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GCSE Mathematics Revision

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GCSE Mathematics Revision

C/D borderline

C/D borderlineChoose your session!

- Session 11
- Session 12
- Session 13
- Session 14
- Session 15
- Session 16
- Session 17
- Session 18
- Session 19
- Session 20

- Session 1
- Session 2
- Session 3
- Session 4
- Session 5
- Session 6
- Session 7
- Session 8
- Session 9
- Session 10

Session 1

- Expand and simplify
5(3x + 4) + 6(2x – 2)

- A circle has radius 3cm. Write the area and circumference of the circle in terms of π.
- a) Find the nth term of the sequence
4, 7, 10, 13, 16, ...

b) Hence, or otherwise, find the 50th term in this sequence.

4. Simplify 5a2b3 x 4a4b2

Ans. 1

Ans. 2

Ans. 3

Ans. 4

- Expand and simplify
5(3x + 4) + 6(2x – 2)

Expand the first bracket

5(3x + 4) = 15x + 20

Expand the second bracket

6(2x – 2) = 12x – 12

Replace the brackets with their expansions

15x + 20 + 12x – 12

Simplify by collecting like terms

27x + 8

Back

- A circle has radius 3cm. Write the area and circumference of the circle in terms of π.

Recall the formula for the area

of a circle

A = πr2

Replace the r with the value

for the radius

A = π x 32

Simplify

A = 9 π

Circumference formula

C = πd

Replace the d with the value for the diameter

C = π x 6

Simplify

C = 6 π

Back

3. a the circle in terms of ) Find the nth term of the sequence

4, 7, 10, 13, 16, ...

b) Hence, or otherwise, find the 50th term in this sequence.

- Find the difference between the terms.
- In this case 3
- The rule is linked to the three times table and starts with 3n
- Find out what needs to be added/subtracted to 3n to make the rule work
- 3n + 1

- The rule is 3n +1
- For the 50th term the value of n is 50
- Substitute
- 3 x 50 + 1 = 151

Back

- Simplify 5a the circle in terms of 2b3 x 4a4b2
Consider numbers first:

5 x 4 = 20

Consider the a’s:

a2 x a4 = a6

Consider the b’s:

b3 x b2 = b5

Put it all back together

20a6b5

Back

Back to sessions the circle in terms of

Session 2

- Find the volume of the shape below
2. Solve the equation

4x + 5 = 15

- Write 60 as a product of prime numbers
- Increase £120 by 30%

3cm

5cm

6cm

Ans. 1

Ans. 2

Ans. 3

Ans. 4

1. Find the volume of the shape below the circle in terms of

3cm

5cm

6cm

Recall the formula for the volume of a prism

Volume of a prism = area of cross section x length

Find the area of the cross section (triangle)

6 x 3 = 9cm2

2

Multiply this by the length

9 x 5 = 45cm3

Back

2. Solve the equation the circle in terms of

4x + 5 = 15

We need to get the x’s on their own

Subtract 5 from each side

4x = 10

Now divide by the number before x

x = 10

4

x = 2.5

Back

3. Write 60 as a product of prime numbers the circle in terms of

Draw a factor tree to help

60

30 2

15 2

5 3

So the answer is

2 x 2 x 3 x 5

Which simplifies to

22 x 3 x 5

Your tree may look different

Back

4. Increase £120 by 30% the circle in terms of

To increase by 30% we have to start by finding

30% of the amount and then add it on.

10% of £120 = £12

30% of £120 = £12 x 3 = £36

Now add it on:

£120 + £36 = £156

Back

Back to sessions the circle in terms of

Session 3

Ans. 1

Ans. 2

Ans. 3

Ans. 4

Put these fractions into order, starting with the smallest

Write the number 2 400 000 in standard form

Calculate the size of an interior angle of a regular hexagon.

Factorise 8x + 12

Put these fractions into order, starting with the smallest the circle in terms of

Start by changing the fractions to equivalent ones with the same denominator.

