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Incorrect: 0
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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
0%
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
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Real-life and non-standard graphs
0%
Gradients and areas under graphs
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Equation of a circle and tangents
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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
0%
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
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Using statistics to describe a population
0%
Scatter graphs and correlation
0%
Avg
score:
–
Topics
done:
0/97

Linear equations

Practise 28 exam-style questions on Linear equations 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.

  • 28 questions
  • 1–5 marks each
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20 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

Solve \(4(3x + 5) = 2\)

Model answer

\(12x + 20 = 2\)
\(12x = -18\)
\(x = -\dfrac{18}{12} = -\dfrac{3}{2}\)

Explanation

Expand the bracket (or divide both sides by 4), then subtract 20 from both sides. The answer is negative because \(2 - 20 = -18\); solutions do not have to be positive whole numbers.

Mark scheme
  1. 1 mark

    M1 for a correct first step, e.g. \(12x + 20 = 2\) or \(3x + 5 = \dfrac{1}{2}\)

    correct answer with no working scores full marks

  2. 1 mark

    A1 for \(x = -\dfrac{3}{2}\)

    oe, e.g. \(-1.5\) or \(-\dfrac{18}{12}\)

Question 2

2 marks

The graphs of \(y = 3x - 1\) and \(y = 6 - x\) are drawn on the grid.

Use the graphs to find an estimate for the solution of \(3x - 1 = 6 - x\)

A coordinate grid with x from −1 to 4 and y from −4 to 7; each grid square is 1 unit across (with 5 small squares along each side of a large square), and the axes cross at the origin O. The line labelled "y = 3x − 1" is a straight line sloping upwards from left to right crossing the y-axis at (0, −1) and crossing the x-axis at (1/3, 0). The line labelled "y = 6 − x" is a straight line sloping downwards from left to right crossing the y-axis at (0, 6) and passing through (1, 5). The line labelled "y = 3x − 1" and the line labelled "y = 6 − x" cross at one point, which can be read from the grid.

Model answer

The lines cross at approximately \((1.75, 4.25)\).
The solution is the \(x\)-coordinate: \(x \approx 1.75\)

Explanation

At the point where the two lines cross, \(3x - 1\) and \(6 - x\) have the same value, so its \(x\)-coordinate solves the equation. Give the \(x\)-coordinate, not the \(y\)-coordinate. Algebra confirms it: \(4x = 7\), so \(x = 1.75\).

Mark scheme
  1. 1 mark

    M1 for using the point where the two lines cross, e.g. reading the \(x\)-coordinate of the intersection

    correct answer with no working scores full marks

  2. 1 mark

    A1 for an answer in the range 1.7 to 1.8

    accept the exact answer 1.75 or \(\dfrac{7}{4}\) from algebra

Question 3

3 marks

Solve \((2x - 1)(x + 4) = 2x(x - 3) + 22\)

Model answer

\(2x^2 + 8x - x - 4 = 2x^2 - 6x + 22\)
\(2x^2 + 7x - 4 = 2x^2 - 6x + 22\)
\(7x + 6x = 22 + 4\)
\(13x = 26\)
\(x = 2\)

Explanation

Expand both sides fully; the \(2x^2\) terms appear on both sides and cancel, leaving a linear equation. Check: \(3 \times 6 = 18\) and \(4 \times (-1) + 22 = 18\).

Mark scheme
  1. 1 mark

    M1 for expanding both sides correctly, \(2x^2 + 7x - 4\) and \(2x^2 - 6x + 22\)

    allow one error in one term; correct answer with no working scores full marks

  2. 1 mark

    M1 for cancelling the \(x^2\) terms and collecting, e.g. \(13x = 26\)

  3. 1 mark

    A1 for \(x = 2\)

    cao

Question 4

4 marks

Solve \(\dfrac{3}{x - 1} + \dfrac{2}{x + 1} = \dfrac{7x}{x^2 - 1}\)

Model answer

\(x^2 - 1 = (x - 1)(x + 1)\)
Multiply every term by \((x - 1)(x + 1)\):
\(3(x + 1) + 2(x - 1) = 7x\)
\(3x + 3 + 2x - 2 = 7x\)
\(5x + 1 = 7x\)
\(1 = 2x\)
\(x = \dfrac{1}{2}\)

Explanation

Factorising \(x^2 - 1\) as a difference of two squares shows that it is the common denominator of all three fractions. Multiplying every term by it clears the fractions and leaves a linear equation. The answer \(x = \dfrac{1}{2}\) does not make any denominator zero, so it is valid.

Mark scheme
  1. 1 mark

    M1 for recognising that \(x^2 - 1 = (x - 1)(x + 1)\) is a common denominator

    correct answer with no working scores full marks

  2. 1 mark

    M1 for multiplying through to get \(3(x + 1) + 2(x - 1) = 7x\)

    oe

  3. 1 mark

    M1 for simplifying to a linear equation, e.g. \(5x + 1 = 7x\)

  4. 1 mark

    A1 for \(x = \dfrac{1}{2}\)

    oe, e.g. 0.5

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