# ### Number Sequences 1

What is the 10th:
a) Odd number; 19
b) Square number; 100
c) Prime number. 29

### Factors

Find all the factors of:

49

1, 7, 49.

### Multiples

Subtract the 7th from the 12th multiples of:

11

55

### 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) 72.68; 72.7
b) 343118; 343000
c) 0.004295; 0.00430

### Area of a Triangle

Find the area of a triangle that has a base of 3cm and a height of 8cm.

12cm2

### Area of a Trapezium

Find the area of a trapezium that has a base of 16cm, a height of 10cm and a top (parallel to base) of 6cm. 110cm2

### Fractions (Adding)

Evaluate:

$$\frac{3}{6} + \frac{8}{11}$$ $$= 1\frac{5}{22}$$

### Fractions (Multiplying)

Evaluate:

$$\frac{1}{3} × \frac{5}{7}$$ $$= \frac{5}{21}$$

### Fractions (Dividing)

Evaluate:

$$\frac{3}{5} ÷ \frac{9}{7}$$ $$= \frac{7}{15}$$

### Circle (Vocabulary)

Name the red part.  ### Venn Diagrams

Describe the red region.  ### Shape Formulas

What is the formula?  ### Formulas (Advanced)

What is it?  ### Fraction to Percentage

Convert this fraction to a percentage to 3 significant figures.

$$\frac{4}{9}$$ $$= 44.4$$%

### 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 5cm. Give your answer to three significant figures.

31.4cm2

### Decimals (Adding)

Calculate the value of:

3.7 + 6.8

= 10.5

### Decimals (Subtracting)

Calculate the value of:

5.2 − 2.9

= 2.3

### Decimals (Multiplying)

Calculate the value of:

4.3 × 2.3

= 9.89

### Decimals (Dividing)

Calculate the value of:

47.5 ÷ 19

= 2.5

### Indices (Simple)

What is the value of:

23

= 8

### Indices (Advanced)

What is the value of:

3-1

= 0.333333333333333

### Basic Addition

Calculate the value of:

46 + 28

= 74

### Basic Subtraction

Calculate the value of:

61 − 28

= 33

### Basic Multiplication

Calculate the value of:

63 × 24

= 1512

### Basic Division 2

Calculate the value of:

1392 ÷ 29

= 48

### Percentage (Of)

Find the value of:

10% of 360

= 36

### Standard Form 1

Find the value of:

6.05 × 102

= 605

### Highest Common Factor

Find the highest common factor of twenty four and twelve.

= 12

### Times Tables (2-5)

 3 × 3 = 9 9 × 5 = 45 6 × 5 = 30 5 × 5 = 25 4 × 5 = 20 7 × 3 = 21 8 × 5 = 40 2 × 5 = 10

### Times Tables (2-12)

 6 × 6 = 36 9 × 9 = 81 8 × 2 = 16 5 × 5 = 25 4 × 6 = 24 3 × 3 = 9 7 × 3 = 21 2 × 5 = 10

### Times Tables (2)

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

### Times Tables (3)

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

### Times Tables (4)

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

### Times Tables (5)

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

### Times Tables (6)

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

### Times Tables (7)

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

### Times Tables (8)

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

### Times Tables (9)

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

### Times Tables (12)

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

### Fractions (Equivalent)

Write this fraction in its simplest form:

$$\frac{24}{32}$$ $$= \frac{3}{4}$$

### Fractions (Mixed)

Evaluate:

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

### Pythagoras

Find BC if AB = 4.7m and AC = 6.4m. 7.94m

### Trigonometry (Angle)

Find angle BCA if AB = 5.4m and BC = 6.7m. 53.7o

### Trigonometry (Side)

Find AC if angle ABC = 25o and AB = 5.4m. 2.52m

### 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.

$$\frac{2}{3}$$ $$= 0.667$$

### Decimal to Fraction

Convert this decimal to a fraction.

$$0.08$$ = $$\frac{2}{25}$$

### Percentage (Increase)

Increase £60 by 5%

£63

### Lowest Common Multiple

What is the lowest common multiple of eight and thirty two.

= 32

### Sequence (Arithmetic)

6,15,24,33,42...

Find the:
a) next term; 51
b) nth term; 9n - 3
c) term number 42; 375

### Sequence (Geometric)

4,12,36,108,324...