Is there a number that is a multiple of 8, 20, 4, 5 and 40?

40

The new fractions you get are

Putting them in order gives

Back

Standard form must start with a number between one and ten. the circle in terms of

2.4

Then it must be multiplied by ten to the power of something.

2.4 x 106

Write the number 2 400 000 in standard form

Back

Calculate the size of an interior angle of a regular hexagon.

First calculate the exterior angle of an hexagon.

A hexagon has six sides.

Exterior angles add to 360o

All exterior angles on a regular shape are equal.

360o ÷ 6 = 60o

Exterior and interior angles lie on a straight line so

must add to 180o

Interior angle = 180o – 60o = 120o

Back

Factorise 8x + 12 hexagon.

Start by finding a common factor.

Is there a number that goes into 8 and 12?

4

Take this value outside the bracket, then work out what needs to go inside the bracket to make it work when expanded.

4(2x + 3)

Back

Back to sessions hexagon.

Session 4

- Write three values that satisfy the inequality
x – 2 < 4.

- One angle in an isosceles triangle is 40o. Find the possible sizes of the other angles.
- David worked out that 21.082 x 9.86 = 438.15 (2dp)
Explain why David must be wrong.

4. Find the average speed of a car which travels 75 miles in one and a half hours

Ans. 1

Ans. 2

Ans. 3

Ans. 4

Write three values that satisfy the inequality hexagon.

x – 2 < 4.

We need three numbers that when we subtract two, give an answer less than 4

Try numbers until you get one that works.

Possible answers include:

5, 4, 3, 2, 1, 0, ...

Back

Angles in a triangle add to 180 hexagon.o

40o

yo

40o

40o

xo

xo

y = 100o

x = 70o

2. One angle in an isosceles triangle is 40o. Find the possible sizes of the other angles.

What do we know about isosceles triangles?

2 sides the same and two angles the same

Sketch the two different types of triangle

Back

3. David worked out that 21.08 hexagon.2 x 9.86 = 438.15 (2dp)

Explain why David must be wrong.

Use estimation to find an approximate answer

Round each number to one significant figure

202 x 10

400 x 10 = 4000

The answer is approximately 4000 so cannot possibly be 438.15

Back

Formula method: hexagon.

Distance = speed x time

75 = speed x 1.5

75 = speed

1.5

Speed = 50mph

Scaling method:

75 miles in 1 and a half hours

25 miles in half an hour

50 miles in one hour

50mph

Easier to use when calculators are allowed

Find the average speed of a car which travels 75 miles in one and a half hours

Back

Back to sessions hexagon.

Session 5

7m

2m

- Find the value of x in the diagram below
- Work out 7.562 + 9.52
14.36 – 3.61

a) write the full calculator display

b) give your answer to two decimal places

- Write the equation of a line parallel to y = 5x + 2
- Rearrange the equation in question 3 to make x the subject

x

Ans. 1

Ans. 2

Ans. 3

Ans. 4

7m hexagon.

2m

x

Recognise the skill required:

Pythagoras’ Theorem

1. Find the value of x in the diagram below

Recall Pythagoras’ Theorem

a2 + b2 = c2 (where c is the hypotenuse)

Substitute the values

x2 + 22 = 72

Simplify

x2 + 4 = 49

Solve

x2 = 45

x = √(45) = 6.71m (2 d.p.)

Back

= 6.202195349 hexagon.

2. Work out 7.562 + 9.52

14.36 – 3.61

a) write the full calculator display

b) give your answer to two decimal places

Either enter this into your calculator as it appears in the question or work out the numerator and denominator first:

a) 66.6736

10.75

b) 6.20

Back

Write the equation of a line parallel to y = 5x + 2 hexagon.

What would be true about any line parallel to the one given?

It would have the same gradient

What is the gradient of the line given?

5 (the number attached to x when the equation is in the form y = mx + c)

Possible answers:

y = 5x + 1 y = 5x + 10 y = 5x – 2 etc.

