Algebra Revision Pack

Algebra

Simplify Substitute Solve Rearrange QUESTION A1 QUESTION B1 QUESTION C1 QUESTION D1

Simplify 3a x 2b

Solve a2 + 2b if a = 4 & b = 3

Find x if 4x = 10

Make q the subject of v = 2k - q

QUESTION A2 QUESTION B2 QUESTION C2 QUESTION D2 Simplify 4a2 x ab

Solve 6a - 2b if a = 4 & b = 0?

Solve 5(x + 6) = 40

Make w the subject of p = tw

QUESTION A3 QUESTION B3 QUESTION C3 QUESTION D3 Simplify

10q – 3q + 2q Evaluate (c + 2d)²

if c = 4 & d = 3?

Solve 9(x-2) = 9

Make h the subject of m = 5 + h2

QUESTION A4 QUESTION B4 QUESTION C4 QUESTION D4 Simplify

9x + 6 - 5x - 1 Evaluate (3c)² - d

if c = 2 & d = 7?

Find p if 11p - 14 = 8

Make z the subject of t = 2(z – 3)

QUESTION A5 QUESTION B5 QUESTION C5 QUESTION D5 Simplify

8p 4p

What is the value of 4(a – b) if

a = 7 & b = 2?

Find x if 30 ÷ x = 5

Make h the subject of m = ½ (h + 4)

QUESTION A6 QUESTION B6 QUESTION C6 QUESTION D6 Simplify

17r – 9r + 3r Solve

2ae + 6cb if a= 4, b= 3, c= 2, e=1

Find x if 14x - 3 = 25

Make b the subject if a = y + 2b

Algebra

Simplify Substitute Solve Rearrange QUESTION A7 QUESTION B7 QUESTION C7 QUESTION D7

Simplify 3x + 2y - 5x + y

Solve 3𝑎3𝑏

where a = 2 & b = -5

Find x if 3𝑥 = 5

Make y the subject if h = 3y + 2b

QUESTION A8 QUESTION B8 QUESTION C8 QUESTION D8 Simplify

3a x 2b x 5

Solve 𝑎!𝑏! Where a = 3 & b = 6

Find x if 𝑥9 = 50

Make b the subject if m = b - h2

QUESTION A9 QUESTION B9 QUESTION C9 QUESTION D9 Express in its simplest

form 4ab x 2b²

Solve 3𝑎!(2𝑝) Where a = 3 & p = - 2

Find x if 4𝑥5 = 8

Make a the subject if a2 + b2 = c2

QUESTION A10 QUESTION B10 QUESTION C10 QUESTION D10 Simplify

4x - 3 + x + 10 Solve !

!

!

Where a = 9

Find x if 2𝑥! − 13 = 5

Make g the subject if 𝑘 =

3𝑔

QUESTION A11 QUESTION B11 QUESTION C11 QUESTION D11 Simplify -3r – 7r

Solve (3𝑏 + 1) Where b = 8

Find x if 2(𝑥 − 2) = 5

Make y the subject if 𝑚 =

𝑦𝑔

QUESTION A12 QUESTION B12 QUESTION C12 QUESTION D12 Simplify

6a 3

Solve 𝑎𝑏!𝑐 If a = 2, b = 3 & c = 7

Find x if 4𝑥 = 𝑥

Make m the subject if 𝑘 =

𝑚3 − 3

Algebra

Simplify Substitute Solve Rearrange QUESTION A13 QUESTION B13 QUESTION C13 QUESTION D13

Express in its simplest form

3a x b x 2c²

What is the value of 6a - b if

a = 4 & b = 7?

Solve 10 - x > 3

Make b the subject if a = 5b

QUESTION A14 QUESTION B14 QUESTION C14 QUESTION D14 Simplify

8x +6y - 5x +y Evaluate 8d + 5c²

if c = 4 & d = 3?

Solve 3x - 7 < 17

Make b the subject of a = 2b - 1

QUESTION A15 QUESTION B15 QUESTION C15 QUESTION D15 Simplify 18a ÷ 2

What is the value of 3a + 2b if

a = 5 & b = 4?

Solve 5x + 7 < 52

Make b the subject if a = 3 + 2b

QUESTION A16 QUESTION B16 QUESTION C16 QUESTION D16 Express in its simplest

form 3c x 2c²

Evaluate 2c² - 4d

if c = 3 & d = 2?

Find x if 4x > 20

Make b the subject if a = 4(b – 7)

QUESTION A17 QUESTION B17 QUESTION C17 QUESTION D17 Simplify 9a - 4a

What is the value of 3a - 8b

if a =10 & b = 3?

Solve 2(x + 4) ≤  18

Make b the subject of a = 2(7 + b)

QUESTION A18 QUESTION B18 QUESTION C18 QUESTION D18 Simplify

4x +3y +5x +8y Evaluate

3c3 if c = 10?

