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Take the Ultimate GCSE Math Practice Test!

Think you can ace this GCSE numeracy test? Start now!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art illustration for GCSE maths skills quiz on a sky blue background

Ready to supercharge your exam prep with our ultimate gcse practice test? This interactive quiz is designed to sharpen your gcse test maths skills and boost confidence before the big day. Dive into our gcse numeracy test for a quick warm-up, then tackle a range of basic maths questions and complex equations. You'll uncover your strengths, pinpoint improvement areas, and build momentum towards acing each section. Perfect for students aiming to top their gcse maths test, this friendly, motivating quiz offers instant feedback and practical tips. Ready to prove your prowess? Click "Start Quiz" now and dominate your next exam!

What is 15% of 200?
30
20
35
25
To find 15% of a number, convert the percentage to a decimal or fraction. 15% is 15/100 = 0.15, then multiply by 200 to get 30. Therefore, 0.15 × 200 = 30. BBC Bitesize: Percentages
Simplify the fraction 8/12.
1/2
2/3
3/4
2/5
To simplify 8/12, divide both numerator and denominator by their greatest common divisor, which is 4. 8 ÷ 4 = 2 and 12 ÷ 4 = 3, giving 2/3. This is the fraction in simplest form. Mathsisfun: Simplifying Fractions
Solve for x: x + 7 = 12.
-5
19
5
7
To isolate x, subtract 7 from both sides of the equation: x + 7 ? 7 = 12 ? 7, so x = 5. This simple one-step equation shows the basic principles of balancing. Always perform the same operation on both sides. BBC Bitesize: Solving Simple Equations
What is 7 × 9?
63
49
56
72
Multiplying 7 by 9 gives 63. Knowing basic times tables helps you calculate such products quickly. This is a fundamental arithmetic skill. Mathsisfun: Multiplication
What is the mean of the numbers 4, 8, and 10?
8
9
6
7
The mean is the sum of the values divided by the count. (4 + 8 + 10) = 22, and there are 3 numbers, so 22 ÷ 3 = 7?, which rounds to 7 when given as a whole number. In exact form it's 22/3 ? 7.33. BBC Bitesize: Averages
Express 0.25 as a fraction.
1/5
25/100
1/4
1/2
0.25 is twenty-five hundredths, which can be written as the fraction 25/100. Simplify by dividing numerator and denominator by 25, giving 1/4. This is the simplest form. Mathsisfun: Converting Decimals to Fractions
Expand and simplify 3(x + 4).
x + 12
12x + 3
3x + 4
3x + 12
Distribute the 3 to both terms inside the parentheses: 3 × x = 3x and 3 × 4 = 12. Adding them yields 3x + 12. This is the standard method for expanding brackets. BBC Bitesize: Expanding Brackets
Solve for x: 2x ? 3 = 9.
3
-6
9
6
Add 3 to both sides: 2x ? 3 + 3 = 9 + 3 gives 2x = 12. Divide both sides by 2 to isolate x: x = 6. This uses two inverse operations. Mathsisfun: Solving Linear Equations
Calculate the area of a triangle with base 8 cm and height 5 cm.
40 cm²
20 cm²
13 cm²
20
Triangle area = ½ × base × height. Here, ½ × 8 × 5 = 20 cm². Always ensure units are squared for area. Mathsisfun: Triangle Area
What is the gradient of the line passing through points (1, 2) and (3, 8)?
2
3
6
1/3
Gradient = (y? ? y?)/(x? ? x?). Here, (8 ? 2)/(3 ? 1) = 6/2 = 3. That gives the steepness of the line. BBC Bitesize: Gradient
Factorise the quadratic x² ? 5x + 6.
(x ? 3)²
(x ? 2)(x ? 3)
(x + 2)(x ? 3)
(x ? 6)(x + 1)
We look for two numbers that multiply to +6 and add to ?5. Those numbers are ?2 and ?3, giving factors (x ? 2)(x ? 3). This method is known as factor by inspection. Mathsisfun: Factorization
What is the median of the data set {12, 15, 20, 22, 25}?
20
15
17
22
The median is the middle value when data are ordered. Here the third value of five is 20. This measure is useful when data have outliers. BBC Bitesize: Median
Expand and simplify (x + 2)(x ? 5).
x² + 10
x² ? 3x + 10
x² + 3x ? 10
x² ? 3x ? 10
Use the distributive law (FOIL): x·x = x², x·(?5) = ?5x, 2·x = 2x, and 2·(?5) = ?10. Combine like terms: x² + (?5x + 2x) ? 10 = x² ? 3x ? 10. Mathsisfun: Expanding Products
Find the roots of x² ? 4x ? 5 = 0.
5 only
5 and ?1
1 and ?5
?1 only
Use the quadratic formula or factorisation. It factors to (x ? 5)(x + 1) = 0, giving x = 5 or x = ?1. These are the two solutions. BBC Bitesize: Quadratic Equations
Calculate the circumference of a circle with radius 7 cm (in terms of ?).
? cm
7? cm
14? cm
49? cm
Circumference = 2?r. Substituting r = 7 gives 2? × 7 = 14? cm. This formula links diameter and ?. Mathsisfun: Circle Circumference
In a right-angled triangle, the legs are 6 cm and 8 cm. What is the length of the hypotenuse?
9 cm
?100 cm
11 cm
10 cm
By Pythagoras' theorem, c² = 6² + 8² = 36 + 64 = 100, so c = ?100 = 10 cm. This applies only to right-angled triangles. BBC Bitesize: Pythagoras Theorem
Simplify the expression 2/5 + 3/10.
8/15
7/10
1/2
5/10
Convert to a common denominator of 10: 2/5 = 4/10, then add 3/10 to get 7/10. Fractions must share the same denominator before adding. Mathsisfun: Adding Fractions
Solve the inequality 3x + 1 < 10.
x > ?3
x > 3
x < 3
x < ?3
Subtract 1 from both sides: 3x < 9, then divide by 3 giving x < 3. Inequalities use the same operations as equations. BBC Bitesize: Inequalities
Solve the simultaneous equations 2x + y = 5 and x ? y = 1.
x = 2, y = 1
x = 2, y = ?1
x = 1, y = 3
x = 3, y = ?1
Add the equations: (2x + y) + (x ? y) = 5 + 1 gives 3x = 6, so x = 2. Substitute x back into x ? y = 1: 2 ? y = 1, so y = 1. Mathsisfun: Simultaneous Equations
Find x if 3^x × 9^(x ? 1) = 81.
1
3
2
4
Write all in base 3: 9 = 3² and 81 = 3^4. So 3^x × (3²)^(x ? 1) = 3^x × 3^(2x ? 2) = 3^(3x ? 2) = 3^4. Equate exponents: 3x ? 2 = 4, so x = 2. BBC Bitesize: Indices
In triangle ABC, AB = 7, AC = 9 and angle A = 60°. Find BC using the Law of Cosines.
?67
?61
?130
8
Law of Cosines: BC² = AB² + AC² ? 2·AB·AC·cos(A). So BC² = 7² + 9² ? 2·7·9·cos60° = 49 + 81 ? 126·0.5 = 130 ? 63 = 67. Thus BC = ?67. Mathsisfun: Law of Cosines
0
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Study Outcomes

