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The maths department are making weekly booklets for you tocomplete at home.

This booklet is some maths work for you to complete at home over the next couple of weeks.

North Gosforth AcademyMathematics Home Booklet

Year 9 Foundation

20th April – 1st May

The topics covered are below. You have already covered these in your maths lessons and being at home gives you a chance to revise! Create yourself a useful revision resource and practise key skills!

Instructions:

There are plenty of examples – write these down. Write down any useful facts.

Complete questions to practise the skills and stretch questions to push yourself. Show working out!

Old maths books and revision guides are useful sources of information if you have them

Any access to the internet, even limited, gives you access to Hegarty maths, Corbett maths and Mathsgenie where tutorial videos are available

Topics in this booklet:

Simplifying expressions Collecting like terms Writing expressions from worded problems Substitution Expanding single brackets

Fill the blanks with these words; collect, expression, variable,like, unknown, equation a x a = a2

Search Google for Khan AcademyA) 2x + 3x B) 2x + 3x = 25

A is an , B is an . In A x is a . In B x is an that you can find the value of. You can the terms in A because they are .

2 x b = 2ba x b = ab 2 ÷ b = 2

b

Origins of Algebra and watch the short video.

Write down ten facts from the videorelating to the origins of algebra.

A – Simplify

1) 5x + 6x + 3x2) 8m + 2m – 3m 3) 9y – 4y + 2y4) 4b + 5b – b5) 9p – 7p + 4p – 5p 6) 4c + 3c – 11c

B – Simplify

1) 3 x t2) 5 x g 3) b ÷ 3 4) 7 ÷ w5) m x n6) p x q

C – Simplify

1) 3 x 4d2) 5 x 2m3) 7f x 24) 8s x 5 5) 14c ÷ 2 6) 20v ÷ 5

D – Simplify by collecting like terms 1) 10a + 8b + 3a2) 2b + 6c + 4b 3) 8a + 4 + 2a + 34) 6h + 2 + h + 115) 7m + 2n + 3m + 4n 6) 5k + 2l – 2k + 3l

E – Simplify

1) 7n2 + 8p – p + 5n2

2) 8x2 – 3x – 3x2

3) -7b + 2a + 3b – 5a4) -3g2 + 2g – 4g2 + 4g5) 5c x 2d6) 6h x 3i7) 7z x 3z8) 8s x 5sF – Which of these expressions simplify to give -3x – 4y

a) 6x + 4y – 9x – 4yb) 12x + 3y – 9x – 7yc) 4x + 7y – 7x – 3yd) x + 2y – 4x – 6y

11a + 4b + 3c

+ 9a2a

2a

2a

+ 9a + b

+ 9a + b + 3c

2a + 3b + 9a + b + 3c

Collecting like termsYou can only collect terms whose letters are the same.

Step 1: Write out the question. 2a + 3b + 9a + b + 3c

Step 2: Circle all the terms with the same letters (like terms). Make sure you also capture the plus or minus on the left.

Step 3: Now put a rectangle around the next group of like terms.

Step 4: If there are any more groups of like terms then put a triangle around them.

Step 5: Now just add up how many of

each group you have got. This is

your answer!

+ 3b + b + 3c

+ 3c

QuestionsCollect the like terms in these expressions:

1. a + a2. a + 2a3. a + 3a + b 4. 2a + b + 3b5. a + b + 2b + 3a6. a + 2b + 3c + 3a + 3b 7. 3x + 7y + 2x +9y8. 8A + 9A + 10B + 5A9. 13d + 2f + f + f + 2d10. x + y + x + y + 2x + 2z

11. 25x + 2y - 19x - y12. A + 15B - A + 5B13. 3x + 45z - 4x + 13y14. d - 2d + 3e + d15. 2f - 3f + 9g +2f - 2f + f 16. -12x -15y -16x +16y17. 34x + 13xy + 12y18. 99x - 12xy + x - 12xy2

19. 2(x + 3y) - 2x20. 3x(2 + x) - x2

+ 3b

+ 3b

Forming Expressions Level Up!

Level One

Write the following in algebra:

a) n plus 5 b) n subtract 4

c) p plus ten d) p subtract 5

e) y add t f) 5 takeaway m

g) n takeaway m h) r add t add 3

Write the following in algebra:

a) 3 times t b) 5 times p

c) r times 5 d) m times 6

e) 3 lots of t f) 4 lots of p

g) t lots of c h) m times 3 times p

Write the following in algebra:

a) t divided by 7 b) m divided by 5

c) Y divided by 9 d) 3 divided by c

e) 4 divided by t f) R divided by t

g) T divided by r h) M divided by e

Write the following in algebra:

a) T squared b) M cubed

c) c squared d) y squared, add one

e) m squared, takeaway three f) T squared, add p squared

g) M squared takeaway c squared h) P squared divided by 2

Forming Expressions Level Up!

Level Two

1. Write the following in algebra:

a) P plus one, all divided by 2 b) c takeaway 2, all divided by 3

c) C divided by 2, add four d) m divided by 3, subtract 5

e) t times 2, add five f) m times 3, subtract t

g) P squared, add t divided by 5 h) P squared add t, all divided by 5

2. Explain the difference between:a) t subtract 3 and 3 subtract tb) Four divided by t and t divided by 4c) Three plus m, all divided by 2 and three plus m divided by 2

Level Three

Write the following in algebra:

a) Three plus m times 2 b) Three plus m, all multiplied by 2

c) T plus three, all times by 4 d) M takeaway t times 3

e) Five subtract m times 2 f) Four subtract t, all times by 2

g) M add t times 4 h) T plus g, all times by 2

i) A plus two, all times by r j) T subtract p times t

Forming Expressions Level Up!

