Student name: Ferris BuellerAssessment : Edexcel 1MA1 1F Jun 2019 1 Foundation - Summer 2019

Date taken : 30-11-2019

Question Topic(s)Total marks

% Marks achievedAverage

of all students

1 time conversions 1 100% 50%2 convert decimal to percentage 1 100% 50%3 order of operations 1 100% 50%4 identify prime numbers 1 100% 50%5 find the midpoint of two numbers 1 0% 0%6 money problems 4 50% 25%7a interpret bar charts 2 100% 50%7b interpret bar charts - find averages 1 100% 50%8 order fractions 2 50% 25%9a speed - find distance 2 100% 50%9b time problems 2 50% 25%

10a solving linear equations 1 100% 50%10b solving linear equations 1 100% 50%10c solving linear equations 2 50% 25%11 multiplication 2 50% 25%

12a angle facts 2 0% 0%12bi angles on parallel lines 2 0% 0%12bii angle facts 1 0% 0%

13form algebraic expressions involving metric conversions

1 100% 50%

14a find fraction of an amount 1 100% 50%14b fraction division - explain errors 1 100% 50%15a square roots 1 100% 50%15b cube numbers 1 100% 50%16a expand single bracket 1 100% 50%16b factorise into single bracket 1 100% 50%17i experimental probability 1 100% 50%17ii experimental probability 1 100% 50%

18functional maths - square and rectangle area

4 100% 50%

19a fractions - add and subtract 2 0% 0%19b fractions - multiply 2 100% 50%20 area of squares and percentage ps 3 0% 0%21 two way tables 4 100% 50%

22a calculate probability from a table 2 50% 25%22b find total given the probability 2 0% 0%23a proportion recipe questions 3 67% 33%

23b proportion recipe questions 2 50% 25%24 find highest common factor 2 100% 50%25 draw shape from plan and elevations 2 100% 50%26 transformations 3 0% 0%27 sharing into a ratio ps 4 0% 0%28 area and perimeter of rectangles ps 4 25% 13%

29aquadratic graphs - give coordinates of turning point and give roots

1 0% 0%

29bquadratic graphs - give coordinates of turning point and give roots

2 0% 0%

Grade boundaries

Max 5 4 3 2 180 61 50 37 24 12

Grade achieved: 3 Number of marks off the next grade: 5

Targets

sharing into a ratio psquadratic graphs - give coordinates of turning point and give rootsangle factsarea and perimeter of rectangles psarea of squares and percentage ps

Notes and work for topic: sharing into a ratio ps

Resources to help with this topic

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28 Dividing into a Ratio Answers

Warm up

1) One quarter of a room is painted blue, the rest white. Write the ratio of blue to

white paint.

2) Simplify the following fractions.

a. 4

6= b.

10

18= c.

66

110=

Stage 1

3) Share 75 into the ratio 3 : 2

4) Share 39 into the ratio 4 : 9

5) Share 25 into the ratio 4 : 1

6) Share 28 into the ratio 3 : 4

7) Share 15 into the ratio 1 : 2

8) Share 40 into the ratio 2 : 3

9) Share 45 into the ratio 8 : 7

10) Share 99 into the ratio 5 : 6

Stage 2

11) Share 204 into the ratio 6 : 11

12) Share 378 into the ratio 13 : 14

13) Share 216 into the ratio 4 : 14

14) Share 420 into the ratio 10 : 4 : 16

15) Share 500 into the ratio 11 : 5 : 9

16) Share 301 into the ratio 1 : 20 : 22

17) Share 496 into the ratio 10 : 4 : 17

18) Share 258 into the ratio 8 : 20 : 15

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Stage 3

19) Laura and Jess share counters in the ratio 7 : 9. If Laura gets 35 how many counters

does Jess get?

20) Ellie and Lily share bananas in the ratio 5 : 3. If Ellie gets 30 how many bananas does

Lily get?

