Engineering and Science Admissions Test

ESAT Maths 1 Units questions

2 original ESAT Maths 1 units questions in the real exam style, each with a step-by-step worked solution and an explanation of why the tempting wrong answers are wrong. Try each one before opening the solution.

Methods on this page: Average speed = total distance ÷ total time

Question 1ESAT Maths 1Standard

A training session repeats this 3-part routine several times:

Walk

400\ \text{m}

at an average speed of

24\ \text{km h}^{-1}

Jog

100\ \text{m}

at an average speed of

4\ \text{km h}^{-1}

Run

100\ \text{m}

at an average speed of

12\ \text{km h}^{-1}

What is the average speed for the whole session, in

\text{km h}^{-1}

A $10$
B $11$
C $12$
D $13$
E $\dfrac{40}{3}$
F $14$
G $15$
H $\dfrac{56}{3}$

Show the answer and worked solution

Answer: C · Method: Average speed = total distance ÷ total time

Total distance: $600\ \text{m} = \dfrac{3}{5}\ \text{km}$ .
Total time: $\tfrac{0.4}{24} + \tfrac{0.1}{4} + \tfrac{0.1}{12} = \dfrac{1}{20}$ hours.
Average speed $= \dfrac{3}{5} \div \dfrac{1}{20} = 12\ \text{km h}^{-1}$ .

Why the tempting wrong answers are wrong

E: You can't average the speeds: each part takes a different amount of time.
H: Weighting the speeds by distance still isn't right. Find the total time.

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Question 2ESAT Maths 1Standard

A training session repeats this 2-part routine several times:

Walk

300\ \text{m}

at an average speed of

12\ \text{km h}^{-1}

Jog

600\ \text{m}

at an average speed of

6\ \text{km h}^{-1}

What is the average speed for the whole session, in

\text{km h}^{-1}

A $6.2$
B $7.2$
C $8$
D $\dfrac{41}{5}$
E $9$
F $\dfrac{46}{5}$

Show the answer and worked solution

Answer: B · Method: Average speed = total distance ÷ total time

Total distance: $900\ \text{m} = \dfrac{9}{10}\ \text{km}$ .
Total time: $\tfrac{0.3}{12} + \tfrac{0.6}{6} = \dfrac{1}{8}$ hours.
Average speed $= \dfrac{9}{10} \div \dfrac{1}{8} = 7.2\ \text{km h}^{-1}$ .

Why the tempting wrong answers are wrong

C: Weighting the speeds by distance still isn't right. Find the total time.
E: You can't average the speeds: each part takes a different amount of time.

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ESAT Maths 1 Units questions

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