Level Four

Make the following table:

Add Subtract Multiply Divide

Place each word under the correct column:

Plus, more than, less than, share, times more, each, per, difference,left over, extra, on top, reduce, increase, older, younger, split, into, group, double half, triple

Level Five1. Tara is m years old, write expressions for her family’s age:a) Her brother is 3 years youngerb) Her sister is 5 years olderc) Her cousin is t years olderd) Her mother is 3 times her agee) Her father is 5 years older than her motherf) Her grandma is 10 times Tara’s age, plus two years

2. Harry got y marks on his most recent test. Write expressions for what his friends achieved:a) Mark got 3 marks more than Harryb) Jenny got 17 marks less than Harryc) Poppy got double the marks Harry gotd) Kane got half the marks Harry gote) Katie got 3 marks more than Poppyf) Ahmed got 4 marks less than Kane

3. Mark goes to a theme park with the school. He goes on 30 rides. Write expressions for how many rides his friends go on:a) Kerri goes on t fewer rides than Markb) Ben goes on p times more rides than Markc) Jenny goes on p fewer rides than Kerrid) Polly goes on 3 rides fewer than Bene) Mustafa goes on t rides more than Ben

LiteracyExplain the links between substitutionand football. Use examples toenhance your explanation.

perimeter of this regular shape?

ℎ RoK3 × 𝑎𝑏 + 𝑏 + 𝑏 + 𝑏𝑎 ÷ 𝑏𝑎 × 𝑎What is the formula for the

1)2)3)4)5)

Simplify the following expressionsMemoryTo substitute, replace the variablewith it’s corresponding value.E.g. Let 𝑎 = 5 4𝑎 = 4 × 𝑎= 4 × 5 = 20

1)𝟏𝟎 − 𝟐𝒙−𝟑𝒙Stretch𝟑𝒙 + 𝟏𝟎𝒙−𝟏 𝒙𝟐𝒙𝟎

If 𝑥 = 5 place the expressions inascending order.Is there a way of reversing the order?Could you make every expressions value the same?

2) Find the values of a and bwhen p = 10.3𝑝3𝑎 =2

2𝑏 = 2𝑝(p−3)7𝑝

Let 𝑥 = 4𝑎𝑛𝑑 𝑦 = −31) 3𝑥 + 62) 3𝑥 − 153) 2𝑦 − 24) 4𝑥 + 95) 3 − 𝑥6) 3 − 𝑦7) 5 − 2𝑥8) 7 + 𝑦

Let x = 2𝑎𝑛𝑑 𝑧 = 51) 𝑥2 + 52) 𝑥2 − 33) 2𝑥2 + 34) 6𝑥2 − 75) 𝑥3 − 76) 𝑧2 + 37) 3𝑧2 − 80

Let s = −2𝑎𝑛𝑑 𝑡 = −41) 𝑠2 + 42) 𝑠2 − 73) 2𝑠2 + 54) 6𝑠2 − 25) 𝑡2 + 76) 𝑡2 − 207) 𝑡3 + 1www.missbsresources.com

Expand and Simplify Single Brackets

Literacy The keyboard had sticking keys and missed out all the vowels. Discover the words and write one

sentenceincluding as many of the words as you can. Which word totals 15?

Use either the claw or the box method to expand expressions. Remember to multiply both terms by the co-efficient.

xpnd mltply smplfy vrbl xprssnClaw

Box

Expand 3(𝑥 + 5)×3 𝑥 + 5 = 3𝑥 + 15

3𝑥 + 15 Skill 1 Expand Skill 2 Expand and Simplify

1) 3 𝑥 + 4=2) 2 𝑥 + 4=3) 3(𝑥 − 4)

=4) 3 𝑥 − 7=

1) 3𝑥 + 2 𝑥 + 5 =2) 6 + 4 𝑥 + 3=3) 4𝑥 + 2(𝑥 − 5)

=4) 5𝑥 − 2 𝑥 + 8 =

Stretch 1Write an expression for the area of these shapes.

5) −5 𝑥 + 8 =6) 2 3𝑥 + 4 =7) 2 3𝑥 − 4 =8) −4 5𝑥 + 3=9) 6 2𝑥 + 𝑦

=10) 5 3𝑥 + 3𝑦 = 5) 5𝑥 − 2 𝑥 − 86) 3 𝑥 + 73𝑥 + 4

7) 4 2𝑥 + 5+ 3 3

𝑥 − 48) 4 3𝑥 + 26(4𝑥 + 3) =9) 6 𝑥 +

BA

𝑥 +53 3𝑥 +15

7 − 3(𝑥 + 4) =10) 3 8𝑥 − 4+ 4(2𝑥 + 5) =2𝑥 + 9

0.25𝑥 + 1.5

3 𝑐𝑚12𝑥 7𝑥 3𝑥 + 1

2D4𝑥 + 3

8 𝑐𝑚

11) 7 2𝑥 − 7𝑦=12) 𝑥 2𝑥 + 4=13) 2𝑥 3𝑥 + 5=14) 3𝑥 5𝑥 − 6=15) 4𝑦 2𝑥 − 3𝑦 =

11) 6 5𝑥 + 7− 2(𝑥 − 4) =12) 5 𝑥 + 7 − 2(𝑥 − 9) =13) 6 𝑦 − 8 − 3(𝑥 + 5) =14) 8 3𝑥 + 7− 3(2𝑥 + 8) =15) 9 8𝑥 − 5− 7(8𝑥 − 9) =www.missbsresources.com

Stretch 2 Expand and Simplify1) (𝑥 + 3) 𝑥 + 5=2) 𝑥 + 3 (𝑥 − 5) =3) (𝑥 − 3)(𝑥 − 5) =4) 2𝑥 + 4 𝑥 − 7 =

C

Mem

ory