DP IB Maths: AA SL

Topic Questions

3.1 Geometry Toolkit

1a
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2 marks

ABCD is an isosceles trapezoid where AB equals 17 space straight m and AD equals BC equals 25 space straight m, as shown in the diagram below.

q1a-3-1-medium-ib-ai-sl-maths

Find the height, h, of the trapezoid.

1b
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4 marks

Find the area of the trapezoid.

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2
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3 marks

The distance between Ho Chi Minh City and Hong Kong is known to be 1500 km. The bearing of Hong Kong from Ho Chi Minh City is 046°. Another city, Brisbane, is 6500 km from Ho Chi Minh City on a bearing of 136°. Calculate the distance between Hong Kong and Brisbane.

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3a
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2 marks

Point straight A has coordinates left parenthesis 4 comma negative 6 right parenthesis and point straight B has coordinates space left parenthesis 8 comma 6 right parenthesis.

Calculate the distance of the line segment AB.

3b
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2 marks

Find the equation of the line connecting points straight A and straight B.

Give your answer in the form y equals m x plus c.

3c
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4 marks
(i)
Find the midpoint of open square brackets AB close square brackets.

(ii)
Find the equation of the perpendicular bisector to the line segment AB.
Give your answer in the form y equals m x plus c.

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4a
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3 marks

The diagram below shows a circle with a 68 degree sector cut from it. The radius of the circle is 5 space cm.

q4a-3-1-medium-ib-ai-sl-maths

Find the length of

(i)
the minor arc AB

(ii)
the major arc AB.
4b
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3 marks

Find the area of the shaded region.

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5a
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4 marks

A lawn sprinkler sprays water over a lawn covering an arc of 160 degree with a maximum spray distance of x m as shown in the diagram below. The lawn sprinkler waters 20 space straight m squared of the lawn.

q5a-3-1-medium-ib-ai-sl-maths

Calculate the value of x.

5b
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3 marks

Calculate the length of the outer arc.

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6a
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4 marks

A windscreen wiper blade is 0.8 space straight m spacelong. When in motion the blade moves through an arc of theta degree and wipes an area of 4 over 15 pi straight m squared.

q6a-3-1-medium-ib-ai-sl-maths

Calculate the value of theta.

6b
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3 marks

Calculate the length travelled by the outer edge of the blade.

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7a
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3 marks

The diagram below shows a dirt racetrack where the straights are 426 space straight m long and the longest distance from one end of the track to the other is 554 straight m.

q7a-3-1-medium-ib-ai-sl-maths

Find the total distance around the racetrack.

7b
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4 marks

Find the total area enclosed by the racetrack.

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8a
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2 marks

The diagram below shows a cookie cutter in the shape of a heart constructed from a triangle and two identical semi circles. The height of the triangle is 8 and its base AB is 13.34 space cm.

q8a-3-1-medium-ib-ai-sl-maths

Find the length of the line AC.

8b
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4 marks

Calculate the total area of the heart.

8c
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2 marks

Bob makes some cookie dough and rolls it out on his kitchen bench. The cookie dough covers 1314 space cm squared.

Find the number of full cookies Bob can cut from the dough.

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9a
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3 marks

The diagram below shows a slice of pizza that forms a sector of a circle with an arc of 60 degree and radius of 15 space cm. The width of the crust is 2.2 space cm.

q9a-3-1-medium-ib-ai-sl-maths

Find the perimeter of the slice of pizza.

9b
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3 marks

Find the area of the crust.

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10a
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2 marks

The diagram below shows an architect’s drawing of the front view of a house. The house is in the shape of a rectangle with a height of 10.8 m and has a roof in the shape of a right-angled isosceles triangle, BCD. BD equals 12.2 space straight m, angle straight B straight C with hat on top straight D space equals space 90 degree. Next to the house is a garage in the shape of a rectangle measuring 4 space straight m cross times 3.6 space straight m with a roof in the shape of a right-angled triangle with a base, GF, of 4 space straight m and angle straight E straight F with hat on top straight G equals 37 degree

q10a-3-1-medium-ib-ai-sl-maths

Find the length of

(i)
EG

(ii)
BC.
10b
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6 marks

Find the total area of the front view of the house.

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