  1. Apply Algebraic Techniques -

    Solve equations and simplify expressions to strengthen your algebra skills. Build confidence in manipulating variables and using algebraic methods across varied question formats.

  2. Interpret Geometrical Concepts -

    Analyze shapes, angles, and measurements to tackle geometry problems with accuracy. Understand the properties of geometric figures and apply formulae effectively.

  3. Strengthen Number Theory Understanding -

    Identify factors, multiples, and prime numbers to deepen your grasp of number theory concepts. Apply divisibility rules and sequences to solve related problems.

  4. Enhance Arithmetic Proficiency -

    Practice calculations involving fractions, percentages, and ratios to boost your overall numeracy skills. Improve speed and accuracy for common GCSE question types.

  5. Utilize Instant Feedback -

    Track your performance with immediate scoring to pinpoint strengths and weaknesses. Leverage targeted insights to focus your revision on topics needing the most improvement.

  6. Develop Exam Strategies -

    Refine time management and approach different question formats methodically. Build confidence in your test-taking skills to maximize your GCSE maths score.

Cheat Sheet

  1. Algebraic Manipulation -

    Master combining like terms and applying the distributive law to simplify expressions quickly - e.g., 2(x + 3) = 2x + 6. This foundational skill, highlighted on BBC Bitesize, is essential for every gcse maths test and will speed up your gcse practice test performance.

  2. Quadratic Formula Recall -

    Learn the quadratic formula x = (−b ± √(b²−4ac))❄(2a) and use the mnemonic "minus b, plus or minus…" to lock it in memory. Official guidance from Cambridge Assessment stresses that accurate recall and substitution into ax² + bx + c = 0 questions can earn you top marks on a gcse numeracy test.

  3. Pythagoras and Circle Theorems -

    Remember a² + b² = c² for right-angled triangles and A = πr² for circle areas; these are staples of the gcse test maths syllabus from the UK Department for Education. Sketching a quick diagram helps you visualise and apply these equations under timed conditions.

  4. Fractions, Decimals & Percentages -

    Practice converting between these forms by moving the decimal two places for percentages and using "keep, change, flip" for fraction division. Proficiency here, as recommended by UK exam boards, will boost your confidence in any gcse practice test scenario.

  5. Data Handling Basics -

    Understand mean, median and mode, and calculate simple probability by dividing favorable outcomes by the total - e.g., P(rolling a 4) = 1/6. Data questions are a common feature of gcse numeracy tests, so quick mental calculations can make all the difference.

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