ESAT (Engineering and Science Admissions Test) · Mathematics 1

Geometry

13 practice questions, each with the answer and an explanation.

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A right-angled triangle has hypotenuse $26$ cm and one other side $10$ cm. What is its area?
In triangle $A B C$ , $A B = 7$ cm, $A C = 8$ cm and angle $A = 6 0^{\circ}$ . What is $B C^{2}$ ?
The point $A$ is $(1, 2)$ and $B$ is $(7, 10)$ . What is the length of $A B$ ?
Triangles $A B C$ and $P QR$ are similar with $A B = 6$ cm corresponding to $P Q = 9$ cm. The area of $A B C$ is $20 cm^{2}$ . What is the area of $P QR$ ?
Line $L_{1}$ has equation $y = 3 x - 2$ . Line $L_{2}$ is perpendicular to $L_{1}$ and passes through $(6, 1)$ . Where does $L_{2}$ cross the $y$ -axis?
Triangle $A B C$ has a right angle at $B$ , $A B = 9$ and $tan A = \frac{4}{3}$ . What is $B C$ ?
Each interior angle of a regular polygon is $15 6^{\circ}$ . How many sides does the polygon have?
A circle has circumference $10 π$ cm. What is the area of a sector of this circle with angle $7 2^{\circ}$ ?
A sphere of radius $3$ cm is melted and recast into a cylinder of radius $3$ cm. What is the height of the cylinder?
A ladder $5.0$ m long leans against a vertical wall with its foot $1.4$ m from the wall. How high up the wall does it reach?
A cone has base radius $6$ cm and slant height $10$ cm. What is its curved surface area? (Curved surface area of a cone $= π r l$ .)
The angle between a tangent and a chord at the point of contact is $5 0^{\circ}$ . What angle does that chord subtend at the circumference in the alternate segment?
A circle has equation $(x - 3)^{2} + (y + 4)^{2} = 25$ . Which of these points lies on the circle?

Geometry

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