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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

Ready to supercharge your PAT Maths performance? Our Ace Your PAT Maths: Free Practice Questions Quiz is designed to help prospective test-takers like you sharpen critical skills, from algebra puzzles to data interpretation. Challenge yourself with authentic pat questions to gauge your strengths and reveal areas for improvement. Dive into pat practice questions that mirror real pat past papers and gain insight into the structure and style of actual exam items. Explore a sample PAT questions session or boost your fundamentals with our algebra refresher . Tackle every example of pat and build the confidence you need - start now!

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. Order of operations
Evaluate 9?.
0
Undefined
1
9
Any nonzero number raised to the power of zero equals 1. Exponents rules
Solve for x: 5x = 20.
15
5
4
1
Divide both sides by 5: x = 20/5 = 4. Solving linear equations
What is the decimal form of 1/2?
0.2
0.25
0.5
2
Divide numerator by denominator: 1 ÷ 2 = 0.5. Fractions to decimals
What is 10% of 200?
50
10
20
2
10% means 10/100 of 200, which is 200 × 0.1 = 20. Percent calculations
Expand 3(x + 2).
x + 6
3x + 6
9x + 6
3x + 2
Distribute 3: 3×x + 3×2 = 3x + 6. Distributive law
What is the greatest common divisor of 12 and 18?
6
2
12
3
The largest integer dividing both 12 and 18 is 6. GCD explanation
Convert 100 cm to meters.
0.1
10
1
0.01
There are 100 cm in a meter, so 100 cm equals 1 m. Unit conversion
What is 7 × 8?
49
54
56
63
Standard multiplication: 7 times 8 equals 56. Multiplication basics
Solve for y: y - 4 = 10.
-6
14
4
6
Add 4 to both sides: y = 10 + 4 = 14. Solving linear equations
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. Square properties
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. Mean calculation
Solve x² = 49.
0
-7
±7
7
Taking square roots gives x = 7 or x = - 7. Square root solutions
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. Laws of exponents
Solve 2x + 3 = 11.
4
3
8
7
Subtract 3 then divide by 2: x = (11 - 3)/2 = 4. Linear equations
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). Difference of squares
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. Gradient of a line
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. Triangle area formula
Simplify 2(x - 4) + 3.
2x - 8
2x - 1
2x - 5
2x + 11
Distribute then combine: 2x - 8 + 3 = 2x - 5. Distributive law
Evaluate sin(30°).
?2/2
1/2
1
?3/2
The sine of 30 degrees is 1/2. Trigonometric values
Convert binary 1010 to decimal.
12
10
8
5
Binary 1010 = 1×8 + 0×4 + 1×2 + 0×1 = 10. Binary conversion
A circle has radius 3. What is its area in terms of ??
9?
3?
6?
?
Area of a circle = ?r² = ?×3² = 9?. Circle area formula
Solve x + y = 5 and x - y = 1. What is x?
4
3
2
1
Adding gives 2x = 6 so x = 3. Simultaneous equations
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. Median definition
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. Quadratic equations
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. Derivative basics
Compute ? 2x dx.
x + C
x² + C
2x² + C
½ x² + C
Integral of 2x is x² plus constant. Integration basics
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. Binomial theorem
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. Absolute value equations
What is log?? 1000?
100
2
10
3
10³ = 1000, so log base 10 of 1000 is 3. Logarithm rules
Solve 1/x = 2.
2
-1/2
1/2
-2
Reciprocate both sides: x = 1/2. Reciprocal equations
What is sin²? + cos²? equal to?
0
1
2
sin2?
The Pythagorean identity states sin²? + cos²? = 1. Trig identities
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°. Right triangle angles
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. Geometric series
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. Rearranging formulas
What is the determinant of the matrix [[1,2],[3,4]]?
-5
-2
1
2
Determinant = 1×4 - 2×3 = 4 - 6 = -2. Matrix determinant
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. Stars and bars method
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. Definite integrals
Compute (e^{i?/3})?.
-1
1
-i
i
(e^{i?/3})? = e^{i2?} = 1 by Euler's formula. 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. Infinite geometric series
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). Inverse trig derivatives
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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