IB Maths AA SL/Question Bank/3 Geometry and trigonometry

IB Maths AA SL 3 Geometry and trigonometry Question Bank

SL239 questions10 previewsSyllabus linked

[Maximum number: 6]

The following diagram shows triangle ABC .
$\mathrm{AB}=7 \mathrm{~cm}, \mathrm{BC}=9 \mathrm{~cm}$ and $\mathrm{A} \hat{\mathrm{B}} \mathrm{C}=120^{\circ}$ .

(a)

Find AC .

[ 3 ]

(b)

Find $\mathrm{B} \hat{\mathrm{A}} \mathrm{C}$ .

[ 3 ]

[Maximum number: 6]

The following diagram shows $\triangle \mathrm{PQR}$ , where $\mathrm{RQ}=9 \mathrm{~cm}, \mathrm{P} \hat{\mathrm{R}} \mathrm{Q}=70^{\circ}$ and $\mathrm{P} \hat{\mathrm{Q}} \mathrm{R}=45^{\circ}$ .

diagram not to scale

(a)

Find $\mathrm{R} \hat{\mathrm{P}} \mathrm{Q}$ .

[ 1 ]

(b)

Find PR.

[ 3 ]

(c)

Find the area of $\triangle \mathrm{PQR}$ .

[ 2 ]

[Maximum number: 5]

In the following diagram, $\overrightarrow{\mathrm{OP}}=\boldsymbol{p}, \overrightarrow{\mathrm{OQ}}=\boldsymbol{q}$ and $\overrightarrow{\mathrm{PT}}=\frac{1}{2} \overrightarrow{\mathrm{PQ}}$ .

Express each of the following vectors in terms of p and q,

(a)

$\overrightarrow{\mathrm{QP}}$ ;

[ 2 ]

(b)

$\overrightarrow{\mathrm{OT}}$ .

[ 3 ]

[Maximum number: 6]

Consider the vectors $\boldsymbol{a}=\binom{2}{-3}$ and $\boldsymbol{b}=\binom{1}{4}$ .

(a)

Find

[ 4 ]

(i)

2 a+b;

(ii)

$|2 \boldsymbol{a}+\boldsymbol{b}|$ .

Let 2 a+b+c=0, where 0 is the zero vector.

[ 4 ]

(b)

Find c.

[ 2 ]

[Maximum number: 10]

The following diagram shows a circle with centre O and radius 5 cm .

The points A, B and C lie on the circumference of the circle, and $\mathrm{A} \hat{\mathrm{O}} \mathrm{C}=0.7$ radians.

(a)

(i)

Find the length of the arc ABC .

[ 4 ]

(ii)

Find the perimeter of the shaded sector.

[ 4 ]

(b)

Find the area of the shaded sector.

[ 2 ]

[Maximum number: 6]

The following diagram shows triangle ABC .

\mathrm{AB}=6 \mathrm{~cm}, \mathrm{BC}=10 \mathrm{~cm}, \text { and } \mathrm{A} \hat{\mathrm{~B}} \mathrm{C}=100^{\circ}

(a)

Find AC.

[ 3 ]

(b)

Find $B \hat{C} A$ .

[ 3 ]

[Maximum number: 5]

The following diagram shows a right-angled triangle, ABC , where $\sin A=\frac{5}{13}$ .

(a)

Show that $\cos A=\frac{12}{13}$ .

[ 2 ]

(b)

Find $\cos 2 A$ .

[ 3 ]

[Maximum number: 6]

The following diagram shows a circle with centre O and radius 3 cm .

diagram not to scale

Points A, B, and C lie on the circle, and $\mathrm{A} \hat{\mathrm{O}} \mathrm{C}=1.3$ radians.

(a)

Find the length of arc ABC .

[ 2 ]

(b)

Find the area of the shaded region.

[ 4 ]

[Maximum number: 6]

The following diagram shows triangle ABC .

\mathrm{BC}=10 \mathrm{~cm}, \mathrm{~A} \hat{\mathrm{~B} \mathrm{C}}=80^{\circ} \text { and } \mathrm{B} \hat{\mathrm{~A}} \mathrm{C}=35^{\circ} .

(a)

Find AC.

[ 3 ]

(b)

Find the area of triangle ABC .

[ 3 ]

[Maximum number: 6]

The following diagram shows a triangle ABC .

\mathrm{AB}=5 \mathrm{~cm}, \hat{\mathrm{~A}} \mathrm{~A}=50^{\circ} \text { and } \mathrm{A} \hat{\mathrm{C}} \mathrm{~B}=112^{\circ}

(a)

Find BC .

[ 3 ]

(b)

Find the area of triangle ABC .

[ 3 ]