Question 1

A sector of a circle with radius $r cm$, where $r > 0$, is shown on the following diagram.
The sector has an angle of 1 radian at the centre.
Let the area of the sector be $A cm^2$ and the perimeter be $P cm$. Given that $A=P$, find the value of $r$.

Accepted Answer

$r=6$

Answer

$r=7$

Answer

$r=5$

Answer

$r=4$

Question 2

Consider the following diagram.
The sides of the equilateral triangle $ABC$ have lengths $1 m$. The midpoint of $[AB]$ is denoted by $P$. The circular arc $AB$ has centre, $M$, the midpoint of $[CP]$.
Find $AM$.

Accepted Answer

$AM =0.661$

Answer

$AM =1.891$

Answer

$AM =1.661$

Answer

$AM =0.891$

Question 3

Consider the following diagram.
The sides of the equilateral triangle $ABC$ have lengths $1 m$. The midpoint of $[AB]$ is denoted by $P$. The circular arc $AB$ has centre, $M$, the midpoint of $[CP]$.
Find angle $AMP$ in radians.

Accepted Answer

$0.857$

Answer

$1.891$

Answer

$1.155$

Answer

$0.891$

Question 4

Consider the following diagram.
The sides of the equilateral triangle $ABC$ have lengths $1 m$. The midpoint of $[AB]$ is denoted by $P$. The circular arc $AB$ has centre, $M$, the midpoint of $[CP]$.     Find the area of the shaded region.

Accepted Answer

$0.158m^2$

Answer

$0.178m^2$

Answer

$0.128m^2$

Answer

$0.258m^2$

Question 5

This diagram shows a metallic pendant made out of four equal sectors of a larger circle of radius $OB=9 cm$ and four equal sectors of a smaller circle of radius $OA=3 cm$.
The angle $BOC= 20°$.  Find the area of the pendant.

Accepted Answer

$78.5 cm^2$

Answer

$68.5 cm^2$

Answer

$63.5 cm^2$

Answer

$73.5 cm^2$

Question 6

Given $ΔABC$, with lengths shown in the diagram below, find the length of the line segment $[CD]$.

Accepted Answer

$CD=4.36$

Answer

$CD=5.76$

Answer

$CD=4.76$

Answer

$CD=5.36$

Question 7

The triangle $ABC$ is shown in the following diagram. Given that $cosB<\frac{1}{4}$, find the range of possible values for $AB$.

Accepted Answer

$2<AB<4$

Answer

$0<AB<4$

Answer

$2<AB<5$

Answer

$1<AB<4$

Question 8

In a triangle $ABC$, $AB=4 cm$, $BC=3 cm$ and angle $BAC=\frac{π}{9}$.
Use the cosine rule to find the two possible values for $AC$.

Accepted Answer

$x=1.09, 6.43$

Answer

$x=2.09, 6.43$

Answer

$x=1.19, 6.53$

Answer

$x=1.09, 5.43$

Question 9

In a triangle $ABC$, $AB=4 cm$, $BC=3 cm$ and angle $BAC=\frac{π}{9}$.
Use the cosine rule to find the two possible values for $AC$, then find the difference between the areas of the two possible triangles ABC.

Accepted Answer

$3.65 cm^2$

Answer

$3.45 cm^2$

Answer

$4.35 cm^2$

Answer

$4.65 cm^2$

Question 10

In triangle $ABC$, $AB = 9 cm$, $AC = 12 cm$, and angle $B$ is twice the size of angle $C$ .
Find the cosine of angle $C$.

Accepted Answer

$cosC=\frac23$

Answer

$cosC=\frac15$

Answer

$cosC=\frac13$

Answer

$cosC=\frac25$

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