University Clinical Aptitude Test (UCAT) Quantitative Reasoning Syllabus

Quantitative Reasoning syllabus — full chapter and topic list

Expand any chapter to see its topics and sub-topics. This is the whole examinable outline for Quantitative Reasoning in University Clinical Aptitude Test (UCAT), not a summary of it.

1. 1

   Subtest Foundations

   3 topics

   • Format and Timing
     • Item count, question sets, and pacing
     • Stand-alone versus shared-data items
   • On-Screen Calculator Skills
     • Efficient keypad and memory function use
     • When mental estimation beats the calculator
   • Estimation and Sense-Checking
     • Approximating before computing
     • Catching unreasonable answers
2. 2

   Core Numeracy

   3 topics

   • Arithmetic and Number
     • Order of operations and rounding
     • Fractions, decimals, and conversions
   • Ratio and Proportion
     • Sharing in a given ratio
     • Direct and inverse proportion
   • Percentages
     • Percentage change, increase, and decrease
     • Reverse percentages and compound change
3. 3

   Rates, Units, and Measures

   3 topics

   • Speed, Distance, and Time
     • Average speed calculations
     • Multi-leg journey problems
   • Unit Conversion
     • Metric and imperial conversions
     • Currency and exchange-rate problems
   • Rates of Consumption
     • Fuel, dosage, and usage rates
     • Work-rate and combined-rate problems
4. 4

   Data Interpretation

   3 topics

   • Tables and Charts
     • Reading bar, line, and pie charts
     • Multi-source data combination
   • Averages and Spread
     • Mean, median, and mode
     • Range and simple interpretation
   • Trends and Projections
     • Extrapolating from trends
     • Identifying anomalies in data
5. 5

   Geometry and Algebra Applications

   3 topics

   • Area, Perimeter, and Volume
     • Composite shape calculations
     • Scaling and real-world dimensions
   • Algebraic Manipulation
     • Rearranging and solving simple equations
     • Formula substitution
   • Applied Word Problems
     • Translating context into equations
     • Multi-step real-world calculations

Quantitative Reasoning flashcards for University Clinical Aptitude Test (UCAT)

25 of 51 cards from the Quantitative Reasoning deck — real questions with worked answers.

1. In the UCAT Quantitative Reasoning subtest, how many questions are there and how much time is allowed (excluding instruction time)?

   There are 36 questions to be answered in 25 minutes, which works out to roughly $\frac{25 \times 60}{36} \approx 40$ seconds per question.

2. How are UCAT Quantitative Reasoning questions structured around the data presented?

   They are grouped into sets, typically of 4 questions each linked to a shared piece of data (a table, chart, graph, or scenario). There are usually 9 such sets making up the 36 questions.

3. What two on-screen tools are provided to help you in the UCAT Quantitative Reasoning subtest?

   A basic on-screen calculator (operated by mouse or numeric keypad) and a laminated whiteboard/noteboard with a pen for rough working.

4. Why is the UCAT on-screen calculator considered a potential time trap, and what is the recommended strategy?

   It is a simple four-function calculator that is slow to click; relying on it for every step wastes time. The strategy is to do simple arithmetic and estimation mentally or on the whiteboard, reserving the calculator for genuinely complex calculations.

5. Which keyboard shortcut speeds up entering numbers into the UCAT calculator, and what useful memory feature does it have?

   You can type digits using the numeric keypad (Num Lock on) rather than clicking. It has a memory function with M+ (add to memory), M- (subtract from memory), MR (recall) and MRC (recall/clear) keys to store intermediate results.

6. What is the value of estimation and sense-checking in UCAT Quantitative Reasoning?

   Estimating lets you eliminate implausible answer options quickly and verify that a calculated answer is the right order of magnitude, catching slips such as misplaced decimal points before committing.

7. Describe a quick way to estimate a percentage like 19% of 412.

   Round to convenient numbers: $19\% \approx 20\%$ and $412 \approx 400$, so $0.20 \times 400 = 80$. The true value is slightly less, about $78$, confirming the order of magnitude.

8. State the standard order of operations used in arithmetic (the BIDMAS/BODMAS rule).

   Brackets, Indices (powers/roots), Division and Multiplication (left to right), then Addition and Subtraction (left to right).

