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Quizzes > High School Quizzes > Mathematics

GCSE Practice Quiz Questions Made Easy

Sharpen your exam skills with quick tests

Difficulty: Moderate
Grade: Grade 11
Study OutcomesCheat Sheet
Colorful paper art promoting a trivia quiz for GCSE students to improve in Mathematics.

What is 25% of 200?
25
50
75
100
25% means one quarter of a whole. Dividing 200 by 4 gives 50, which is the correct answer.
Which of the following is a prime number?
9
15
17
21
A prime number has only two distinct positive divisors: 1 and itself. Among the options, 17 meets that criterion.
Simplify: 3x + 2x.
5x
6x
x^2
5
You combine like terms by adding their coefficients. Adding 3 and 2 gives 5, so the expression simplifies to 5x.
What is the value of 7 - 3?
4
3
10
5
Subtracting 3 from 7 is a basic arithmetic operation. The result is 4, making it the correct answer.
What is the area of a rectangle with length 8 and width 3?
24
11
16
22
The area of a rectangle is calculated by multiplying its length by its width. Multiplying 8 by 3 gives 24, which is the correct area.
Solve for x: 2x + 3 = 11.
4
5
3
2
Subtracting 3 from both sides of the equation gives 2x = 8. Dividing by 2 yields x = 4, which is the correct solution.
If y = 3 and z = 2, what is the value of 2y + 3z?
12
11
14
10
Substitute y = 3 and z = 2 into 2y + 3z: 2(3) + 3(2) = 6 + 6 = 12. This makes 12 the correct answer.
Which of the following represents a quadratic equation?
x^2 - 5x + 6 = 0
2x + 3 = 0
3/x = 2
x^3 + 1 = 0
A quadratic equation is one in which the highest exponent of the variable is 2. The equation x^2 - 5x + 6 = 0 fits this definition.
What is the gradient of the line represented by the equation y = 3x - 7?
3
-7
y-intercept is 3
Cannot be determined
The gradient (or slope) of a line given in the form y = mx + c is m. In this equation, m is 3, making it the correct gradient.
Find the value of x in the proportion: 3/4 = x/8.
6
4
3
5
Cross-multiplying the proportion gives 3 × 8 = 4 × x, which simplifies to 24 = 4x. Dividing both sides by 4 results in x = 6.
What is the median of the following set of numbers: 5, 8, 12, 7, 10?
8
7
10
12
When the numbers are arranged in order (5, 7, 8, 10, 12), the median is the middle number. The middle number in this ordered list is 8, which is correct.
What is (3/4) + (1/2)?
5/4
1
3/4
2/3
To add the fractions, convert 1/2 to 2/4 so that they have a common denominator. Adding 3/4 and 2/4 gives 5/4, which is the correct result.
If the circumference of a circle is 31.4 cm, what is the approximate radius? (Use π ≈ 3.14)
5 cm
10 cm
3 cm
2 cm
The formula for the circumference of a circle is 2πr. Dividing 31.4 by (2 × 3.14) gives 5, indicating that the radius is approximately 5 cm.
Expand the expression: 2(3x + 4).
6x + 8
6x + 4
2x + 12
3x + 8
Distribute the 2 across the terms inside the parentheses: 2 × 3x gives 6x, and 2 × 4 gives 8. The expanded expression is therefore 6x + 8.
Which of the following is the correct factorization of x^2 - 9?
(x + 3)(x - 3)
x(x - 9)
(x - 3)^2
x^2 - 3x
The expression x^2 - 9 is a difference of squares, which factors as (x + 3)(x - 3). This is the standard factorization for such an expression.
Solve the equation: 2(x - 3) = x + 4.
10
7
8
11
First, distribute the 2 to get 2x - 6 = x + 4. Subtracting x from both sides and adding 6 gives x = 10, which is the correct solution.
The angles of a triangle are in the ratio 3:4:5. What is the measure of the largest angle?
75°
90°
60°
80°
The sum of the ratio parts is 3 + 4 + 5 = 12. Since the total angles in a triangle add up to 180°, each part is 15° and the largest angle (5 parts) is 75°.
Solve the simultaneous equations: 2x + y = 10 and x - y = 3.
x = 13/3, y = 4/3
x = 4, y = 2
x = 3, y = 1
x = 5, y = 0
Using substitution, solve x - y = 3 for y (y = x - 3) and substitute into 2x + y = 10 to get 2x + (x - 3) = 10. This simplifies to 3x = 13, so x = 13/3 and y = 13/3 - 3 = 4/3.
If f(x) = 2x^2 - 3x + 1, what is f(3)?
10
12
9
11
Substitute x = 3 into the function: f(3) = 2*(3^2) - 3*3 + 1 = 18 - 9 + 1. This simplifies to 10, making it the correct answer.
A bag contains 3 red, 4 blue, and 5 green marbles. If one marble is selected at random, what is the probability of picking a blue marble?
1/3
1/4
1/2
1/5
There are a total of 3 + 4 + 5 = 12 marbles, and 4 of them are blue. The probability is therefore 4/12, which simplifies to 1/3.
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Study Outcomes