21) Ellie and Jamie share pencils in the ratio 4 : 5. If Jamie gets 20 how many pencils do

they share altogether?

22) Toby and Steve share sweets in the ratio 5 : 6. If Steve gets 60 how many sweets do

they share altogether?

Stage 4

23) £240 is shared between Aaron, Brenda, Crista and Debbie.

The ratio of the amount Aaron gets to the amount Brenda gets is 3 : 5

Crista and Debbie each get 2 times the amount Aaron gets.

Work out the amount of money that Brenda gets.

24) £288 is shared between Eric, Fred, Grace and Heidi.

The ratio of the amount Eric gets to the amount Fred gets is 7 : 2

Grace and Heidi each get 3.5 times the amount Eric gets.

Work out the amount of money that Fred gets.

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25) £375 is shared between Austin, Chloe, Ethan and Joanne.

The ratio of the amount Austin gets to the amount Chloe gets is 5 : 7

Ethan and Joanne each get 1.5 times the amount Eric gets.

Work out the amount of money that Ethan gets.

Stage 5

26) Bill and Ted bought a present for their maths teacher. They paid in the ratio 3 : 5.

Ted paid £4 more than Bill. How much did the gift cost?

27) Tina and Sam own shoes in the ratio 5 : 7.

Sam owns 6 pairs of shoes more than Tina. How many pairs of shoes do they own

altogether?

28) A box of model cars has red and silver models in a ratio of 2:7.

There are 300 more silver cars than red ones.

a. How many cars are in the crate altogether?

b. How many are red?

29) Ed and Jack collect football cards, and their football cards are in a ratio of 3:4.

If Jack has 14 more phone cards than Ed, how many cards does Ed have?

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Stage 6 - Worked example

There are some small cubes and some large cubes in a bag. The cubes are red or the cubes are yellow.

The ratio of the number of small cubes to the number of large cubes is 4 : 7

The ratio of the number of red cubes to the number of yellow cubes is 3 : 5

(a) Explain why the least possible number of cubes in the bag is 88

All the small cubes are yellow.

(b) Work out the least possible number of large yellow cubes in the bag.

Stage 6 - Questions

30) There are some small cubes and some large cubes in a bag. The cubes are red or the cubes are yellow.

The ratio of the number of small cubes to the number of large cubes is 3 : 7

The ratio of the number of red cubes to the number of yellow cubes is 2 : 1

(a) Explain why the least possible number of cubes in the bag is 30

All the small cubes are yellow.

(b) Work out the least possible number of large yellow cubes in the bag.

The least possible number of cubes has to be the lowest common multiple of

(4 + 7) and (3 + 5), i.e. the LCM of 11 and 8, which is 88.

The number of small cubes =88

11× 4 = 32 (divide the 88 cubes into the 4 : 7 ratio).

The number of yellow cubes =88

8× 5 = 55 (divide the 88 cubes into the 3 : 5 ratio).

Since all the small cubes are yellow:

The number of large yellow cubes

= number of

yellow cubes −

number of small yellow cubes

= 55 − 32

= 𝟐𝟑

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31) There are some small balls and some large balls in a bag. The balls are orange or the balls are green.

The ratio of the number of small balls to the number of large balls is 5 : 2

The ratio of the number of orange balls to the number of green balls is 3 : 4

(a) Explain why the least possible number of balls in the bag is 49

All the large balls are orange.

(b) Work out the least possible number of small orange balls in the bag.

32) There are some small sweets and some large sweets in a bag. The sweets are black or the sweets are white.

The ratio of the number of small sweets to the number of large sweets is 2 : 7

The ratio of the number of black sweets to the number of white sweets is 5 : 3

(a) Explain why the least possible number of sweets in the bag is 72

All the small sweets are black.

(b) Work out the least possible number of large black sweets in the bag.

33) There are some small blocks and some large blocks in a bag. The blocks are purple or the blocks are blue.

