Practice ECAT Mathematics questions with answers and explanations.
Choose an option to check your answer.
Equal sides in an isosceles triangle face equal angles.
This is the base-angle theorem.
Choose an option to check your answer.
Corresponding angles between parallel lines are equal.
Therefore, the other angle is also 110°.
Choose an option to check your answer.
The path forms a right triangle with legs 5 and 12.
By Pythagoras, distance is √(25 + 144) = 13 km.
Choose an option to check your answer.
When multiplying powers with the same base, add the exponents.
Thus, a³ × a⁵ = a⁸.
Choose an option to check your answer.
The first part takes 2 hours and the second takes 1 hour.
The total travel time is 3 hours.
Choose an option to check your answer.
When dividing powers with the same base, subtract the exponents.
Thus, x⁷ ÷ x³ = x⁴.
Choose an option to check your answer.
The speed is 90 × 5/18 = 25 m/s, so total distance is 25 × 24 = 600 m.
Subtracting the train length gives a bridge length of 400 m.
Choose an option to check your answer.
Square the coefficient and multiply the exponent by 2.
This gives 2²a⁶ = 4a⁶.
Choose an option to check your answer.
Downwind speed is 300 km/h and upwind speed is 200 km/h.
Wind speed is half their difference: 50 km/h.
Choose an option to check your answer.
Subtract 7 from both sides of the equation.
This gives x = 19 - 7 = 12.
Choose an option to check your answer.
Divide both sides by the coefficient 3.
Thus, x = 27 ÷ 3 = 9.
Choose an option to check your answer.
Subtract 5 to get 2x = 12.
Dividing by 2 gives x = 6.
