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Quizzes > Mathematics > Advanced Math

Ace PAT Maths: Take the Free Practice Quiz!

Think you can master PAT practice questions? Dive in today!

Difficulty: Moderate
2-5mins
Learning OutcomesCheat Sheet
Paper art quiz with math symbols on sky blue background, promoting free PAT practice questions and past papers

This PAT Maths quiz helps you practice core question types and check your gaps before the exam. You'll see algebra, number, and data problems that feel like past papers, with instant feedback to guide what to study next. For a quick start, try a short PAT practice set or warm up with an algebra review .

What is the value of 2 + 3 × 4?
24
8
20
14
According to the order of operations, multiplication is performed before addition, so 3 × 4 = 12 and then 2 + 12 = 14.
Evaluate 9?.
0
Undefined
1
9
Any nonzero number raised to the power of zero equals 1.
Solve for x: 5x = 20.
15
5
4
1
Divide both sides by 5: x = 20/5 = 4.
What is the decimal form of 1/2?
0.2
0.25
0.5
2
Divide numerator by denominator: 1 ÷ 2 = 0.5.
What is 10% of 200?
50
10
20
2
10% means 10/100 of 200, which is 200 × 0.1 = 20.
Expand 3(x + 2).
x + 6
3x + 6
9x + 6
3x + 2
Distribute 3: 3×x + 3×2 = 3x + 6.
What is the greatest common divisor of 12 and 18?
6
2
12
3
The largest integer dividing both 12 and 18 is 6.
Convert 100 cm to meters.
0.1
10
1
0.01
There are 100 cm in a meter, so 100 cm equals 1 m.
What is 7 × 8?
49
54
56
63
Standard multiplication: 7 times 8 equals 56.
Solve for y: y - 4 = 10.
-6
14
4
6
Add 4 to both sides: y = 10 + 4 = 14.
What is the perimeter of a square with side length 5?
25
20
15
10
Perimeter of a square is 4 × side = 4 × 5 = 20.
What is the mean of the data set {2, 4, 6, 8}?
4
6
5
2
Mean is (2 + 4 + 6 + 8) ÷ 4 = 20 ÷ 4 = 5.
Solve x² = 49.
0
-7
±7
7
Taking square roots gives x = 7 or x = - 7.
Simplify (x² y³) / (x y).
x y
x² y
x² y²
x y²
Subtract exponents: x²/x = x¹ and y³/y¹ = y², giving x y².
Solve 2x + 3 = 11.
4
3
8
7
Subtract 3 then divide by 2: x = (11 - 3)/2 = 4.
Factorise x² - 9.
(x - 9)(x + 1)
(x - 3)(x + 3)
(x - 3)²
(x + 3)²
Difference of squares: a² - b² = (a - b)(a + b).
What is the gradient of the line y = 3x + 2?
3
1/3
2
-2
Line in slope-intercept form y = mx + c has gradient m = 3.
What is the area of a triangle with base 6 and height 5?
30
6
11
15
Area = ½ × base × height = ½ × 6 × 5 = 15.
Simplify 2(x - 4) + 3.
2x - 8
2x - 1
2x - 5
2x + 11
Distribute then combine: 2x - 8 + 3 = 2x - 5.
Evaluate sin(30°).
?2/2
1/2
1
?3/2
The sine of 30 degrees is 1/2.
Convert binary 1010 to decimal.
12
10
8
5
Binary 1010 = 1×8 + 0×4 + 1×2 + 0×1 = 10.
A circle has radius 3. What is its area in terms of ??
9?
3?
6?
?
Area of a circle = ?r² = ?×3² = 9?.
Solve x + y = 5 and x - y = 1. What is x?
4
3
2
1
Adding gives 2x = 6 so x = 3.
What is the median of {3, 1, 4, 2, 5}?
3
2
1
4
Order the data {1,2,3,4,5}, the middle value is 3.
Solve x² - 5x + 6 = 0.
{1, 6}
{-1, -6}
{-2, -3}
{2, 3}
Factorise to (x-2)(x-3)=0 giving solutions x=2 or x=3.
What is the derivative of f(x) = x³ at x = 2?
12
4
8
6
f?(x)=3x² so at x=2, f?(2)=3×4=12.
Compute ? 2x dx.
x + C
x² + C
2x² + C
½ x² + C
Integral of 2x is x² plus constant.
Expand (x + 2)².
x² + 2x + 4
x² + 2x + 2
x² + 4x + 4
x² + x + 2
Binomial expansion: a² + 2ab + b² = x² + 2×x×2 + 4.
Solve |x - 3| = 5.
x = -8 or x = 2
x = -8 or x = -2
x = 8 or x = -2
x = 8 or x = 2
Absolute value gives x - 3 = ±5, so x = 8 or x = -2.
What is log?? 1000?
100
2
10
3
10³ = 1000, so log base 10 of 1000 is 3.
Solve 1/x = 2.
2
-1/2
1/2
-2
Reciprocate both sides: x = 1/2.
What is sin²? + cos²? equal to?
0
1
2
sin2?
The Pythagorean identity states sin²? + cos²? = 1.
In a right triangle, one acute angle is 30°. What is the other acute angle?
45°
60°
90°
30°
The angles sum to 180°, and one is 90°, so the remaining 90° split as 30° + 60°.
What is the sum of the geometric series 1 + 2 + 4 + 8 + 16?
31
32
16
30
Sum is (2? - 1)/(2 - 1) = (32 - 1)/1 = 31.
Solve 3x - 2y = 6 for y.
y = (3x - 6)/2
y = (2y - 6)/3
y = (6 - 3x)/2
y = (3x + 6)/2
Rearrange: 2y = 3x - 6, so y = (3x - 6)/2.
What is the determinant of the matrix [[1,2],[3,4]]?
-5
-2
1
2
Determinant = 1×4 - 2×3 = 4 - 6 = -2.
How many non-negative integer solutions are there to x + y + z = 10?
45
55
120
66
Using stars and bars, the count is C(10+3-1, 3-1) = C(12,2) = 66.
Evaluate the integral ??¹ x² dx.
1/4
2/3
1/3
1/2
Integral x³/3 from 0 to 1 gives (1³/3) - 0 = 1/3.
Compute (e^{i?/3})?.
-1
1
-i
i
(e^{i?/3})? = e^{i2?} = 1 by Euler's formula.
Find the sum of the infinite series ????? (1/2)?.
2
1
?
1/2
Sum is a/(1-r) with a=1/2 and r=1/2: (1/2)/(1/2)=1.
What is the derivative of f(x) = arctan(x)?
1/x² + 1
x/(1 + x²)
1/(1 + x²)
-1/(1 + x²)
The derivative of arctan(x) is 1/(1 + x²).
0
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Study Outcomes

