S4 (4.2) N5 Equations.notebook November 24, 2015

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1 Daily Practice Q1. Write in completed square form x 2-14x + 8 Q2. Factorise fully 2x 2 + 6x - 20 Q3. Calculate a - 2b where a = and b = Today we will be revising over equations. A Q4. Calculate the length of AC 22cm B 28cm C Daily Practice Q1. Calculate the volume of the cylinder shown. Round your answer to 2 significant figures 12cm Q2. Write in scientific notation Q3. Find the value of a house that was bought for and appreciated in value by 5% per year for 4 years. 3cm Today we will be learning how to solve equations with fractions. Homework Online due Q4. Equations Revision Q1. Solve the following equations (a) 3x + 7 = 32-2x (d) 5(2h + 3) = 4(2h + 1) + 15 (b) 5(2k - 4) + 1 = 3(2k - 1) (e) 3(j - 1) = 18-5(j + 1) (c) 4(m - 2) - 9 = 3 - (m + 5) (f) 3(5t + 7) + 2(3t - 5) = 5(2t + 11) (g) x = x(x + 4) (h) x 2 - x(x + 5) + 20 = 5 (i) (j) (k) -2(4x + 1) - 3(x - 3) = x + 35 Equations with Fractions Given an equation with a fraction in it, always try to get rid of the fraction first by multiplying both sides by the denominator of the fraction. If there is more than one fraction (with different denominators). Find the Common Denominator. Create a single fraction. Multiply both sides by the new denominator. Solve from there.

2 Equations with Fractions Examples: Solve the following Q1. Solve the equation Daily Practice Q2.State the equation of the line joining ( 2, 3) and (1, 4) Q3. Write the answer to 6.5 x 5 x 10 8 in scientific notation Q4. Calculate the size of the internal angle of a pentagon Q5. If two bottles are similar in size, the volume of the smaller bottle is 330ml and the diameter of the base is 5cm, calculate the volume of the larger bottle if the diameter of the base is 6.5cm Equations with Fractions Questions: Solve the following (a) (e) (i) Equations4.pdf (b) (f) (j) Today we will be learning how to solve equations with fractions. (c) (g) (k) Homework Online due (d) (h) (l)

3 Inequalities From left to right: Today will be learning how to solve inequalities. Homework due < means less than > means greater than means less than or equal to means greater than or equal to Daily Practice Q1. Round 6177 to 1 significant figure Q2. A group of witches are ages 25, 37, 48, 43, 64, 77 and 82. Calculate their mean age Q3. Solve ½(7x - 1) = x + 17 Q4. Ghostbusters blasted the ghost population (12000) by 30% every minute for 3 minutes. How many ghosts were there after 3 mins? Today will be learning how to solve inequalities. Homework due Website Q5. A witch's hat is made from a special material. The material is made into a hat by using a template in the sector of a circle. Calculate the area of material a witch needs to make her hat 15cm 71 0 Inequalities Write expressions for the following: x is less than 6 Solving Inequalities Solving inequalities follows the same process as solving equations. Examples: Solve the following (a) 5x - 4 > 26 (b) 9-3a < 12 (c) 2(c + 5) 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 (d) 2(4b - 7) 3b - 14 (e) N5 Books Page 117

4 Daily Practice Q1.Calculatethevolumeofaconewithradius7cmandheight18cm Q2.Round to2significantfigures Q3.Karenput 800inthebankat4.2%interestcompoundedannually for2years.howmuchwasinheraccountattheendof2years? Q4.m 5 (2m 2 +3m) Q5.Solve3(x-2)<5x-4 Today we will be working out algebraic problems in context. Homework due!

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6 Q1. Multiply out and simplify 7x 2 - (3x + 4)(x - 1) Daily Practice A b F B C Q2. Express in terms of a and b E a D Today we will be creating and solving equations from questions in context. Q3. Rearrange the formula such that t is the subject Problem Solving with Equations Examples: Problem Solving using Algebra Example: Write down an expression for the perimeter and the area of the triangle shown 1. 4x cm y cm (x + 2)cm Daily Practice Q1. Express x 2-6x + 7 in the form (x - a) 2 + b Q2. Calculate the volume of a sphere with diameter 15cm Q3. Today we will be continuing with problem solving equations questions. Q4.

7 Examples: 2) Problem Solving with Equations Examples: 3. Daily Practice Q1. Solve the equation 6(2x 3) = 11x 4 Q2. Calculate the median and interquartile range of 2, 3, 5, 6, 8 Q3. Work out the value of a house that was worth and appreciated by 6.2% per annum for 3 years Today we will be continuing to practise worded problems with equations. Q4. Express the equation shown in terms of x The rectangle shown has an area of 16cm 2. 2 cm a) Write down an equation in terms of x b) Calculate the dimensions of the rectangle

8 Daily Practice Questions Mental Maths Today we will be completing a check-up on equations.

9 Attachments Equations4.pdf