Find the:
a) next term; 972
b) nth term; 4 × 3n-1
c) term number 9; 26244

### Interest (Simple)

If £220 is invested for 8 years with a simple interest rate of 5%, find the amount of interest earned. £88.00

### Interest (Compound)

If £240 is invested with an interest rate of 6% compounded annually, find the value of the investment after 8 years. £382.52

### Currency Exchange

If £1 is worth $1.58, convert: a) £100 to dollars;$158.00

b) \$220 to pounds; £63.29

### Coordinates (Midpoint)

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

$$(-7,-2) \text{ and } (3,6)$$

(-2,2)

### Gradient

What is the gradient of the line joining:

$$(8,6) \text{ and } (13,11)$$

1

### Coordinates (Square)

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

$$(4,3),(7,8),(-1,6)$$

(2,11)

### Negative Numbers

a) 8 − 19 = -11
b) 8 × (-11) = -88
c) (10−20)(8−19) = 110
d) 88 ÷ (-11) = -8
e) (-11)2 = 121

### Substitution

If p = 5, q = 24 and
r = -5 evaluate:

a) 2q − p = 43
b) pq + r = 115
c) p2 − 5q - r = -90

### Equations (Type 1)

Solve:

$$3x = 24$$

$$x = 8$$

### Equations (Type 2)

Solve:

$$3x -2= 22$$

$$x = 8$$

### Equations (Type 3)

Solve:

$$8x -2= 6x + 8$$

$$x = 5$$

### Equations (Type 4)

Solve:

$$4(3x +2)-10= 46$$

$$x = 4$$

### Equations (Type 5)

Solve:

$$6(2x + 3)= 5(5x + 3)$$

$$x = 0.231 \text{(to 3 sf)}$$

### Equations (Simultaneous 1)

Solve:

$$4x+2y = 18$$
$$2x-2y = -6$$

$$x = 2, y = 5$$

### Equations (Simultaneous 2)

Solve:

$$4x-2y = 2$$
$$2x-4y = -8$$

$$x = 2, y = 3$$

### Equations (Simultaneous 3)

Solve:

$$2x-3y = 9$$
$$4x+2y = -54$$

$$x = -9, y = -9$$

### Sets (Union)

Find the union of:

{1,3,5,7,9} and
{1,3,6,10,15}

{1,3,5,6,7,9,10,15}

### Sets (Intersection)

Find the intersection of:

{5,6,7,8,9,10} and
{1,3,6,10,15}

{6,10}

### Bearings

A plane flies from point A to point B on a bearing of 294o. What bearing would it return on from B to A? 114o

### Probability

A number is picked at random from the set

{3,6,9,12,15}

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

Evaluate:

16 ÷ 2 × 40 ÷ 5

64

### Simplify

Simplify the following by collecting like terms:

$$2y+2y^2-5y+y^2$$

$$3y^2-3y$$

### Ratio

Divide 96 in the ratio

6:2

72 and 24

### Graph (Linear)

Draw a rough sketch of the graph of:

$$y=x-2$$

Gradient 1
y intercept -2

### Prime Factors

Express the following number as the product of prime numbers:

38

2 x 19

### Percentage (Reverse)

In a sale an item costs £90 after a 10% reduction. What was the original price?

£100

### Averages

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

2,6,12,6,14

Mean = 8, mode = 6,
median = 6 and range = 12

### 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.

0.161616... $$\frac{16}{99}$$

### Percentage (Decrease)

Decrease £40 by 5%

£38

### Brackets (Linear)

Expand:

$$6(6x-2)$$

$$36x-12$$

### Brackets (Quadratic)

Expand:

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

$$4x^2-11x-3$$

### Factorise (Linear)

Factorise:

$$35x-20$$

$$5(7x-4)$$

### Factorise (Quadratic 1)

Factorise:

$$x^2-x-6$$

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

### Factorise (Quadratic 2)

Factorise:

$$4x^2-1$$

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

### Circle Theorems

Which theorem?  ### Standard Form 2

Find the value of:

3.87 × 10-2

= 0.0387

### Standard Form 3

Write in standard form:

431000

= 4.31 × 105

### Standard Form 4

Write in standard form:

0.00808

= 8.08 × 10-3

### Sequence (Quadratic)

Find the nth term:

$$14, 24, 40, 62, 90,$$

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

### Standard Form 5

Multiply 5 × 103
by 8 × 104 and give the answer in standard form.

= 4 × 108

### 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:

$$4x^2-5x-2 = 0$$

$$x = 1.57$$ and $$-0.319$$

### Polygon Angles

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

40° ### Change The Subject

Make $$e$$ the subject of the formula
$$f=g(e+h)$$

$$e=\frac{f}{g}-h$$

### Basic Division 1

Calculate the value of:

4295 ÷ 5

= 859

### Number Sequences 2

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

## A Mathematics Lesson Starter Of The Day

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