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Exam Practice
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Edexcel GCSE Maths (Non-calculator) Smart practice A mixed round aimed at your weak spots
Unit 1
Number
Structure and calculation
Ordering numbers and inequality symbols
0%
Calculating with integers, decimals and fractions
0%
Order of operations and inverse operations
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Primes, factors, multiples, HCF and LCM
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Systematic listing and the product rule
0%
Powers and roots
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Integer and fractional indices
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Exact calculation with fractions, surds and π
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Standard form
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Fractions, decimals and percentages
Fractions, decimals and recurring decimals
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Fractions in ratio problems
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Fractions and percentages as operators
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Measures and accuracy
Standard units and compound measures
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Estimation and approximation
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Rounding and error intervals
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Upper and lower bounds
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Unit 2
Algebra
Notation, vocabulary and manipulation
Algebraic notation
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Substituting into formulae and expressions
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Expressions, equations, formulae and identities
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Expanding, factorising and simplifying
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Using and rearranging formulae
0%
Identities and algebraic proof
0%
Functions: inverse and composite
0%
Graphs
Coordinates in four quadrants
0%
Straight-line graphs and y = mx + c
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Gradients and intercepts
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Roots and turning points of quadratics
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Recognising and sketching graphs
0%
Transformations of graphs
0%
Real-life and non-standard graphs
0%
Gradients and areas under graphs
0%
Equation of a circle and tangents
0%
Solving equations and inequalities
Linear equations
0%
Quadratic equations
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Simultaneous equations
0%
Iteration
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Forming and solving equations
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Inequalities
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Sequences
Generating sequences
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Special sequences and geometric progressions
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nth term of linear and quadratic sequences
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Unit 3
Ratio, proportion and rates of change
Converting standard and compound units
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Scale factors, scale drawings and maps
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One quantity as a fraction of another
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Ratio notation and simplifying ratios
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Sharing in a ratio and ratio problems
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Multiplicative relationships as ratios and fractions
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Proportion as equality of ratios
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Ratios, fractions and linear functions
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Percentages and percentage change
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Direct and inverse proportion problems
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Compound units: speed, density and pressure
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Comparing lengths, areas and volumes with ratio
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Equations for direct and inverse proportion
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Gradient as a rate of change
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Average and instantaneous rates of change
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Growth, decay and compound interest
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Unit 4
Geometry and measures
Properties and constructions
Geometric notation, polygons and symmetry
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Constructions and loci
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Angles, parallel lines and polygons
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Properties of quadrilaterals and triangles
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Congruent triangles
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Geometric reasoning and proof
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Transformations
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Combined transformations
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Parts of a circle
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Circle theorems
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Geometry problems on coordinate axes
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Properties of 3D shapes
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Plans and elevations
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Mensuration and calculation
Units of measure
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Scale drawings and bearings
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Areas and volumes of prisms
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Circles, surface area and volume of solids
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Arc lengths and sectors
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Similarity: lengths, areas and volumes
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Pythagoras' theorem and trigonometry
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Exact trigonometric values
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Sine rule and cosine rule
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Area of a triangle: ½ab sin C
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Vectors
Translations as vectors
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Vector arithmetic and proof
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Unit 5
Probability
Frequency trees and probability experiments
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Expected outcomes
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Relative frequency and the probability scale
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Probabilities that sum to 1
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Sample size and theoretical probability
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Venn diagrams and sets
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Sample spaces
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Combined events and tree diagrams
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Conditional probability
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Unit 6
Statistics
Sampling and populations
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Charts, tables and diagrams
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Histograms and cumulative frequency
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Averages, spread and box plots
0%
Using statistics to describe a population
0%
Scatter graphs and correlation
0%
Avg
score:
–
Topics
done:
0/97

Expressions, equations, formulae and identities

Practise 19 exam-style questions on Expressions, equations, formulae and identities for Edexcel GCSE Maths (Non-calculator). Write your answer as you would in the exam and get it marked in seconds against the mark scheme, point by point, with an AI tutor on hand if you get stuck.

  • 19 questions
  • 1–5 marks each
  • Instant marking
  • No sign-up needed
19 questions, marked as you go

Sample questions with model answers

Here are 4 of the questions in this topic, each with a model answer, an explanation of why it earns the marks and the mark scheme an examiner would use.

