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Maths Test 010

Maths Test 010

Test 010 covers chapter 9 of the Edexcel Maths AS course.
There is no time limit - the average person should complete the test in an hour and a half.
The test will remain available until midnight on 10 August 2020.
The test total is 220 marks.

1. Find all the missing sides and angles for each of the following triangles                                                     (30)
   1. triangle \(ABC\) with side \(AB = 5\)cm, side \(BC = 7\)cm, and side \(AC = 6\)cm
   2. triangle \(PQR\) with side \(PQ = 7.1\)cm, side \(PR = 9.5\)cm, and angle \(QPR = 50\)°
   3. angle \(GHI = 120\)° in triangle \(GHI\) with side \(HI = 100\)mm and \(HG = 87\)mm
   4. side \(MN = 195\)cm, side \(LM = 145\)cm, and side \(NL = 209\)cm in triangle \(LMN\)
   5. side \(DE = 3.5\)cm, angle \(DEF = 65\)° and \(EDF = 40\)° in triangle \(DEF\)
   6. triangle \(XYZ\) with side \(XY = 9.2\)m, side \(YZ = 8.8\)m, and angle \(XYZ = 130\)°


2. A helicopter flies on a bearing of \(080\)° from \(A\) to \(B\), where \(AB = 50km\). It then flies for \(60\)km to point \(C\). Given that \(C\) is \(80\)km from \(A\), calculate the bearing of \(C\) from \(A\).                                          (10)


3. In triangle \( ABC\), \(AB = (x - 3)\)cm, \(BC = (x + 3)\cm, \(AC = 8\)cm, and angle \( BAC = 60 \)°. Find the value of \( x \).                                          (10)


4. The length of the sides of a triangle are in a ratio of 2:3:4.                                          (10)
   1. Find the size of each angle.
   2. If the smallest side is 9cm, find the other three sides.


5. In triangle \(ABC\), \(AB = (5 - x)\)cm, \( BC = (x + 4)\)cm, angle \( ABC = 120\)°, \( AC = y\)cm.                                          (10)
   1. Show that \( y^2 = x^2 - x + 61 \).
   2. By completing the square, find the minimum value of \( y^2 \) and \( y \).
   3. Find the value of \( x \) for the minimum value of \( y^2 \) and the length of each side of the triangle.


6. The triangle \(ABC\) has angles \(A\), \(B\), and \(C\), and sides \(a\), \(b\), and \(c\).                                          (40)
   1. Given that \( a = 8\)cm, \( A = 30\)°, \( B = 72\)°, find the missing sides and angles.
   2. Given that \( a = 24\)cm, \( A = 110\)°, \( C = 22\)°, find the missing sides and angles.
   3. Given that \( b = 14.7\)cm, \( A = 30\)°, \( C = 95\)°, find the missing sides and angles.
   4. Given that \( c = 9.8\)cm, \( B = 68.4\)°, \( C = 83.7\)°, find the missing sides and angles.


7. The triangle \( ABC \), \(AB = x\)cm, \(BC = (4 - x)\)cm, angle \(BAC = y\) and \(BCA = 30\)°. Given that \(sin y = \frac{1}{\sqrt{2}} \), show that \( x = 4(\sqrt{2} - 1) \)                                          (10)


8. Find the area of each triangle PQR.                                          (10)
   1. \( PQ = 8.6\)cm, \( PR = 7.8\)cm, and \( QPR = 45\)°
   2. \( PQ = 3.5\)cm, \( QR = 2.5\)cm, and \( PQR = 100\)°


9. In triangle \( ABC \), \( AB = (x + 2) \)cm, \( AC = (5 - x) \)cm and \( BAC = 30 \)°. The area of the triangle is \( A \)cm².                                          (10)
   1. Show that \( A = \frac{1}{4}(10 + 3x - x^2) \).
   2. Find the maximum value of \( A \), and the associated value of \( x \).


10. Four phone masts \( A \),\( B \),\( C \), and \( D \), form a quadrilateral. \( B\) and \( C \) are \( 75\)m apart, \( C\) and \( D\) are \( 80\)m apart, and \( A \) and \( D \) are \( 70\)m apart. In addition, the angle \( BCD = 55 \)° and \( ADC = 140 \)°.                                          (20)
    1. Sketch the quadrilateral that is formed by the phone mast.
    2. Work out the distance between \( A \) and \( B \).
    3. Find the angle \( BAD \).
    4. The area of triangle \( BAD \).
    5. The area of quadrilateral \( ABCD \).


11. Sketch the trigonometric graphs for the ranges given                                          (10)
    1. \( y = sin(x) \) for \( -180° \le x \le 180° \).
    2. \( y = tan(x) \) for \( -270° \le x \le 360° \).


12. Sketch the trigonometric graphs for the given ranges                                          (60)
    1. \( y = 1 - tan(x) \) for \( -180° \le x \le 180° \)
    2. \( y = - 3sin(x) + 2 \) for \( -90° \le x \le 360° \)
    3. \( y = cos(\frac{x}{3}) - 2 \) for \( -720° \le x \le -180° \)
    4. \( y = 1 - \frac{1}{3}tan(-x + 30°) \) for \( -270° \le x \le 360° \).
    5. \( y = sin(\frac{x + 20}{2}) - 4 \) for \( -360° \le x \le 360° \).

End of Maths Test 010