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Quizzes > Mathematics > Basic Math & Arithmetic

Take the Math Diagnostic Test and Discover Your Strengths

Challenge yourself with a fun math diagnostic exam - see where you excel!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art scene with pencils rulers math symbols and numbers on dark blue background for free math diagnostic quiz

This math diagnostic test helps you check your level and find gaps in key topics. You'll get quick results that show where to focus next, so you can practice smarter before class or an exam. For extra practice, try a related quiz .

What is 5 + 7?
10
11
13
12
Adding 5 and 7 gives 12 because when you combine the two values, the sum is 12. Basic addition skills help build more complex arithmetic knowledge. Learn more about addition at .
What is 12 – 4?
8
9
7
6
Subtracting 4 from 12 leaves 8. Subtraction is the inverse of addition and helps in understanding number relationships. For more details, see .
What is 3 × 4?
9
24
12
7
Multiplying 3 by 4 gives 12 because multiplication is repeated addition (3 + 3 + 3 + 3). Mastering multiplication tables is key to faster calculations. Read more at .
What is 15 ÷ 3?
3
4
5
6
Dividing 15 by 3 results in 5 because 3 goes into 15 exactly five times. Division is splitting into equal parts. For more on division, visit .
What is 10% of 200?
10
200
2
20
Ten percent means one-tenth, so one-tenth of 200 is 20. Percent calculations are based on parts per hundred. See more at .
Simplify 2(x + 3).
2x + 6
x + 5
x + 6
2x + 3
Using the distributive property, multiply 2 by each term inside the parentheses: 2·x + 2·3 = 2x + 6. The distributive law is fundamental in algebra. Learn more at .
Solve for x: x + 5 = 12.
x = 6
x = 7
x = 17
x = -7
Subtract 5 from both sides: x = 12 – 5 = 7. This is a basic one-step equation. For solving linear equations, see .
Which of these numbers is prime?
9
7
8
12
A prime number has only two divisors: 1 and itself. Seven meets this criterion. For an overview of prime numbers, visit .
What is the square of 6?
18
12
42
36
The square of a number is that number times itself: 6 × 6 = 36. Squares are key in area calculations. More at .
What is the perimeter of a rectangle with length 5 and width 3?
8
16
15
10
Perimeter equals 2×(length + width) = 2×(5 + 3) = 16. Understanding perimeter is essential in geometry. See .
Convert 1/2 to a decimal.
2
0.5
0.2
5
One half as a decimal is 0.5 because 1 divided by 2 equals 0.5. Converting fractions to decimals is a key skill. More at .
Solve 2x + 3 = 11 for x.
x = -4
x = 4
x = 3
x = 7
Subtract 3 then divide by 2: x = (11 – 3)/2 = 4. This two-step linear equation reinforces algebra basics. See .
Factor x² – 9.
(x + 3)(x – 3)
(x – 9)(x + 1)
(x – 3)(x – 3)
(x + 9)(x – 1)
x² – 9 is a difference of squares: (x + 3)(x – 3). Recognizing special products speeds factoring. More at .
Evaluate f(x) = 2x + 1 at x = 3.
7
6
5
8
Plugging in x = 3 gives f(3) = 2·3 + 1 = 7? Actually 2·3 + 1 = 6 + 1 = 7. Correction: answer is 7, not 6. So adjust: Score of 1 on 7. Let me correct answers.
Simplify (3x²)(2x).
3x³
6x³
6x²
5x²
Multiply coefficients (3·2 = 6) and add exponents on x (2 + 1 = 3) giving 6x³. Understanding exponent rules is crucial. More at .
Solve the system: x + y = 5 and x – y = 1.
x = 4, y = 1
x = 3, y = 2
x = 2, y = 3
x = 1, y = 4
Add the equations: 2x = 6 ? x = 3, then y = 5 – 3 = 2. Systematic elimination simplifies solving. More at .
Simplify the fraction 45/60.
5/6
4/5
3/4
9/12
Both numerator and denominator are divisible by 15: 45/60 = (45÷15)/(60÷15) = 3/4. Simplifying fractions is essential. Learn more at .
What is the area of a triangle with base 4 and height 3?
12
6
24
7
Area = ½ × base × height = ½ × 4 × 3 = 6. Understanding area formulas is key in geometry. See .
What is the slope of the line through (1, 2) and (3, 6)?
3
2
4
1
Slope = (6 – 2)/(3 – 1) = 4/2 = 2. The slope measures change in y over change in x. More at .
What is |–8|?
–1
0
–8
8
Absolute value removes the sign, so |–8| = 8. It's the distance from zero on the number line. Learn more at .
Convert 75% to a fraction.
75/100
3/4
1/4
7/5
75% = 75/100 which simplifies by 25 to 3/4. Converting percents to fractions builds number fluency. Details at .
Solve x² – 5x + 6 = 0.
x = –2 or x = –3
x = 1 or x = 6
x = 2 or x = 3
x = 3 only
Factor into (x – 2)(x – 3) = 0 giving x = 2 or x = 3. Solving quadratics by factoring is efficient when possible. More at .
Simplify (x³y²)/(x y?).
x²/y³
x?y?³
x/y³
x²y³
Subtract exponents: x^(3–1) y^(2–5) = x² y^(–3) = x²/y³. Exponent rules help in algebraic simplification. See .
Simplify 2³ × 2?¹.
2?
2¹
2²
2?²
Add exponents: 3 + (–1) = 2, so the result is 2² = 4. This is a key exponent rule. More at .
Evaluate log??(1000).
10
2
1000
3
Log base 10 of 1000 asks for the power that gives 1000: 10³ = 1000, so the log is 3. Understanding logs is crucial in higher math. See .
Solve |2x – 4| = 6.
x = 1 or x = 2
x = 4 or x = –2
x = 5 or x = –1
x = 3 or x = –3
Set 2x – 4 = 6 ? x = 5 or 2x – 4 = –6 ? x = –1. Absolute equations yield two solutions. Details at .
What is the probability of drawing an ace from a standard 52-card deck?
4/52
1/52
4/13
1/13
There are 4 aces in 52 cards, so probability is 4/52 = 1/13. Probabilities express favorable outcomes over total. Learn more at .
Find the circumference of a circle with radius 7.
14?
7?
4?
14?
14?
Circumference formula is 2?r = 2?·7 = 14?. Understanding circle formulas is key in geometry. Details at .
Find the midpoint between (2, –1) and (8, 5).
(10, 4)
(3, 2)
(4, 3)
(5, 2)
Midpoint = ((2+8)/2, (–1+5)/2) = (5, 2). Midpoints average coordinates. More at .
Simplify (x² – 4)/(x – 2).
x² + 2
x + 2
x + 4
x – 2
Factor numerator: (x – 2)(x + 2)/(x – 2) = x + 2, valid for x ? 2. Cancel common factors in rational expressions. See .
Solve the system 2x + 3y = 7 and 4x – y = 5.
x = –1, y = 3
x = 3, y = –1
x = 1, y = 2
x = 2, y = 1
Use substitution or elimination: multiply second by 3 then add to first to find x = 2, then y = (7 – 2·2)/3 = 1. Solving systems with multiple equations is advanced algebra. More at .
For f(x) = x² + 2x + 1, what is the vertex of the parabola?
(-1, -1)
(-1, 1)
(1, -1)
(-1, 0)
The vertex of x² + 2x + 1 = (x + 1)² is at (–1, 0)? Actually expanding gives (x + 1)² so vertex is (–1, 0). Correction: Score should be on (–1, 0). Adjust answer accordingly.
Simplify x^(1/2) × x^(1/3).
x^(1/5)
x^(2/3)
x^(5/6)
x^(3/6)
Add exponents: 1/2 + 1/3 = 3/6 + 2/6 = 5/6, so x^(5/6). Combining fractional exponents extends exponent rules. More at .
Find the sum of the infinite geometric series 3 + 2 + 4/3 + ...
8
7.5
6
9
Common ratio r = (2/3), first term a = 3, sum = a/(1 – r) = 3/(1 – 2/3) = 3/(1/3) = 9. Infinite series sum formula applies when |r| < 1. Details at .
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Study Outcomes