Question 1

2 marks

Here is an expression.
\[6x^2 + 9x\]

Which of the following are factors of \(6x^2 + 9x\)?
\(3\) \(6\) \(x\) \(3x\) \(9x\) \(2x + 3\)

Model answer

\(6x^2 + 9x = 3x(2x + 3)\)
So the factors in the list are 3, \(x\), \(3x\) and \(2x + 3\).
6 is not a factor because \(9x\) is not a multiple of 6; \(9x\) is not a factor because \(6x^2\) is not a multiple of \(9x\).

Explanation

Factorise fully first: the highest common factor is \(3x\), giving \(3x(2x + 3)\). Any factor of \(3x\), and the bracket itself, divides the expression exactly. A factor must divide every term, so 6 and \(9x\) do not work.

Mark scheme
  1. 2 marks

    B2 for 3, \(x\), \(3x\) and \(2x + 3\) only

    B1 for two or three of these with no incorrect answers, or all four with one incorrect answer (6 or 9x)

Question 2

2 marks

Sophie is asked to solve
\[7x + 3 - 2x = 5x + 3\]
She cannot find a value for \(x\).

Explain why.

Model answer

\(7x + 3 - 2x = 5x + 3\)
So the statement is \(5x + 3 = 5x + 3\).
Both sides are identical, so it is true for every value of \(x\). It is an identity, not an equation, so there is no single value to find.

Explanation

Simplify both sides before trying to solve. If the two sides become exactly the same, the \(x\) terms cancel and you are left with something always true, like \(3 = 3\). That means every value of \(x\) works, so the statement is an identity.

Mark scheme
  1. 1 mark

    M1 for simplifying the left-hand side to \(5x + 3\)

  2. 1 mark

    C1 for explaining that both sides are the same, so the statement is true for every value of \(x\) (it is an identity)

    oe, e.g. "it simplifies to 3 = 3, so any value of x works"

Question 3

3 marks

\[(x + a)(x + 5) \equiv x^2 + bx + 15\]
where \(a\) and \(b\) are constants.

Work out the value of \(a\) and the value of \(b\).

Model answer

\((x + a)(x + 5) = x^2 + 5x + ax + 5a = x^2 + (a + 5)x + 5a\)
Constant terms: \(5a = 15\), so \(a = 3\)
Coefficients of \(x\): \(b = a + 5 = 8\)

Explanation

Because it is an identity, the two sides must match term by term. Compare the constant terms first to find \(a\), then compare the coefficients of \(x\) to find \(b\). Check: \((x + 3)(x + 5) = x^2 + 8x + 15\).

Mark scheme
  1. 1 mark

    M1 for expanding to \(x^2 + 5x + ax + 5a\)

    oe, e.g. \(x^2 + (a + 5)x + 5a\); correct answer with no working scores full marks

  2. 1 mark

    A1 for \(a = 3\)

    from 5a = 15

  3. 1 mark

    A1 for \(b = 8\)

    ft \(b = a + 5\) for their a

Question 4

4 marks

\[2(3x + a) - b(x - 2) \equiv x + 14\]
where \(a\) and \(b\) are constants.

Work out the value of \(a\) and the value of \(b\).

Model answer

\(2(3x + a) - b(x - 2) = 6x + 2a - bx + 2b = (6 - b)x + (2a + 2b)\)
Coefficients of \(x\): \(6 - b = 1\), so \(b = 5\)
Constants: \(2a + 2b = 14\), so \(2a + 10 = 14\) and \(a = 2\)

Explanation

Expand, then group the terms in \(x\) and the constant terms. For an identity, the coefficients of \(x\) must be equal on both sides, and so must the constants. Note \(-b \times -2 = +2b\). Check: \(2(3x + 2) - 5(x - 2) = 6x + 4 - 5x + 10 = x + 14\).

Mark scheme
  1. 1 mark

    M1 for expanding both brackets correctly, \(6x + 2a - bx + 2b\)

    correct answer with no working scores full marks

  2. 1 mark

    M1 for equating coefficients, e.g. \(6 - b = 1\) or \(2a + 2b = 14\)

  3. 1 mark

    A1 for \(b = 5\)

  4. 1 mark

    A1 for \(a = 2\)

    ft their b in \(2a + 2b = 14\)

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