Solve 20 - 4x ≥ 0

Make t the subject of p = 2t - 4

3x

2x

5x

2x x+1

x+1

2x

½ x

2x + 1

Algebra

Sequences Factorising Expanding Expressions QUESTION E1 QUESTION F1 QUESTION G1 QUESTION H1

Write down the next number in this

sequence 10, 7, 4 , 1, ?

Factorise 15a + 25

Expand 7(4x - 3)

Write the perimeter

QUESTION E2 QUESTION F2 QUESTION G2 QUESTION H2 Write down the next

number in this sequence

6, 13, 20, 27, ?

Factorise 7x + 21x 2

Expand and simplify 10a + 3a(a - 2)

Write the perimeter

QUESTION E3 QUESTION F3 QUESTION G3 QUESTION H3 Write down the next

number in this sequence

1.3, 1.8 , 2.3, ?

Factorise 4a + 6b

Expand 3(2x + 5)

Write the perimeter

QUESTION E4 QUESTION F4 QUESTION G4 QUESTION H4 Write down the next

number in this sequence

3, 4.5, 6, 7.5, ?

Factorise 9x 2– 12x

Expand and simplify 4a(a + 2) + 3a

Write the perimeter

QUESTION E5 QUESTION F5 QUESTION G5 QUESTION H5 Write down the next

number in this sequence

1, 4, 9, 16, ?

Factorise 15a – 20b

Expand 3(5 + 4x)

Write the perimeter

QUESTION E6 QUESTION F6 QUESTION G6 QUESTION H6 Write down the next

number in this sequence 1,12 ,14 ,18 ,… ?

Factorise 21x + 3x 2

Expand and simplify 7a - 2(a + 2)

Write the perimeter

2x2

½ x + 2h

x+3

2x

3x

x

3x

x

Algebra

Sequences Factorising Expanding Expressions QUESTION E7 QUESTION F7 QUESTION G7 QUESTION H7

Find the nth term of this sequence: 2, 5, 8, 11,

Factorise 6p + 2pq

Expand 2(7x - 3)

Write the perimeter

QUESTION E8 QUESTION F8 QUESTION G8 QUESTION H8 Find the nth term of

this sequence: 10, 5, 0,−5,

Factorise fully 14x - 35x 2

Expand and simplify 9a - a(a + 4)

Write the perimeter

QUESTION E9 QUESTION F9 QUESTION G9 QUESTION H9 Find the nth term of

this sequence: 20, 40, 60, 80

Factorise 14 – 7x

Expand -2(4x + 5)

Write the perimeter

QUESTION E10 QUESTION F10 QUESTION G10 QUESTION H10 Find the nth term of

this sequence: 13, 15, 17, 19

Factorise fully 12x – 15x2

Expand and simplify 3a(2a + 1) - 7a

Write the area

QUESTION E11 QUESTION F11 QUESTION G11 QUESTION H11 Find the nth term of

this sequence: 10, 7, 4, 1

Factorise: 3𝑥 + 9

Expand and simplify (𝑥 + 2)(𝑥 + 3)

Write the area

QUESTION E12 QUESTION F12 QUESTION G12 QUESTION H12 Find the nth term of

this sequence: 11, 111, 211, 311

Factorise: 18𝑎 + 24𝑏

Expand and simplify (𝑥 + 2)(𝑥 − 3)

Write the area

2x

2x+1

2x

4x

2x

4x2

2x

6x

4x2

Algebra

Sequences Factorising Expanding Expressions QUESTION E13 QUESTION F13 QUESTION G13 QUESTION H13

Find the 100th term of this sequence: 17, 20, 23, 26

Factorise: 4𝑥 + 10𝑥!

Expand and simplify (𝑥 + 4)(𝑥 + 3)

Write the area

QUESTION E14 QUESTION F14 QUESTION G14 QUESTION H14 Find the 100th term of

this sequence: 41, 39, 37, 35

Factorise: 2𝑣! + 6𝑣𝑤

Expand and simplify (𝑥 − 2)(𝑥 − 3)

Write the area

QUESTION E15 QUESTION F15 QUESTION G15 QUESTION H15 Find the 100th term of

this sequence: 55, 60, 65, 70

Factorise: 9𝑝! − 9𝑝𝑞

Expand and simplify (𝑥 + 2)(2𝑥 + 3)

Write the area

QUESTION E16 QUESTION F16 QUESTION G16 QUESTION H16 Find the 100th term of

this sequence: 19, 15, 11, 7

Factorise: 21𝑣! + 49𝑣𝑤

Expand and simplify (𝑥 + 1)(𝑥 − 1)

Write the area

QUESTION E17 QUESTION F17 QUESTION G17 QUESTION H17 Find the 100th term of

this sequence: -5, -10, -15, -20

Factorise: 77𝑏! + 14𝑏𝑐

Expand and simplify (𝑥 + 8)(𝑥 + 3)

Write the area

QUESTION E18 QUESTION F18 QUESTION G18 QUESTION H18 Find the 100th term of

this sequence: -16, -26, -36, -46

Factorise: 40𝑔! + 70𝑔ℎ

Expand and simplify 𝑥 + 5 !

