KUS objectives BAT expand brackets BAT build and

KUS objectives BAT expand brackets BAT build and solve linear equations BAT solve simultaneous equations Starter: work these out 4 x × 5 x 3 x × 5 x 2 7 x 4 × 3 x 6 2 xy × 2 x 8 xyz × 4 xy 4 z 2 (-3 x 4) × (-5 x 3 y 6 z)

Chapter 1: Expanding BRACKETS To remove a single bracket, we multiply every term in the bracket by the number or the expression on the outside: There are two multiply sums First 3 times x Then 3 times 2 y There are two multiply sums First -2 times 2 x Then -2 times -3

Chapter 1: Expanding BRACKETS To expand two brackets, we must multiply everything in the first bracket by everything in the second bracket. We can do this in a variety of ways, including * FOIL (Fronts Outers Inners Last) * using a grid. There are four multiply sums Fronts x times x Outers x times 2 Inners 1 times x Last 1 times 2 Then collect together There are four multiply sums Fronts x times 2 x Outers x times 3 Inners -2 times 2 x Last -2 times 3 Then collect together

Chapter 1: Expanding BRACKETS Brackets squared and a difference of squares (DOTs): For example: There are four multiply sums The x terms cancel out in DOTs There are four multiply sums Then collect together

Chapter 1: Expanding BRACKETS Harder Expansions Use the same methods but with more multiplications and more terms in the answer There are six multiply sums Lets try doing this in a table Now collect similar terms First expand any two brackets Now collect similar terms

Chapter 2: LINEAR EQUATIONS Solve these equations

Chapter 2: Equations containing fractions Solve these equations Check that all terms on both sides have been multiplied by two

Chapter 2: Equations containing fractions Solve these equations This next step can be done in other ways e. g. brackets OR in your head (extension)

Chapter 2: Forming equations 8. Find three consecutive numbers so that their sum is 96 Think what’s true about consecutive numbers – how can they be written as expressions? Form an equation So the numbers are 31, 32 and 33

Chapter 3: Simultaneous equations elimination method Step 1 = make the same coefficient of one letter Multiply each equations by a number Step 2 = compare the two new equations Use STOP (same sign take, opposite sign plus) compare Step 3 = solve to find the value of one variable check Step 4 = use the original equations to find the other variable and check both work

SOLUTIONS TO THE EXERCISES

KUS objectives BAT expand brackets BAT build and solve linear equations BAT solve simultaneous equations One thing I will do For the next lesson …. One thing I need to remember for next lesson …. One thing I understood well is ….

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