Back

4. Rearrange the equation in question 3 to make x the subject

Equation is: y = 5x + 2

We need to get the x on its own on one side of the equation

Subtract 2 from both sides

y – 2 = 5x

Divide both sides by 5

y – 2 = x

5

Back

Back to sessions subject

Session 6

- Factorise x2 + 5x
- Solve the equation 2x + 3 = 14
- Write a fraction equivalent to 0.3
- The length of a rectangle is 3 more than its width.
a) Show that the perimeter of the rectangle can be written as 4x + 6

b) The perimeter is 20cm. Find the dimensions of the rectangle

Ans. 1

Ans. 2

Ans. 3

Ans. 4

1. Factorise x subject2 + 5x

Look for the common factor in the terms

x

Take this value outside the bracket.

x( )

Find what x must be multiplied by to make the original terms

x (x + 5)

Back

2. Solve the equation 2x + 3 = 14 subject

To get the 2x on its own we need to get rid of the +3.

To do this we subtract three from each side.

2x = 11

Now we need to divide both sides by two.

x = 5.5

Back

Write a fraction equivalent to 0.3 subject

The column after the decimal point is called the tenths column.

We have three of these, so we have three tenths.

3

10

Back

x subject

x + 3

Width = 3.5cm

Length = 6.5cm

4.The length of a rectangle is 3 more than its width.

a) Show that the perimeter of the rectangle can be written as 4x + 6

b) The perimeter is 20cm. Find the dimensions of the rectangle

Sketch the rectangle

a) The perimeter is the total distance around the outside of the shape:

x + x + 3 + x + x + 3

Which simplifies to 4x + 6

b) Solve the equation 4x + 6 = 20

Subtract 6 from each side

4x = 14

Divide each side by 4

x = 3.5

Back

Back to sessions subject

Session 7

- Write down the first five multiples of 6
- A ball bounces to 80% of its previous height. I drop the ball from 2m, calculate the height after its first bounce
- Calculate the area of a circle with radius 4.5cm. Give your answer to 3 significant figures.
- £1 = $1.65
Use this to find the cost in pounds of sunglasses bought in America for $96.97

Ans. 1

Ans. 2

Ans. 3

Ans. 4

Write down the first five multiples of 6 subject

The first five multiples of six are the first five numbers in the six times table.

6, 12, 18, 24, 30

Back

10% of 2m = 20cm subject

80% of 2m = 160cm

New height = 160cm or 1.6m

80% as a decimal is 0.8

Height after first bounce

2 x 0.8 = 1.6m

2. A ball bounces to 80% of its previous height. I drop the ball from 2m, calculate the height after its first bounce

Back

Calculate the area of a circle with radius 4.5cm. Give your answer to 3 significant figures.

Recall the formula for the area of a circle:

A = πr2

Substitute the value of r and calculate:

A = π x 4.52 = 63.61725124

Round to 3 significant figures

A = 63.6cm2

Back

4. £1 = $1.65 answer to 3 significant figures.

Use this to find the cost in pounds of sunglasses bought in America for $96.97

To convert dollars into pounds we divide by

1.65

So $96.97 ÷ 1.65 = £58.77

(rounded to d.p. for money)

Back

Back to sessions answer to 3 significant figures.

Session 8

- Expand 3(4x + 2)
- Solve the equation 7x – 5 = 3x + 27
- You are given the formula v = u + at
Find the value of v when u = 3, a = 4 and t = 2

- Make t the subject of the formula in question 3

Ans. 1

Ans. 2

Ans. 3

Ans. 4

Write the terms out: answer to 3 significant figures.

12x + 6

12x

6

Expand 3(4x + 2)

Use a suitable method for expansion

e.g. grid method

4x +2

3

Back

2. Solve the equation 7x – 5 = 3x + 27 answer to 3 significant figures.

Use a suitable method

e.g. Do the same thing to both sides to keep the equation balanced

add 5 to each side

7x = 3x + 32

subtract 3x from each side

4x = 32

divide both sides by 4

x = 8

Back

3. You are given the formula answer to 3 significant figures.v = u + at

Find the value of v when u = 3, a = 4 and t = 2

Substitute the values in for the correct letter.