  1. Analyze Your Skill Level -

    Interpret your math diagnostic test scores to gauge proficiency across algebra, geometry, and other core topics.

  2. Identify Strengths and Gaps -

    Pinpoint specific areas of mastery and improvement in diagnostic maths to focus your study efforts effectively.

  3. Understand Question Formats -

    Familiarize yourself with the types of questions featured in a math diagnostic exam to reduce test-day surprises.

  4. Apply Targeted Techniques -

    Learn problem-solving strategies tailored to your performance on this diagnostic math assessment.

  5. Develop a Study Plan -

    Create a personalized roadmap based on your diagnostic test in mathematics results to boost your overall math skills.

  6. Build Confidence -

    Gain assurance in your abilities by tracking progress and celebrating improvements as you work through practice questions.

Cheat Sheet

  1. Master Linear Equations -

    Balancing equations is crucial for any diagnostic math assessment; practice isolating the variable by inverting operations - e.g., for 3x+5=20, subtract 5 then divide by 3 to get x=5. According to Khan Academy, solving equations reliably boosts confidence across algebra topics and ensures you're ready for more complex problem-solving in a math diagnostic test.

  2. Utilize Order of Operations (PEMDAS) -

    Memorize "Please Excuse My Dear Aunt Sally" to recall Parentheses, Exponents, Multiplication/Division (left to right), and Addition/Subtraction (left to right). This rule is a staple in diagnostic maths and helps you avoid simple arithmetic mistakes under time pressure, as endorsed by the National Council of Teachers of Mathematics. Practicing with mixed-operation problems ensures fluency for your math diagnostic exam.

  3. Know Geometry Basics -

    Review key formulas for area and perimeter - rectangle area = length×width, circle area = πr² and circumference =2πr - so you can quickly solve shape-related questions on your diagnostic test in mathematics. Sketching figures to scale, as suggested by Stanford's math department, clarifies spatial reasoning and reduces careless errors. Keep a quick-reference sheet of these formulas in mind while working through geometry sections of a diagnostic maths quiz.

  4. Understand Functions and Graphs -

    Interpret linear functions in slope-intercept form y=mx+b to identify slope m and intercept b at a glance, which is vital for algebra and pre-calculus sections of a math diagnostic test. Practice plotting a few points and drawing the line to solidify the relationship between equations and graphs. Resources like MIT OpenCourseWare recommend this visual approach to reinforce function concepts before any diagnostic maths quiz.

  5. Master Number Theory Essentials -

    Get comfortable with prime factorization to find greatest common divisors (GCD) and least common multiples (LCM) - for example, GCD(24,36)=12 and LCM(4,6)=12 - since many diagnostic math assessment questions rely on number properties. Learn Euclid's algorithm as a fast mental strategy, and test yourself with random pairs to build speed. The University of Cambridge's math resources highlight that strong number sense underpins success across arithmetic and algebra sections.

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