Algebraic Notation and Vocabulary

Look at the number attached to the x term.

Which term does not depend on p?

Keep the sign immediately before the term.

Separate the expression at the outer addition and subtraction signs.

The signs are multiplication signs, not addition signs. In algebra the multiplication signs are left out.

Count how many times each letter is multiplied.

1. There are three factors of b, so b\times b\times b=b^3.
2. There is one factor of c, giving b^3c.

A fraction bar represents division.

1. A fraction bar means divide. The number being divided goes on top.
2. k\div6=\frac{k}{6}. \frac{6}{k} would mean 6\div k.

Look at how the two parts are joined.

1. The expression is a sum of two terms, 7r and 2s.
2. A term is a part joined to other terms by addition or subtraction.

Equations and inequalities compare two sides. An expression does not.

1. 5u-8 has terms and operations but no =, < or > sign, so it is an expression.
2. The other options each have an equals sign or an inequality sign.

Decide whether 7 itself is allowed.

1. “At least 7” includes 7 and every value greater than 7.
2. The symbol \geq includes equality, so t\geq7.

An identity keeps the same value on both sides for every input.

1. Expanding the left side of the last option gives 2x+6, exactly its right side.
2. It is an identity: it is true for every x. The other equalities only hold for particular values.

What do the letters C and d stand for?

1. C=3d+4 shows how one quantity, the cost, can be worked out from another, the distance. That makes it a formula.
2. It has an equals sign, so it is not just an expression. The coefficient of d is 3, not 4, and the cost changes with the distance, so it is not always £7.

Is 4p multiplied by the bracket, or added to it?

1. 4p(p+3) means 4p\times(p+3): the whole expression is one product.
2. So 4p and (p+3) are its factors. Inside the bracket, p and 3 are unlike terms.

Which letter is already alone?

1. The subject is the letter isolated on one side of the equals sign.
2. V is on its own, so V is the subject.

Identify the multiplier and the term without a variable.

Part (a)

1. The first term is \frac34\times x.
2. Its coefficient is \frac34.

Part (b)

1. The term without x is -2.
2. The subtraction sign belongs to that term.

The brackets change the base of the power.

Part (a)

1. Only b is squared: ab^2=3\times2^2.
2. 2^2=4, so 3\times4=12.

Part (b)

1. The brackets make the whole product the base: (3\times2)^2=6^2.
2. 6^2=36. This is different from squaring only b.

Look for an equals sign first, then decide whether the statement is true for every value.

Part (a)

1. Expanding the left side gives 4x-4, exactly the right side.
2. It is true for every value of x, so it is an identity.

Part (b)

1. 4x-1 has no equals sign, so it is not an equation, formula or identity.
2. It is an expression.

An even number plus an odd number is odd.

1. 2n is always even. Adding 5, an odd number, makes 2n+5 odd.
2. The expressions n+1 and n^2 can be even or odd depending on n.

An identity must hold for every permitted input.

Part (a)

1. 2(3+4)=2\times7=14.
2. The whole bracket is multiplied by 2.

Part (b)

1. The right side is 2\times3+4=10, which differs from 14.
2. An identity must work for every value. One counterexample is enough to show this is not an identity.

Check whether each statement is true at one value of x or at every value.

Part (a)

1. Subtract 2 from both sides: 4x=16.
2. Divide by 4: x=4. Check: 4(4)+2=18.

Part (b)

1. A is an equation with the single solution x=4.
2. In B, expanding the left side gives the right side for every x, so B is an identity.