The ratio of the number of small blocks to the number of large blocks is 4 : 1

The ratio of the number of purple blocks to the number of blue blocks is 8 : 5

(a) Explain why the least possible number of blocks in the bag is 65

All the large blocks are blue.

(b) Work out the least possible number of small blue blocks in the bag.

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Stage 7 - Worked example

A shop sells packs of black pens, packs of red pens and packs of green pens.

There are

2 pens in each pack of black pens

5 pens in each pack of red pens

6 pens in each pack of green pens

On Monday,

number of packs of black pens sold

: number of packs of red pens sold

: number of packs

of green pens sold = 7 : 3 : 4

A total of 212 pens were sold.

Work out the number of green pens sold.

Stage 7 - Questions

34) A shop sells packs of blue pens, packs of gold pens and packs of red pens.

There are

6 pens in each pack of blue pens

3 pens in each pack of gold pens

5 pens in each pack of red pens

On Monday,

number of packs of blue pens sold

: number of packs

of gold pens sold :

number of packs of red pens sold

= 6 : 2 : 3

A total of 114 pens were sold.

Work out the number of gold pens sold.

Step 1: Ratio of pens = 14 : 15 : 24 (multiply the number of pens in a pack by the ratio).

Step 2: Find the total of this ratio, so 14 + 15 + 24 = 53

Step 3: 212 ÷ 53 = 4

Step 4: Multiply the number of green pens in the ratio by the answer from step 3.

So 24 × 4 = 96

So 96 green pens were sold.

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35) A shop sells packs of chocolate biscuits, packs of ginger biscuits and packs of plain

biscuits.

There are

8 biscuits in each pack of chocolate biscuits

10 biscuits in each pack of ginger biscuits

12 biscuits in each pack of plain biscuits

On Monday,

number of packs of blue pens sold

: number of packs

of gold pens sold :

number of packs of red pens sold

= 11 : 3 : 8

A total of 642 biscuits were sold.

Work out the number of chocolate biscuits sold.

36) A shop sells packs of black pens, packs of red pens and packs of yellow pens.

There are

8 pens in each pack of black pens

5 pens in each pack of red pens

3 pens in each pack of yellow pens

On Monday,

number of packs of black pens

sold :

number of packs of red pens

sold :

number of packs of yellow pens

sold

= 9 : 5 : 2

A total of 515 pens were sold.

Work out the number of black pens sold.

Notes and work for topic: quadratic graphs - give coordinates of turning point

and give roots

Resources to help with this topic

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1) Here is the graph for 𝑦 = 𝑥2 + 8𝑥 + 15

(a) Write down the coordinates of the turning point on the graph of

𝑦 = 𝑥2 + 8𝑥 + 15

(b) Use the graph to find the roots of the equation 𝑥2 + 8𝑥 + 15 = 0

166 Quadratic graphs - solving and

turning points

𝑦

𝑥

© EviEd Ltd

2) Here is the graph for 𝑦 = 𝑥2 − 4𝑥 + 3

(a) Write down the coordinates of the turning point on the graph of

𝑦 = 𝑥2 − 4𝑥 + 3

(b) Use the graph to find the roots of the equation 𝑥2 − 4𝑥 + 3 = 0

𝑦

𝑥

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3) Here is the graph for 𝑦 = 𝑥2 + 8𝑥 + 12

(a) Write down the coordinates of the turning point on the graph of

𝑦 = 𝑥2 + 8𝑥 + 12

(b) Use the graph to find the roots of the equation 𝑥2 + 8𝑥 + 12 = 0

𝑦

𝑥

© EviEd Ltd

4) Here is the graph for 𝑦 = −𝑥2 − 4𝑥 − 3

(a) Write down the coordinates of the turning point on the graph of

𝑦 = −𝑥2 − 4𝑥 − 3

(b) Use the graph to find the roots of the equation −𝑥2 − 4𝑥 − 3 = 0

𝑦

𝑥

Notes and work for topic: angle facts

Resources to help with this topic

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61 Angle Facts

What you need to know…

There are 360° in one full turn (or one full circle) and 180° in half a turn (or semicircle).