Remember that at means a x t

v = 3 + (4 x 2)

v = 3 + 8

v = 11

Back

4. Make answer to 3 significant figures.t the subject of the formula in question 3

The formula was v = u + at

subtract u from each side of the equation

v – u = at

divide each side by a

v – u= t

a

Back

Back to sessions answer to 3 significant figures.

Session 9

x

20o

- Find the size of the angle marked x
- Find the length of the side marked y
- A circular pond has diameter 5m, find the area of the pond’s surface
4. The shapes below have the same area. Find the value of h

y m

7.2m

7.6m

2.5cm

h cm

Ans. 1

Ans. 2

Ans. 3

Ans. 4

8cm

8cm

x answer to 3 significant figures.

20o

1. Find the size of the angle marked x

Angles in a triangle add up to 180 degrees

We already have

90o + 20o = 110o

So,

x = 180o – 110o = 70o

Back

y answer to 3 significant figures. m

7.2m

7.6m

Find the length of the side marked y

Recall Pythagoras’ Theorem

a2 + b2 = c2 (where c is the hypotenuse)

Substitute the values

7.62 + 7.22 = y2

Simplify

109.6= y2

Solve

y = √(109.6) = 10.47m (2 d.p.)

Back

3. answer to 3 significant figures.A circular pond has diameter 5m, find the area of the pond’s surface

Recall the formula for the area of a circle

A = πr2

Replace the r with the value for the radius

A = π x 2.52

A = 19.63m2 (2 d.p.)

Back

Find the area of the answer to 3 significant figures.

parallelogram

A = base x height

A = 8 x 2.5 = 20cm2

Recall the formula for the area of a

triangle:

A = base x height

2

20 = 8 x h

2

Solve the equation:

40 = 8h

h = 5cm

2.5cm

h cm

8cm

8cm

4. The shapes below have the same area. Find the value of h

Back

Back to sessions answer to 3 significant figures.

40o

xo

Session 10

Ans. 1

Ans. 2

Ans. 3

Ans. 4

From the numbers 3 9 24 40

Write down (i) A prime number

(ii) A square number

(iii) A multiple of 6

2. A straight line has a gradient of 2 and passes through the point (0,3). What is the equation of the line?

3. 60 = 22 x 3 x 5. Write 600 as a product of primes.

4. Find the size of the angle marked x

From the numbers 3 9 24 40 answer to 3 significant figures.

Write down (i) A prime number

(ii) A square number

(iii) A multiple of 6

(i) A prime number has exactly two factors, one and itself

3

(ii) A square number is the what you get when you multiply any whole number by itself

9 (because 3 x 3 = 9)

(iii) We need a number in the six times table

24

Back

2. answer to 3 significant figures.A straight line has a gradient of 2 and passes through the point (0,3). What is the equation of the line?

Straight line graphs are in the form y = mx + c where m is the gradient and c is the y-intercept

Gradient = 2

y-intercept = +3

Equation: y = 2x + 3

Back

3. answer to 3 significant figures.60 = 22 x 3 x 5. Write 600 as a product of primes.

Either go through the process of drawing a factor tree, e.g.

600

60 10 etc.

or,

600 is ten times bigger than 60, so an extra 2 x 5

Hence, 600 = 22 x 3 x 5 x 2 x 5 = 23 x 3 x 52

Back

40 answer to 3 significant figures.o

xo

4.Find the size of the angle marked x

Triangle is isosceles, so the bottom two angles are the same:

180 – 40 = 140

140 ÷ 2 = 70o

70o and x lie on a straight line, so add to 180o

x = 180 – 70 = 110o

Back

Back to sessions answer to 3 significant figures.