  1. Apply effective problem-solving strategies -

    Use PAT practice questions to develop systematic approaches for solving algebra, geometry, and calculus problems commonly found in PAT questions.

  2. Analyze common question patterns -

    Identify recurring question types from PAT past papers and example of PAT challenges to recognize patterns and streamline your study focus.

  3. Practice under exam-like conditions -

    Engage with timed quizzes to enhance time management and accuracy, mirroring the pressure of the actual PAT exam.

  4. Evaluate your performance -

    Review detailed feedback on your quiz results to spot strengths and weaknesses and tailor your study plan accordingly.

  5. Master complex mathematical concepts -

    Build confidence in advanced topics by working through representative sample problems drawn from real PAT questions.

Cheat Sheet

  1. Algebraic Manipulation & Factorisation -

    Mastering expansion, factorisation and simplifying rational expressions is key for many pat questions; practice decomposing quadratics and common factors to avoid algebraic errors. Techniques like grouping and the difference of squares (a² - b²=(a - b)(a+b)) frequently appear in pat practice questions. Consistent drills from University of Oxford's official PAT past papers build both speed and accuracy.

  2. Quadratic Equations & Discriminant Analysis -

    Understanding the discriminant (Δ=b² - 4ac) helps predict the nature of roots without solving the equation fully, a tip highlighted in many example of PAT solutions. Use the quadratic formula x=( - b±√Δ)/(2a) and memorize completing-the-square steps to tackle tougher questions. Reviewing past papers shows this technique cuts down on calculation time and errors.

  3. Coordinate Geometry & Line Equations -

    Familiarize yourself with distance √[(x₂ - x₝)²+(y₂ - y₝)²], midpoint ((x₝+x₂)/2,(y₝+y₂)/2) and gradient m=(y₂ - y₝)/(x₂ - x₝) formulas - these form the backbone of many pat questions. Practice sketching lines and circles from pat past papers to strengthen spatial reasoning. A clear diagram and labeling each point boosts confidence under timed conditions.

  4. Trigonometric Identities & Angle-Solving Techniques -

    Keep SOHCAHTOA handy for basic ratios and learn addition formulas like sin(A±B)=sinA cosB±cosA sinB to simplify complex angles in pat practice questions. Visualizing angles on the unit circle, as recommended by Cambridge University resources, reduces sign errors. Regularly solving example of PAT trig problems ensures these identities become second nature.

  5. Series & Binomial Expansion -

    Master arithmetic and geometric series formulas - S_n=n/2(2a+(n - 1)d) and S_n=a(1 - r^n)/(1 - r) - to answer sequence questions swiftly. The binomial theorem (a+b)^n=Σₖ₌₀❿ C(n,k)a^{n - k}b^k shows up in algebraic expansions on pat questions; memorize small-n cases and Pascal's triangle for quick coefficients. Drilling pat past papers reveals common patterns and boosts calculation speed.

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