A right angle is 90° and is a quarter turn, and can be shown by a small square.

An acute angle is an angle less than 90°.

An obtuse angle is an angle between 90° and 180°.

A reflex angle is an angle between 180° and 360°.

The angles that meet at a point add to 360°, and the angles on a straight line add to 180°.

The angles in a triangle add to 180°

360o

180o 90o

Angles add to 360° Angles add to 180°

Acute angle Obtuse angle Reflex angle

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Stage 1

1. State whether each angle is acute, reflex or obtuse.

What you need to know continued…

The angles in a triangle add to 180°.

An equilateral triangle has 3 sides of equal length (the dashes on the lines show they are

equal in length). All of the angles are also equal and are 60°.

An isosceles triangle has 2 sides of equal length. The angles at the base of the equal sides

are equal.

Equilateral triangle

Each angle = 60°

Isosceles triangle

Angles at the base of the equal sides are equal

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2. State whether each labelled angle is either acute, reflex or obtuse.

Stage 2 - For each question, find the unknown angle, x.

1. 2.

9.

3. 4. 5.

6.

A

B C

25°

35°

𝑥°

10.

x = 20o

A

B C

20°

20°

𝑥°

7. A

B C

30°

40°

𝑥°

8.

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Stage 3 - For each question, find the unknown angle, x or the angle indicated.

`

1. 2. 3.

4.

5. 6.

7.

A

B C

32°

18° 𝑥°

𝑥°

8.

9.

A

B C

30° 15°

10° 𝑥°

10. Find angle 𝐴𝐵𝐶.

𝐴

𝐸 𝐷

𝐶 𝐵

11. Find angle 𝐴𝐵𝐷.

𝐴

𝐸 𝐷

𝐶 𝐵

Notes and work for topic: area and perimeter of rectangles ps

Resources to help with this topic

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86 Area of rectangles

Stage 1

Find the area of the following rectangles:

1)

2)

3)

4)

5) A rectangle with a length of 8 cm and width of 12 cm.

6) A rectangle with a width of 40 cm and length of 60 cm.

Stage 2

7) A garden is in the shape of a rectangle 50 m by 40 m.

Vegetables are grown in 25% of the garden.

The rest of the garden is grass.

Work out the area of the garden that is grass.

8) A driveway is in the shape of a rectangle 3 m by 4 m.

Moss covers 40% of the driveway.

Work out the area of the driveway which is not covered by moss.

5 cm

2 cm

8 cm

6 cm

9 cm

5 cm

50 m

40 m

3 m

4 m

30 cm

25 cm

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9) A door is in the shape of a rectangle 0.75 m by 2 m.

60% of the door area is glass.

Work out the area of the door which is not glass.

10) A biscuit is in the shape of a rectangle 5 cm by 3 cm.

55% of the biscuit is covered in chocolate.

Work out the area of the biscuit which is not covered in chocolate.

Stage 3

11) A rectangle has an area of 4 cm2.

List all the different values for the length and width of the rectangle.

12) A rectangle has an area of 12 cm2.

List all the different values for the length and width of the rectangle.

13) A rectangle has an area of 21 cm2.

List all the different values for the length and width of the rectangle.

14) A rectangle has an area of 30 cm2.

Gemma says “The rectangle could have a length of 5 cm.”

Is Gemma correct? You must show your working.

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Stage 3

15) Here are two rectangles.

𝐹𝐺 = 12 cm

𝐵𝐶 = 𝐸𝐹

The perimeter of 𝐴𝐵𝐶𝐷 is 30 cm.

The area of 𝐸𝐹𝐺𝐻 is 60 cm2.