9. How do you convert a fraction such as $\frac{3}{8}$ into a percentage?

   Divide numerator by denominator and multiply by 100: $\frac{3}{8} = 0.375$, so $0.375 \times 100 = 37.5\%$.

10. What is a ratio, and what does it mean to express a ratio in its simplest form?

    A ratio compares two or more quantities of the same kind, e.g. $a:b$. Simplest form means dividing all parts by their highest common factor so the terms are the smallest possible whole numbers, e.g. $12:18 = 2:3$.

11. To divide a quantity in a given ratio (e.g. share £200 in the ratio $3:5$), what is the process?

    Add the parts to get the total number of shares ($3+5=8$), divide the quantity by the total ($200 \div 8 = 25$ per share), then multiply by each part: $3 \times 25 = £75$ and $5 \times 25 = £125$.

12. What is the difference between direct proportion and inverse proportion?

    In direct proportion, as one quantity increases the other increases by the same factor ($y = kx$). In inverse proportion, as one increases the other decreases proportionally ($y = \frac{k}{x}$, so their product stays constant).

13. How do you solve a direct-proportion problem, e.g. 5 items cost £40, find the cost of 8 items?

    Find the unit value then scale: cost per item $= \frac{40}{5} = £8$, so 8 items cost $8 \times 8 = £64$.

14. How do you calculate a percentage increase or decrease from an original value to a new value?

    $$\text{percentage change} = \frac{\text{new} - \text{original}}{\text{original}} \times 100$$ A positive result is an increase, a negative result a decrease.

15. To increase a quantity by 15% or decrease it by 15% using a multiplier, what multipliers do you use?

    Multiply by $1.15$ to increase by 15%, and by $0.85$ to decrease by 15% (since $1 + 0.15$ and $1 - 0.15$).

16. How do you reverse a percentage change to find an original value (e.g. a price of £90 after a 10% discount)?

    Divide by the multiplier, not subtract. £90 represents 90% of the original, so original $= \frac{90}{0.90} = £100$.

17. How do you combine two successive percentage changes, e.g. a 20% rise followed by a 10% fall?

    Multiply the multipliers: $1.20 \times 0.90 = 1.08$, an overall increase of 8%. They are not simply added or subtracted.

18. State the formula linking speed, distance and time, and its two rearrangements.

    $$\text{speed} = \frac{\text{distance}}{\text{time}}$$ Rearranged: $\text{distance} = \text{speed} \times \text{time}$ and $\text{time} = \frac{\text{distance}}{\text{speed}}$.

19. A car travels 150 km in 2 hours 30 minutes. What is its average speed in km/h?

    Convert time to hours: $2\text{ h }30\text{ min} = 2.5$ h. Speed $= \frac{150}{2.5} = 60$ km/h.

20. How do you convert a speed of 72 km/h into metres per second?

    Multiply by $\frac{1000}{3600} = \frac{5}{18}$: $72 \times \frac{5}{18} = 20$ m/s.

21. List the common metric prefixes and their factors for kilo, centi, milli, and micro.

    kilo $= 10^{3}$, centi $= 10^{-2}$, milli $= 10^{-3}$, micro $= 10^{-6}$. So 1 km $= 1000$ m, 1 cm $= 0.01$ m, 1 mm $= 0.001$ m.

22. How many millilitres are in a litre, and how many grams in a kilogram?

    $1$ litre $= 1000$ mL and $1$ kg $= 1000$ g.

23. How do you convert an area from $\text{m}^2$ to $\text{cm}^2$?

    Since $1$ m $= 100$ cm, area scales by the square: $1\text{ m}^2 = 100^2 = 10{,}000\text{ cm}^2$. Multiply the area in $\text{m}^2$ by $10{,}000$.

24. In a rates-of-consumption problem, how do you find how long a supply lasts (e.g. a 600 L tank used at 25 L per hour)?

    Divide the total amount by the rate of use: $\frac{600}{25} = 24$ hours.

25. If a machine produces 18 units per minute, how many units does it produce in 2.5 hours?

    Convert time to minutes and multiply: $2.5 \times 60 = 150$ minutes, then $18 \times 150 = 2700$ units.

See more Quantitative Reasoning flashcards →

Planning Quantitative Reasoning for University Clinical Aptitude Test (UCAT)

Quantitative Reasoning (University Clinical Aptitude Test (UCAT)) FAQ