Worksheets · Foundation and Higher

Identities and algebraic reasoning

3 exam-style questions. Answers and the mark for each step are on the last page.

Question 1Non-calculator · 2 marks
Ellie says, " $x + x + x$ is the same as $x^3$ ."
(a) Is Ellie correct? Give a reason for your answer. (1)
1. Ellie is correct
2. Ellie is not correct
(b) Simplify $x + x + x$ (1)
Question 2Non-calculator · 4 marks
Decide whether each statement is an identity or an equation.
(a) $(x + 1)^2 - x^2 = 2x + 1$ (2)
(b) $4(x - 2) = 2(x + 3)$ (2)
Question 3Calculator · 4 marks
(a) The identity (2x + a)(x $-$ 3) + b $\equiv$ $2x^{2}$ + x + 7 is true for every x. Find a + b. (4)

Answers and marks

(a) No: $x + x + x = 3x$ , but $x^3 = x \times x \times x$ .

C1 "No", with a reason such as $x + x + x = 3x$ or a value that gives different answers.

(b) $3x$

(a) An identity: expanding gives x² + 2x + 1 - x² = 2x + 1 for every value of x.

M1 Expand the square and simplify the left side.
C1 Correct conclusion with supporting reasoning: An identity: expanding gives x² + 2x + 1 - x² = 2x + 1 for every value of x.

(b) An equation: it is true only when x = 7.

M1 Expand both sides and solve.
C1 Correct conclusion with supporting reasoning: An equation: it is true only when x = 7.

(a) $35$

Identities and algebraic reasoning

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