Session 11

Ans. 1

Ans. 2

Ans. 3

Ans. 4

Sketch a scatter graph that has a strong positive correlation

Find the probability of rolling a prime number on a ten sided dice

Write three numbers that have a median of 9 and a range of 4

Draw a stem and leaf diagram for the recorded car speeds below

38, 33, 42, 45, 40, 39, 42, 38, 42, 47, 29, 28, 30

Sketch a pair of axes answer to 3 significant figures.

Mark points going from bottom left to top right on your axes

1. Sketch a scatter graph that has a strong positive correlation

Back

2. answer to 3 significant figures.Find the probability of rolling a prime number on a ten sided dice

List all the primes from 1 to 10

2, 3, 5, 7

There are four primes out of ten numbers, so

P(prime) =

Back

3. answer to 3 significant figures.Write three numbers that have a median of 9 and a range of 4

Median = 9, so the middle number is 9

…, 9, …

Difference between biggest and smallest numbers must be 4, so possible solutions include:

7, 9, 11

8, 9, 12

9, 9, 13 etc.

Back

8 9 answer to 3 significant figures.

0 3 8 8 9

0 2 2 2 5 7

4.Draw a stem and leaf diagram for the recorded car speeds below

38, 33, 42, 45, 40, 39, 42, 38, 42, 47, 29, 28, 30

Stems first, then the leaves in order:

2

3

4

Back

Back to sessions answer to 3 significant figures.

Session 12

19 m

x m

Ans. 1

Ans. 2

Ans. 3

Ans. 4

15 m

Calculate the mean from the numbers below:

5, 7, 7, 4, 6, 8, 9, 6

2. Write 9.2 x 105 as an ordinary number

3. Solve 3x – 4 = 12 – 5x

4. Find the value of x in the diagram below:

Calculate the mean from the numbers below: answer to 3 significant figures.

5, 7, 7, 4, 6, 8, 9, 6

We need to start by adding all of the numbers together

5 + 7 + 7 + 4 + 6 + 8 + 9 + 6 = 52

Now divide this value by how many numbers there are

52 ÷ 8 = 6.5

Back

Write 9.2 x 10 answer to 3 significant figures.5 as an ordinary number

We need to move the decimal point 5 times to the right

920 000

Back

Solve 3x – 4 = 12 – 5x answer to 3 significant figures.

Collect the unknowns on the left hand side, as there are more x’s on this side to start with.

add four to each side

3x = 16 – 5x

add 5x to each side

8x = 16

divide both sides by 8

x = 2

Back

19 m answer to 3 significant figures.

x m

15 m

4. Find the value of x in the diagram below:

Recall Pythagoras’ Theorem

a2 + b2 = c2 (where c is the hypotenuse)

Substitute the values

152 + x2 = 192

Simplify

225 + x2 = 361

Solve

x2 = 136

x = √(136) = 11.66m (2 d.p.)

Back

Back to sessions answer to 3 significant figures.

Session 13

4cm

Ans. 1

Ans. 2

Ans. 3

Ans. 4

10cm

Write 0.35 as a decimal and a fraction in its simplest form

Barry and Dave share £400 in the ratio 5:3. How much money does Dave get?

The price of a plasma television is £600. In the sale everything is reduced by 30%. Find the sale price of a plasma television.

Calculate the volume of the cylinder below. Leave your answer in terms of π.

Write 0.35 as a fraction in its simplest form answer to 3 significant figures.

We know that 0.35 goes into the hundredths column

So we have 35 hundredths

35

100

To simplify we need to find a number that goes into 35 and 100 and divide the numerator and denominator by that number.

Dividing both sides by five gives

7

20

Back

2. Barry and Dave share £400 in the ratio 5:3. How much money does Dave get?

Add the ratios to find the total number of shares:

5 + 3 = 8

Find out how much each share is worth:

£400 ÷ 8 = £50

Dave gets 3 shares:

£50 x 3 = £150

Back

3. The price of a plasma television is £600. In the sale everything is reduced by 30%. Find the sale price of a plasma television.