Find the length of 𝐴𝐵.

16) Here are two rectangles.

𝐹𝐺 = 8 cm

𝐵𝐶 = 𝐸𝐹

The perimeter of 𝐴𝐵𝐶𝐷 is 32 cm.

The area of 𝐸𝐹𝐺𝐻 is 36 cm2.

Find the length of 𝐴𝐵.

𝐴 𝐵

𝐶 𝐷

𝐸 𝐹

𝐺 𝐻

𝐴 𝐵

𝐶 𝐷

𝐸 𝐹

𝐺 𝐻

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17) Here are two rectangles.

𝑄𝑅 = 3.5 cm

𝑆𝑅 = 𝑇𝑊

The perimeter of 𝑇𝑈𝑊𝑉 is 45 cm.

The area of 𝑃𝑄𝑅𝑆 is 21 cm2.

Find the length of 𝑇𝑈.

18) Here are two rectangles.

𝑆𝑅 = 7 cm

𝑄𝑅 = 𝑇𝑈

The perimeter of 𝑇𝑈𝑊𝑉 is 32.5 cm.

The area of 𝑃𝑄𝑅𝑆 is 35 cm2.

Find the length of 𝑇𝑊.

𝑃 𝑄

𝑅 𝑆

𝑇 𝑈

𝑉 𝑊

𝑃 𝑄

𝑅 𝑆

𝑇 𝑈

𝑉 𝑊

Notes and work for topic: area of squares and percentage ps

Resources to help with this topic

© EviEd Ltd

Warm up

1) Find the area of the following squares:

2) Find the area of the following triangles:

Stage 1 Example

Here are two squares, A and B.

The length of the side of square A is 60% of the length of the side of square B.

Express the area of square A as a percentage of the area of square B.

5 cm

2 cm

10 cm

7 cm

165 Area of squares and percentage

problems

Give square B a side length of 10 cm. This will give square B an area of 100 cm2.

Since the length of the side of square A is 60% of the length of the side of square B, the

length of square A would be 6 cm.

Area of square A = 6 × 6 = 36 cm2

So, percentage area =36

100× 100 = 36%

5 cm

8 cm

4 cm

6 cm

10 cm

12 cm

A B

© EviEd Ltd

Stage 1 Questions

3) Here are two squares, A and B.

The length of the side of square A is 50% of the length of the side of square B.

Express the area of square A as a percentage of the area of square B.

4) Here are two squares, A and B.

The length of the side of square A is 10% of the length of the side of square B.

Express the area of square A as a percentage of the area of square B.

5) Here are two squares, A and B.

The length of the side of square A is 80% of the length of the side of square B.

Express the area of square A as a percentage of the area of square B.

B A

B A

B A

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Stage 2 Example

Here are two squares, A and B.

The length of the side of square A is 40% of the length of the side of square B.

Express the area of the shaded region of square A as a percentage of the area of square B.

Stage 2 Questions

6) Here are two squares, A and B.

The length of the side of square A is 20% of the length of the side of square B.

Express the area of the shaded region of square A as a percentage of the area of

square B.

Give square B a side length of 10 cm. This will give square B an area of 100 cm2.

Since the length of the side of square A is 40% of the length of the side of square B, the

length of square A would be 4 cm.

Area of shaded triangle =1

2× 4 × 4 = 8 cm2

So, percentage area =8

100× 100 = 8%

B A

B A

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7) Here are two squares, A and B.

The length of the side of square A is 50% of the length of the side of square B.

Express the area of the shaded region of square A as a percentage of the area of

square B.

8) Here are two squares, A and B.

The length of the side of square A is 30% of the length of the side of square B.

Express the area of the shaded region of square A as a percentage of the area of

square B.

9) Here are two squares, A and B.

The length of the side of square A is 60% of the length of the side of square B.

Express the area of the shaded region of square A as a percentage of the area of

square B.

B A

B A

B A