S2 (2.2) Equations.notebook€¦ · 1. Janet is three times as old as her daughter Mary. Five years ago, Janet was four times as old as Mary. How old is Janet now? Daily Practice

S2 (2.2) Equations.notebook November 24, 2015

Daily Practice 7.10.2015Q1. Multiply out and simplify 7(x - 3) + 2(x + 1)

Q2. Simplify the ratio 14:21

Q3. Find 17% of 5000

Q4. Given a = -3 and b = 4, what is the value of 2a + 4b?

Q5.

Today we will be learning to solve equations.

Homework Due tomorrow.

Equations

An equation is an algebraic expression with an equals sign in it.

To solve an equation, we must treat each side of the equals like a balance. What you do to one side, you must do to the other.

Always think opposite operations!!

Equations

Examples: Solve the following

(a) x + 15 = 34 (b) 4g = 24 (c) 7 - x = -4

Equations

Solve the following:

(i) x + 4 = 11

(ii) x - 5 = 16

(iii) 2x = 8

(iv) 3x = -48

(v) 7 - x = -2

(vi) 14 + x = 37

(vii) 2x = -14

(viii) 0.5x = 6

(ix) x - 5 = 98

(x) 2x + x = 18

(xi) 3x - 2x + 4 = 22

(xii) -2= x + 7

(xiii) 36 = 6x

(xiv) x2 = 49

Daily Practice 8.10.2015Q1. State the mean, median, mode and range of the following

2, -2, 3, 4, 6, 7, 2 , 10,

Q2. Multiply out and simplify 7(x - 4) + 2(3x + 3)

Q3. State the size of the angle a0

Q4. Given a = -3 and b = 4, what is the value of 4a2b?

330

a0


Today we will be continuing to learn how to solve equations.

Homework Due Today.

Equations

(e) 3h - 9 = 3 (f) - 2x + 4 = -10(d) 2x + 3 = 13

Examples:

Equations


(i) 2x + 4 = 20

(ii) 7x - 5 = 30

(iii) 12x + 4 = 100

(iv) 3x - 8 = -5

(v) 7 - 2x = 13

(vi) 14 + 5x = 64

(vii) 2x - 1 = -11

(viii) 3k - 7 = 20

(ix) 4x - 5 = -9

(x) 2m + 3 = 19

(xi) - 6j - 4 = 32

(xii) 2h = 1 + 9

(xiii) 8p = 16 + 16

Daily Practice 21.10.15

Q1. Round 18.5411 to 1 decimal place

Q2. Multiply out and simplify 6x - 2(x + 3)

Q3. Work out the cost of getting a car service if it is £120 + VAT at 20%

Q4. Simplify the ratio 30:15

Q5. Solve the equation 2x - 9 = 15

Today we will be learning how to solve equations with unknowns on both sides.


Equations with unknowns both sides

Unknowns can be added/subtracted from both sides too.

Examples:

1. 3x + 2 = x + 10 2. 6p - 3 = 3p + 12 3. 5 - 4h = h -15


Q1. Find the value of a car that was worth £4000 and depreciated in value by 6%

Q2. Solve the equation 5x - 3 = 2x + 12

Q3. Multiply out and simplify 6(2x - 1) + 4

Q4.

Today we will be continuing to learn how to solve equations.

Equations with unknowns both sides


(i) 2k + 7 = k - 4 (viii) 17t - 1 = 12t + 14

(ii) 13k - 8 = 2k + 14 (ix) 18y - 4 = -6y + 44

(iii) 10x + 12 = 4x + 48 (x) 6c - 15 = 12 - 3c

(iv) -3x + 2 = x + 10

(v) 5x - 5 = 3x + 15

(vi) 9x - 8 = x + 24

(vii) 12g + 7 = 2g - 33


Q1. Find the value of a house that was worth £95 000 and appreciated in value by 7%?

Q2. Solve the equation 9k - 1 = 2k + 13

Q3. Round 81.445 to the nearest unit

Q4. Q5. Multiply out and simplify 6h - 3(2h + 1)


Today we will be learning to solve equations with brackets.

Homework online due Friday 30.10.15

Equations with brackets

To solve equations with brackets, first multiply out and simplify where possible, then solve as normal.