Find 30% of £600

10% of £600 = £60

30% of £600 = £180

Subtract this value from the original price

£600 – £180 = £420

Back

4cm everything is reduced by 30%. Find the sale price of a plasma television.

10cm

Calculate the volume of the cylinder below. Leave your answer in terms of π.

Find the area of the cross section

A = πr2

A = π x 42

A = 16 π

Volume = area of cross section x height

V = 16 π x 10

V = 160 π

Back

Back to sessions everything is reduced by 30%. Find the sale price of a plasma television.

95o

115o

xo

70o

Session 14

Ans. 1

Ans. 2

Ans. 3

Ans. 4

Simplify the expression a6 x a4

Expand 3x (4x – 2)

Factorise completely 4x2 – 8x

Find the size of the angle marked x

Simplify the expression a everything is reduced by 30%. Find the sale price of a plasma television.6 x a4

Using the laws of indices, when we multiply we add the indices

a6 x a4 = a10

Back

Expand 3x (4x – 2) everything is reduced by 30%. Find the sale price of a plasma television.

Multiplying everything inside the bracket by the term on the outside (3x) gives:

12x2 – 6x

Back

Factorise completely 4x everything is reduced by 30%. Find the sale price of a plasma television.2 – 8x

Look for common factors, numbers and letters

The highest common factor here is 4x

Take 4x outside the bracket 4x ( )

Now consider what needs to go inside the bracket

4x (x – 2)

Back

95 everything is reduced by 30%. Find the sale price of a plasma television.o

115o

xo

70o

Find the size of the angle marked x

Angles in a quadrilateral add to 360o

Add up the ones we know 95o + 70o + 115o = 280o

x = 360 – 285 = 80o

Back

Back to sessions everything is reduced by 30%. Find the sale price of a plasma television.

x + 1

x + 4

Session 15

Ans. 1

Ans. 2

Ans. 3

Ans. 4

Five people weigh 79kg, 64kg, 72kg, 75kg and 70kg.

a) Find the mean weight of the five people

b) Find the range of the weights

2. Write 0.000 061 in standard form

3. The perimeter of the rectangle below is 58cm. Find the value of x.

4. Two angles lie on a straight line. One angle is 43o, find the size of the other angle.

Five people weigh 79kg, 64kg, 72kg, 75kg and 70kg. everything is reduced by 30%. Find the sale price of a plasma television.

a) Find the mean weight of the five people

b) Find the range of the weights

a)Find the total weight of the five people

79 + 64 + 72 + 75 + 70 = 360

Divide this total by 5 (because there are five numbers)

360 ÷ 5 = 72kg

b) Find the difference between the highest and lowest value

79 – 64 = 15kg

Back

2. Write 0.000 061 in standard form everything is reduced by 30%. Find the sale price of a plasma television.

Start with a number between one and ten:

6.1

Consider how many times the decimal point has to move (remember that really small numbers have a negative index)

6.1 x 10-5

Back

x + 1 everything is reduced by 30%. Find the sale price of a plasma television.

x + 4

The perimeter of the rectangle below is 58cm. Find the value of x.

Find the perimeter of the shape in terms of x

x + 1 + x + 4 + x + 1 + x + 4

4x + 10

The question says this is 58cm, so

4x + 10 = 58

Solving the equation gives

x = 12

Back

Two angles lie on a straight line. One angle is 43 everything is reduced by 30%. Find the sale price of a plasma television.o, find the size of the other angle.

We know that angles on a straight line add up to 180o

So to find the other angle we need to know

180o – 43o = 137o

Back

Back to sessions everything is reduced by 30%. Find the sale price of a plasma television.

4cm

2cm

6cm

Session 16

Ans. 1

Ans. 2

Ans. 3

Ans. 4

Billy and David share £600 in the ratio 7:5. How much does David get?

