ESAT practice questions with worked solutions

Try these original ESAT-style questions. The real pace is about 1.5 minutes per question.

Mathematics 1

1. 3x + 2y = 12 and x − y = −1. What is x?
A) 1 B) 2 C) 3 D) 4 E) 5

Solution

From the second equation x = y − 1. Substituting: 3(y − 1) + 2y = 12, so 5y = 15 and y = 3, giving x = 2. Answer B.

2. A price is reduced by 20%, and the new price is then increased by 20%. What is the overall change?
A) no change B) 4% decrease C) 4% increase D) 2% decrease E) 40% decrease

Solution

Multiply the scale factors: 0.8 × 1.2 = 0.96, which is a 4% decrease. Answer B.

Mathematics 2

3. The curve y = x³ − 6x² + 9x has stationary points. At which value of x is there a local maximum?
A) x = 0 B) x = 1 C) x = 2 D) x = 3 E) there is none

Solution

dy/dx = 3x² − 12x + 9 = 3(x − 1)(x − 3), so the stationary points are at x = 1 and x = 3. The second derivative 6x − 12 equals −6 at x = 1, which is negative, so x = 1 is the local maximum. Answer B.

Physics

4. A ball is dropped from rest and falls 20 m. Taking g = 10 m s⁻² and ignoring air resistance, how fast is it moving when it lands?
A) 10 m/s B) 14 m/s C) 20 m/s D) 40 m/s E) 200 m/s

Solution

Use v² = u² + 2as = 0 + 2 × 10 × 20 = 400, so v = 20 m/s. Answer C.

5. A 6 Ω resistor and a 3 Ω resistor are connected in parallel across a 12 V supply. What current flows from the supply?
A) 1.3 A B) 2 A C) 4 A D) 6 A E) 36 A

Solution

The combined resistance is (6 × 3) / (6 + 3) = 2 Ω, so I = V / R = 12 / 2 = 6 A. Answer D.

Chemistry

6. How many moles are in 4.0 g of sodium hydroxide, NaOH? (Relative atomic masses: Na = 23, O = 16, H = 1)
A) 0.01 B) 0.1 C) 0.4 D) 1 E) 10

Solution

Mr of NaOH = 23 + 16 + 1 = 40, so moles = 4.0 / 40 = 0.1. Answer B.

Practise every topic

Chick Run ESAT organises its question bank by the official specification codes (M1–M7, MM1–MM8, P1–P7, C1–C17, B1–B11), so you can practise any single topic, with diagrams for geometry questions and a worked solution for every question.

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FAQ

What topics are in ESAT Mathematics 1?

Mathematics 1 covers units, number, ratio and proportion, algebra, geometry, statistics and probability, at roughly GCSE higher level, and it is taken by almost every ESAT candidate.

What is in ESAT Mathematics 2?

Mathematics 2 covers further algebra and functions, sequences, coordinate geometry, trigonometry, exponentials and logarithms, and differentiation and integration, at roughly AS and A-level standard.

Can I use a calculator in the ESAT?

No. Calculators are not allowed in any ESAT module.

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