(a) 3(2x + 1) = 21 (ii) 7h + 2(h - 5) = 26 (iii) 2(h + 4) - (h + 6) = 7


10 Questions Mental MathsToday we will be continuing to learn how to multiply out brackets and simplify.

Homework due Friday


Daily Practice 28.10.2015Q1. Find 17% of 9000

Q2. Multiply out and simplify 2(3x - 1) + 4(x - 6)

Q3. Solve the equation 9x - 13 = -40

Q4. Calculate the area of the rhombus shown

Q5.

18cm 15cm

Today we will be learning about equations with fractions.

Homework due Friday.

Equations with fractions

Examples: Solve

(a) (b)

Equations with fractions

Questions:

(a)

(b)

(c)

(d)

(e)

(f)

(g)

(h)

(i)

(j)

(k)

(l)


Q1. Multiply out and simplify 7(x - 3) + 2(x + 1)

Q2. John has savings of £5000, he earns simple interest of 4% per annum. How much interest does he earn in 2 years?

Q3. Factorise 5gh - 25h2

Q4. Solve 5x - 1 = 2x + 8 Q5.


Today we will be learning about inequalities.

Homework due tomorrow!

Inequalities

From left to right:

<

>

≤

≥

means less than

means greater than

means less than or equal to

means greater than or equal to

Inequalities

Write expressions for the following:

x is less than 6

y is greater than -15

k is greater than or equal to 0

h is greater than or equal to -4 and is less than 7

p is greater than -1 and is less than or equal to 4

j lies between -3 and 5 but isn't -3 or 5

Solving Inequalities


(a) 5x > 25 (b) a - 1 < 12 (c) 3x + 15 ≥ 27

Solving inequalities follows the same process as solving equations.



(a) 2x > 6 (b) 5t < 20 (c) x + 4 > 10

(d) 2g + 3 ≤ 15 (e) 10k > 120 (f) 4x - 5 ≤ 15

(g) 2(x + 3) < 14 (h) 7j - 6 ≥ 42 (i) 2x + 7 ≤ 16

(j) 4(3x + 11) ≥ 10x + 50 (k) 8(2y - 1) ≤ 14y

Daily Practice 30.10.2015Q1. Round 61.77 to 1 decimal place

Q2. A group of witches are ages 25, 37, 48, 43, 64, 77 and 82. Calculate their mean age

Q3. 22 x 3 + 24

Q4. Ghostbusters blasted the ghost population (12000) by 30%. How many ghosts are left?

Q5. Solve the equation 13W - 4 = 9W + 12


Today we will be marking the homework on equations and finishing the inequalities questions.



Q1. Multiply out and simplify 6c - 3(2c + 1)

Q2. A dress costs £65, it is marked 15% off in the sale. How much is it in the sale?

Q3. Solve the equation 7x - 4 = 2x + 21

Q4. 36 - 7 x 5

Q5.

Today we will be learning how to create equations from context and solving them.



(a) 2x > 6 (b) 5t < 20 (c) x + 4 > 10

(d) 2g + 3 ≤ 15 (e) 10k > 120 (f) 4x - 5 ≤ 15

(g) 2(x + 3) < 14 (h) 7j - 6 ≥ 42 (i) 2x + 7 ≤ 16

(j) 4(3x + 11) ≥ 10x + 50 (k) 8(2y - 1) ≤ 14y


Using Equations to solve Worded Problems

1. Janet is three times as old as her daughter Mary. Five years ago, Janet was four times as old as Mary. How old is Janet now?


Q1. Round 18.112 to 1 decimal place

Q2. Solve the inequality 5t ‐ 14 ≤ 4t + 13

Q3. Find 91% of 2000

Q4.

Q5. 42 x 4000

Today we will be continuing to practise worded equations.

2. Together Joe and Harry have £30. Joe has £6 more than Harry. How much does each person have?


20 Questions Mental Maths


Today we will be completing a check-up on Equations.

Documents

S2 (2.2) Equations.notebook€¦ · 1. Janet is three times as old as her daughter Mary. Five years ago, Janet was four times as old as Mary. How old is Janet now? Daily Practice