Simplify a) t6 x t3 x p4 x p2

b) h13 ÷ h7

3. Write 140 as a product of prime numbers

Find the volume of the cuboid below

1. Billy and David share £600 in the ratio 7:5. How much does David get?

How many parts altogether? (add the ratios)

12

How much is each part worth? (divide the total by 12)

£600 ÷ 12 = £50

David gets 5 parts, so

5 x £50 = £250

Back

2. Simplify a) t does David get?6 x t3 x p4 x p2

b) h13 ÷ h7

a) The laws of indices state that when we multiply we add the indices

t6+3 x p4+2

t9 x p6 (or t9p6)

b) When we divide we subtract the indices

h13-7

h6

Back

Write 140 as a product of prime numbers does David get?

Draw a factor tree to help

140

14 10

7 2 5 2

So, as a product of primes:

7 x 2 x 5 x 2

22 x 5 x 7

Back

4cm does David get?

2cm

6cm

4. Find the volume of the cuboid below.

Find the area of the cross section

6 x 4 = 24cm2

Multiply this by the length

Volume = 24 x 2 = 48cm3

Back

Back to sessions does David get?

8cm

Session 17

Ans. 1

Ans. 2

Ans. 3

Ans. 4

The area of the triangle below is 12cm2. Find the height of the triangle.

Find the size of the interior and exterior angles of a regular decagon.

I have 5 toffee, 3 chocolate and 2 fruit sweets in a bag. Anne picks a sweet at random. Find the probability that it is a fruit sweet.

Calculate a) 0.6 x 0.3

b) 0.4 x 0.5

8cm does David get?

The area of the triangle below is 12cm2. Find the height of the triangle.

The formula for the area of a triangle is

base x height

2

So 8 x h = 12

2

So 8 x h = 24

h = 3

Back

2. Find the size of the interior and exterior angles of a regular decagon.

The sum of exterior angles is 360o

In a regular shape the exterior angles are all equal

A decagon has ten sides

Therefore,

exterior angle = 360 ÷ 10 = 36o

The interior and exterior angles lie on a straight line

Therefore

interior angle = 180 = 36 = 144o

Back

3. I have 5 toffee, 3 chocolate and 2 fruit sweets in a bag. Anne picks a sweet at random. Find the probability that it is a fruit sweet.

How many sweets are in the bag?

10

How many fruit sweets are there?

2

So the probability of selecting a fruit sweet is

2

10

Back

4. Calculate a) 0.6 x 0.3 Anne picks a sweet at random. Find the probability that it is a fruit sweet.

b) 0.4 x 0.5

a) We know that 6 x 3 = 18

There are two numbers after the decimal point in the question

There must be two numbers after the d.p. in the answer

0.6 x 0.3 = 0.18

b) 4 x 5 = 20

We need two numbers after the d.p.

0.4 x 0.5 = 0.20

(0.2)

Back

Back to sessions Anne picks a sweet at random. Find the probability that it is a fruit sweet.

Session 18

Ans. 1

Ans. 2

Ans. 3

Ans. 4

Expand and simplify 4(x + 3)

Rearrange y = 5x + 2 to make x the subject

Simplify the ratio 12000 : 28000

A flagpole is supported by a wire as shown in the diagram. The length of the wire is 10m and the distance from the base of the flagpole from where the wire meets the ground is 6m. Find the height of the flagpole.

1. Expand and simplify 4(x + 3) Anne picks a sweet at random. Find the probability that it is a fruit sweet.

Multiply everything in the bracket by the term on the outside of the bracket

4x + 12

Back

2. Rearrange Anne picks a sweet at random. Find the probability that it is a fruit sweet.y = 5x + 2 to make x the subject

We need to end up with either x = ... or ... = x

To get the x’s on their own we get rid of the +2 by subtracting two from each side:

y – 2 = 5x

Now we need to divide both sides by 5

y – 2 = x

5

Back

You may have divided by two, then by two again. Anne picks a sweet at random. Find the probability that it is a fruit sweet.

3. Simplify the ratio 12000 : 28000

Find a number that is a factor of both numbers, then divide each number by the factor.

The easiest number to start with here is 1000, since this will cancel all of the zeros when we divide.

