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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
S2 (2.2) Equations.notebook November 24, 2015
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
Solve the following:
(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.
S2 (2.2) Equations.notebook November 24, 2015
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
Daily Practice 22.10.2015
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
Solve the following:
(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
Daily Practice 23.10.2015
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)
S2 (2.2) Equations.notebook November 24, 2015
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.
Examples: Solve the following
(a) 3(2x + 1) = 21 (ii) 7h + 2(h - 5) = 26 (iii) 2(h + 4) - (h + 6) = 7
Daily Practice 26.10.15
10 Questions Mental MathsToday we will be continuing to learn how to multiply out brackets and simplify.
Homework due Friday
S2 (2.2) Equations.notebook November 24, 2015
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)
Daily Practice 29.10.2015
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.
S2 (2.2) Equations.notebook November 24, 2015
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
Examples: Solve the following
(a) 5x > 25 (b) a - 1 < 12 (c) 3x + 15 ≥ 27
Solving inequalities follows the same process as solving equations.
Solving Inequalities
Solve the following:
(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
S2 (2.2) Equations.notebook November 24, 2015
Today we will be marking the homework on equations and finishing the inequalities questions.
S2 (2.2) Equations.notebook November 24, 2015
Daily Practice 2.11.2015
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.
Solving Inequalities
Solve the following:
(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
S2 (2.2) Equations.notebook November 24, 2015
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?
Daily Practice 4.11.15
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?
Daily Practice 5.11.2015
20 Questions Mental Maths
S2 (2.2) Equations.notebook November 24, 2015
Today we will be completing a check-up on Equations.