and range = 7

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.

0.373737... $$\frac{37}{99}$$

Percentage (Decrease)

Decrease £100 by 20%

£80

Brackets (Linear)

Expand:

$$6(4x-4)$$

$$24x-24$$

Expand:

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

$$9x^2-3x-6$$

Factorise (Linear)

Factorise:

$$25x-40$$

$$5(5x-8)$$

Factorise:

$$x^2-x-6$$

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

Factorise:

$$2x^2-x-3$$

$$(x+1)(2x-3)$$

Which theorem?

Standard Form 2

Find the value of:

5.99 × 10-5

= 0.0000599

Standard Form 3

Write in standard form:

22300

= 2.23 × 104

Standard Form 4

Write in standard form:

0.00378

= 3.78 × 10-3

Find the nth term:

$$4, 9, 16, 25, 36,$$

$$n^2+2n+1$$

Standard Form 5

Multiply 7 × 104
by 6 × 105 and give the answer in standard form.

= 4.2 × 1010

Solve:

$$x^2-3x-10= 0$$

$$x = 5$$ and $$-2$$

Solve this equation giving the solutions to 3 significant figures:

$$3x^2-x-5 = 0$$

$$x = 1.47$$ and $$-1.14$$

Polygon Angles

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

120°

Change The Subject

Make $$c$$ the subject of the formula
$$d=\frac{3c+1}{2}$$

$$c=\frac{2d-1}{3}$$

Basic Division 1

Calculate the value of:

2616 ÷ 6

= 436

Number Sequences 2

What is the 12th:
a) Cube number; 1728
b) Triangular number; 78
c) Fibonacci number. 144

Square Numbers

What is the difference between the 5th and the 6th square numbers?

11

Prime Numbers

What are the next three prime numbers after
29

31, 37, 41

Last Lesson

Write down something you learnt in the previous mathematics lesson.

Last Week

Write down something you learnt in one of the mathematics lessons last week.

Angles

Calculate $$x$$.

Decimals (Ordering)

Write down these numbers: 3.33, 3.03, 0.33, 0.3, 3.3, 3, 0.03, in ascending order.
0.03, 0.3, 0.33, 3, 3.03, 3.3, 3.33,

Lengths (Ordering)

Write down these lengths: 1.08m, 1.8m, 107cm, 17cm, 18mm, 1.7cm, in order.
1.7cm, 18mm, 17cm, 107cm, 1.08m, 1.8m,

Capacities (Ordering)

Write down these capacities: 173ml, 17cl, 21cl, 18cl, 200ml, 18ml, in order.
18ml, 17cl, 173ml, 18cl, 200ml, 21cl,

f = 132

d = 91

Bringing Memories Back To Life

• 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.

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• Mr Barton, Podcast #183
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• … very common practise in UK maths classrooms would be the first five minutes of the lesson the students would be presented with four questions on four topics they've encountered some time in the past. A classic structure for this is a question from last lesson a question from last week a question from last term and a question from last year which is quite nice for spacing and that for me seems very clear that's retrieval practise because the kids have been taught it and then having to try and remember things from long term memory.

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