12 : 28

The biggest number that is a factor of 12 and 28 is 4, so we divide each number by 4.

3 : 7

Back

10m Anne picks a sweet at random. Find the probability that it is a fruit sweet.

h m

6m

A flagpole is supported by a wire as shown in the diagram. The length of the wire is 10m and the distance from the base of the flagpole from where the wire meets the ground is 6m. Find the height of the flagpole.

Write the lengths on the diagram.

Apply Pythagoras’ Theorem to give

h2 + 62 = 102

Simplify the equation

h2 + 36 = 100

Solve

h2 = 64

h = 8m

Back

Back to sessions Anne picks a sweet at random. Find the probability that it is a fruit sweet.

Session 19

6cm

Ans. 1

Ans. 2

Ans. 3

Ans. 4

2cm

Round 28.3952 to one decimal place

Billy buys a motorbike for £160 and ends up having to sell it for of the price. How much does he sell the bike for?

Carol travels 15 miles in twenty minutes. Calculate her average speed in miles per hour.

Calculate the volume of the cylinder below, giving your answer to three decimal places and stating the units clearly in your answer.

Round 28.3952 to one decimal place Anne picks a sweet at random. Find the probability that it is a fruit sweet.

We need one number after the decimal point.

28.3952

The number after this (9) tells us we have to round up.

28.4

Back

Billy buys a motorbike for £160 and ends up having to sell it for of the price. How much does he sell the bike for?

We need to find five eighths of £160.

One eighth

£160 ÷ 8 = £20

So five eighths = £20 x 5 = £100

Billy sells the bike for £100

Back

X 3 it for of the price. How much does he sell the bike for?

X 3

3. Carol travels 15 miles in twenty minutes. Calculate her average speed in miles per hour.

15 miles travelled in 20 minutes. We want to know how many miles in 60 minutes (1 hour)

15 miles in 20 minutes

__ miles in 60 minutes

15 x 3 = 45 miles per hour

Back

6cm it for of the price. How much does he sell the bike for?

2cm

Calculate the volume of the cylinder below, giving your answer to three decimal places and stating the units clearly in your answer.

Volume = area of cross section x length

Area of cross section (circle)

A = πr2

A = π x 62 = 113.0973355

Volume = 36 π x 2 = 226.1946711

Volume = 226.195 cm3

Back

Back to sessions it for of the price. How much does he sell the bike for?

Session 20

50o

60o

Ans. 1

Ans. 2

Ans. 3

Ans. 4

y

x

Estimate the volume of a cuboid whose dimensions are 5.1cm, 2.7cm and 4.2cm

The ratio of teachers to pupils in a school is 1:20. If there are 860 pupils, how many teachers are there?

Factorise 6x + 9

Find the size of the lettered angles below, giving reasons for your answers.

1. Estimate the volume of a cuboid whose dimensions are 5.1cm, 2.7cm and 4.2cm

To estimate the answer we need to round each of the values first

5.1 is approximately 5

2.7 is approximately 3

4.2 is approximately 4

For the volume of a cuboid we multiply the three dimensions

5 x 3 x 4 = 60cm3

Back

This grid may also help 5.1cm, 2.7cm and 4.2cm

2. The ratio of teachers to pupils in a school is 1:20. If there are 860 pupils, how many teachers are there?

There are 20 pupils for every one teacher.

We need to know how many twenties go into 860.

860 ÷ 20 =

43

There are 43 teachers

Back

Factorise 6x + 9 5.1cm, 2.7cm and 4.2cm

Find a common factor to both terms

3

Take this outside the bracket

3( )

Now find what needs to be multiplied by three to make the terms we were given in the question

3 (2x + 3)

Back

50 5.1cm, 2.7cm and 4.2cmo

60o

y

x

Find the size of the lettered angles below, giving reasons for your answers.

Use the parallel lines to find angle x

x = 50o because they are alternate angles

Now use angles in a triangle to find y

60o + 50o = 110o

y = 70o because angles in a triangle add up to 180o

Back

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