Unit notes and practice questions
Everything here is for unit 5 of the Grade 10 Mathematics textbook: what the chapter covers, the short notes, practice questions with their answers, and the lesson video where one exists.
The cards filed under this chapter on the Grade 10 Mathematics page. Open one at a time.
When you use it
Use this formula when two chords intersect inside a circle to find the angle formed from their intercepted arcs.
Watch out
Add the two intercepted arcs together, do not subtract them.
Drafted from Grade 10 Mathematics, pages 238-271, then checked twice before it went up
When you use it
Use this formula to calculate the length of a circular arc when the radius and the central angle in degrees are known.
Watch out
Ensure the angle theta is the central angle in degrees before dividing by 360 degrees.
Drafted from Grade 10 Mathematics, pages 238-271, then checked twice before it went up
When you use it
Use this formula to find the area of a circle sector bounded by two radii and an arc.
Watch out
Do not square the product of pi and r, only the radius r is squared.
Drafted from Grade 10 Mathematics, pages 238-271, then checked twice before it went up
When you use it
Use this formula to calculate the length of a chord subtended by a central angle theta.
Watch out
Divide the angle theta by 2 before evaluating the sine function.
Drafted from Grade 10 Mathematics, pages 238-271, then checked twice before it went up
When you use it
Reach for this reminder whenever asked to calculate the perimeter of a circular sector.
Watch out
Calculating only the arc length gives the wrong answer. The perimeter of a sector must include both straight edges, P = s + 2r.
Drafted from Grade 10 Mathematics, pages 238-271, then checked twice before it went up
10 multiple-choice questions written against this chapter, each with its answer and the reason. Try one before you open the answer.
Question 1
A circle is the set of points in a plane that are all the same distance from one fixed point. What is this fixed point called?
Answer: B center
Why
The fixed point is called the center of the circle. The constant distance from the center is the radius.
Question 2
How many lines of symmetry does a circle have?
Answer: D infinite
Why
A circle has infinite lines of symmetry. Any diameter of a circle is a line of symmetry, and a circle has infinitely many diameters.
Question 3
A circular plot of teff in Bahir Dar has radius 7 m. Using π = 22/7, what is the perimeter of the plot?
Answer: B 44 m
Why
The perimeter of a circle is P = 2πr.
P = 2 × (22/7) × 7 = 44 m.
Question 4
A line is drawn from the center O of a circle, perpendicular to a chord AB. The line meets AB at N. What does this line do to the chord AB?
Answer: A It cuts AB into two equal parts, so AN = NB.
Why
Theorem 5.2 says that a line drawn from the center perpendicular to a chord bisects the chord. This means it cuts the chord into two equal parts, so AN = NB.
Question 5
In a circle, an inscribed angle and a central angle both cover the same arc. The inscribed angle is 35°. What is the central angle?
Answer: C 70°
Why
Theorem 5.6 says the inscribed angle is half of the central angle. So the central angle is twice the inscribed angle.
Central angle = 2 × 35° = 70°.
Question 6
A chord AB of a circle with radius 10 cm is 16 cm long. What is the distance from the center of the circle to the chord?
Answer: A 6 cm
Why
The perpendicular from the center cuts the chord in half, so MB = 8 cm. Use the right triangle OMB, where OB is the radius.
OM = √(OB² − MB²) = √(10² − 8²) = √(100 − 64) = √36 = 6 cm.
Question 7
A sector of a circular garden in Addis Ababa has radius 6 m and a central angle of 210°. Using π = 22/7, what is the area of the sector?
Answer: B 66 m<sup>2</sup>
Why
The area of a sector is A = πr² × (θ/360°).
A = (22/7) × 6² × (210/360) = (22/7) × 36 × (7/12) = 66 m2.
Question 8
AB is the diameter of a circle. C is another point on the circle, so triangle ABC is formed. Angle ABC = 55°. What is angle BAC?
Answer: C 35°
Why
An angle in a semicircle is a right angle (Thales' Theorem). So angle ACB = 90°.
The angles of a triangle add up to 180°, so angle BAC = 180° − 90° − 55° = 35°.
Question 9
The four angles of a cyclic quadrilateral are (4y + 2)°, (y + 20)°, (5y − 2)° and 7y°. What is the value of y?
Answer: B 20
Why
The four angles of a cyclic quadrilateral add up to 360°.
(4y + 2) + (y + 20) + (5y − 2) + 7y = 360
17y + 20 = 360
17y = 340
y = 20.
Question 10
A chord of a circle with radius 6 cm subtends a central angle of 120°. What is the length of the chord?
Answer: B 6√3 cm
Why
The chord length is 2r sin(θ/2).
Chord = 2 × 6 × sin(60°) = 12 × (√3/2) = 6√3 cm.
The app holds 12 questions on this unit, marked as you go. These are the first 10.
Unit 5 runs from page 237 to page 270 of the Ministry of Education edition.
Ministry of Education edition, English, 373 pages
Temari turns this chapter into timed practice and marks it as you go, with an AI tutor to explain anything that did not land.
Start free
Temari.et is also an Android app, free on Google Play.