Write the area

Answers

Section A J L A1 6𝑎𝑏 A2 4𝑎!𝑏 A3 9𝑞 A4 4𝑥 + 5 A5 2 A6 11𝑟 A7 −2𝑥 + 3𝑦 A8 30𝑎𝑏 A9 8𝑎𝑏! A10 5𝑥 + 7 A11 −10𝑟 A12 2𝑎 A13 6𝑎𝑏𝑐! A14 3𝑥 + 7𝑦 A15 9𝑎 A16 6𝑐! A17 5𝑎 A18 9𝑥 + 11𝑦 Section E J L E1 −2 E2 34 E3 2.8 E4 9 E5 25 E6 1/16 E7 3𝑛 − 1 E8 −5𝑛 + 15 E9 20𝑛 E10 2𝑛 + 11 E11 −3𝑛 + 13 E12 100𝑛 − 89 E13 314 E14 −157 E15 550 E16 −377 E17 −500 E18 −1006

Section B J L B1 22 B2 24 B3 100 B4 29 B5 20 B6 44 B7 −0.4 B8 1944 B9 −108 B10 20.25 B11 5 B12 126 B13 17 B14 104 B15 23 B16 10 B17 6 B18 3000 Section F J L F1 5(3𝑎 + 5) F2 7𝑥(1+ 3𝑥) F3 2(2𝑎 + 3𝑏) F4 3𝑥(3𝑥 − 4) F5 5(3𝑎 − 4𝑏) F6 3𝑥(7+ 𝑥) F7 2𝑝(3+ 𝑞) F8 7𝑥(2− 5𝑥) F9 7(2− 𝑥) F10 3𝑥(4− 5𝑥) F11 3(𝑥 + 3) F12 6(3𝑎 + 4𝑏) F13 2𝑥(2+ 5𝑥) F14 2𝑣(𝑣 + 3𝑤) F15 9𝑝(𝑝 − 𝑞) F16 7𝑣(3𝑣 + 7𝑤) F17 7𝑏(11𝑏 + 2𝑐) F18 10𝑔(4𝑔 + 7ℎ)

Section C J L C1 𝑥 = 2.5 C2 𝑥 = 2 C3 𝑥 = 3 C4 𝑥 = 2 C5 𝑥 = 6 C6 𝑥 = 2 C7 𝑥 = 0.6 C8 𝑥 = 450 C9 𝑥 = 10 C10 𝑥 = 3 C11 𝑥 = 4.5 C12 𝑥 = 2 C13 𝑥 < 7 C14 𝑥 < 8 C15 𝑥 < 9 C16 𝑥 > 5 C17 𝑥 ≤ 5 C18 𝑥 ≤ 5 Section G J L G1 28𝑥 − 21 G2 3𝑎! + 4𝑎 G3 6𝑥 + 15 G4 4𝑎! + 7𝑎 G5 12𝑥 + 15 G6 5𝑎 − 4 G7 14𝑥 − 6 G8 −𝑎! + 5𝑎 G9 −8𝑥 − 10 G10 6𝑎! − 4𝑎 G11 𝑥! + 5𝑥 + 6 G12 𝑥! − 𝑥 − 6 G13 𝑥! + 7𝑥 + 12 G14 𝑥! − 5𝑥 + 6 G15 2𝑥! + 7𝑥 + 6 G16 𝑥! − 1 G17 𝑥! + 11𝑥 + 24 G18 𝑥! + 10𝑥 + 25

Section D J L D1 𝑞 = 2𝑘 − 𝑣 D2 𝑤 = 𝑝/𝑡 D3 ℎ = 𝑚 − 5 D4 𝑧 = !!!

!

D5 ℎ = 2𝑚 − 4 D6 𝑏 = !!!

!

D7 𝑦 = !!!!!

D8 𝑏 = 𝑚 + ℎ! D9 𝑎 = 𝑐! − 𝑏! D10 𝑔 = 3/𝑘 D11 𝑔 = 𝑦/𝑚 D12 𝑚 = 3𝑘 + 9 D13 𝑏 = 𝑎/5 D14 𝑏 = !!!

!

D15 𝑏 = !!!!

D16 𝑏 = !!!"

!

D17 𝑏 = !!!"!

D18 𝑡 = !!!

!

Section H J L H1 12𝑥 H2 14𝑥 H3 4𝑥 + 2 H4 16𝑥 H5 3.5𝑥 H6 12𝑥 + 6 H7 10𝑥! H8 2𝑥 + 8ℎ H9 4𝑥 + 12 H10 6𝑥! H11 3𝑥! H12 𝑥! H13 2𝑥! + 𝑥 H14 4𝑥! H15 4𝑥! H16 4𝜋𝑥! H17 9𝜋𝑥! H18 4𝜋𝑥!