Expanding and factorising, solving linear and quadratic equations, rearranging formulae, inequalities and simultaneous equations.
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1.What does collecting like terms mean?
Adding or subtracting terms that have exactly the same letters and powers.
2.Simplify 5x + 3y - 2x + y.
3x + 4y
3.How do you expand a single bracket?
Multiply everything inside the bracket by the term outside it.
4.Expand 3(2x - 5).
6x - 15
5.How do you expand double brackets?
Multiply every term in the first bracket by every term in the second, then collect like terms.
6.Expand (x + 3)(x + 4).
x squared + 7x + 12
7.Expand (x + 5)(x - 2).
x squared + 3x - 10
8.What does factorising mean?
Writing an expression as a product, by taking out a common factor or into brackets.
9.Factorise 6x + 9.
3(2x + 3)
10.Factorise x squared + 7x + 10.
(x + 5)(x + 2), because 5 and 2 multiply to 10 and add to 7.
11.What two numbers do you look for when factorising a quadratic?
Two numbers that multiply to give the constant term and add to give the coefficient of x.
12.Factorise x squared - 9.
(x + 3)(x - 3). This is the difference of two squares.
13.What is the difference of two squares?
a squared minus b squared factorises to (a + b)(a - b).
14.How do you solve a linear equation?
Do the same operation to both sides until the letter is on its own.
15.Solve 3x + 7 = 22.
Subtract 7 to get 3x = 15, then divide by 3 to get x = 5.
16.Solve 5x - 3 = 2x + 9.
Subtract 2x to get 3x - 3 = 9, add 3 to get 3x = 12, so x = 4.
17.How do you rearrange a formula?
Use the same operations on both sides to make the required letter the subject.
18.Make x the subject of y = 3x + 4.
Subtract 4 then divide by 3: x = (y - 4) divided by 3.
19.How do you solve a quadratic by factorising?
Rearrange so it equals zero, factorise, then set each bracket equal to zero.
20.Solve x squared + 5x + 6 = 0.
Factorise to (x + 2)(x + 3) = 0, so x = -2 or x = -3.
21.State the quadratic formula.
x = minus b plus or minus the square root of (b squared minus 4ac), all divided by 2a.
22.When would you use the quadratic formula?
When the quadratic does not factorise, or when the question asks for a decimal answer.
23.How do inequalities differ from equations when solving?
They are solved the same way, except that multiplying or dividing by a negative number reverses the inequality sign.
24.Solve 2x + 1 > 9.
Subtract 1 to get 2x > 8, so x > 4.
25.How do you solve simultaneous equations by elimination?
Multiply one or both equations so one variable has matching coefficients, then add or subtract to eliminate it.
26.How do you solve simultaneous equations by substitution?
Rearrange one equation to make a variable the subject, then substitute that expression into the other equation.
27.After finding one variable in simultaneous equations, what next?
Substitute it back into either original equation to find the other variable.
28.How can you check a simultaneous equations answer?
Substitute both values into the equation you did not use to find the second variable.
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