  1. Analyze exam-style questions to identify key mathematical concepts.
  2. Apply problem-solving techniques to tackle common GCSE math challenges.
  3. Evaluate personal performance to recognize strengths and areas needing improvement.
  4. Interpret quiz results to guide targeted revision strategies.

GCSE Test Questions Cheat Sheet

  1. Master the quadratic formula - The formula x = (-b ± √(b² − 4ac)) / 2a unlocks any quadratic equation. Calculate the discriminant first (b² − 4ac), then apply the ± to find both roots. Practice with varied a, b and c values to boost speed and confidence. AQA Mathematical Formulae
    2. AQA Mathematical Formulae
  2. Understand circle formulas - Circumference = 2πr and Area = πr² are your go-to formulas for circles. Remember that 'C' works with radius for circumference and 'A' for radius squared in area. Sketch circles, label r, and plug in values to make these concepts stick. AQA Mathematical Formulae
    3. AQA Mathematical Formulae
  3. Grasp Pythagoras' theorem - In a right-angled triangle, a² + b² = c² links the two legs (a, b) with the hypotenuse (c). Visualize squares on each side to see why it works. Use it to find missing sides and confirm right angles during problem solving. AQA Mathematical Formulae
    4. AQA Mathematical Formulae
  4. Learn trigonometric ratios - sin θ = opposite/hypotenuse, cos θ = adjacent/hypotenuse, tan θ = opposite/adjacent are keys for right-angled triangles. Use the mnemonic SOH‑CAH‑TOA to lock them in. Draw triangles, label sides, and practice with different angles. AQA Mathematical Formulae
    5. AQA Mathematical Formulae
  5. Use sine and cosine rules - The Sine Rule (a/sin A = b/sin B = c/sin C) and Cosine Rule (c² = a² + b² − 2ab cos C) crack non-right-angled triangles. Identify known sides/angles, then choose the rule that fits. Tackle mixed problems to see them in action. AQA Mathematical Formulae
    6. AQA Mathematical Formulae
  6. Find triangle area with trig - For any triangle, Area = ½ ab sin C uses two sides (a, b) and the included angle C. Sketch the triangle, label a, b, and C, then plug in. This method shines when right-angle formulas won't work. AQA Mathematical Formulae
    7. AQA Mathematical Formulae
  7. Learn laws of indices - a^m × a^n = a^(m+n), a^m ÷ a^n = a^(m−n), (a^m)^n = a^(m × n) make power rules a breeze. Remember: multiply adds, divide subtracts, power multiplies. Simplify step by step and check exponents carefully. BBC Bitesize: Index Laws
    8. BBC Bitesize: Index Laws
  8. Practice simultaneous equations - Use substitution or elimination to solve systems of two (or more) equations. Line up like terms, eliminate a variable, then back‑substitute for the other. Start simple and build up to word‑problem applications. BBC Bitesize: Simultaneous Equations
    9. BBC Bitesize: Simultaneous Equations
  9. Know number properties - Primes have exactly two factors; squares are n×n; cubes are n×n×n. Spotting these powers and factors helps in factorization and simplifying expressions. Keep quick-reference lists to save time on tests. BBC Bitesize: Number Types
    10. BBC Bitesize: Number Types
  10. Master direct & inverse proportion - Direct proportion: y increases as x increases (y = kx). Inverse: y decreases as x increases (y = k/x). Set up equations, plug in known values, and solve for k or the unknown. Apply to real-world ratio problems for extra practice. BBC Bitesize: Proportion
    11. BBC Bitesize: Proportion
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