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TRIGONOMETRY Question 5    Ray OP forms an angle of α to the positive x axis, 5 tan α = 12 and α  ∈  [90°; 270°]. 5.1 Draw a sketch showing ray OP in the Cartesian plane. (2) 5.2   Determine the value of each of the following trigonometric ratios without the use of a calculator.   Show each step in your calculations. 5.2.1 cos α (3) 5.2.2 tan (180° – α) (2) 5.2.3 sin (30° – α) (3)   TOTAL [10]  

TRIGONOMETRY Question 7 7.1   Sketch the following graphs for x ∈ [–180°; 180°]:

Which of the following refers to something essential to the body because it helps maintain, generate, and repair tissues?

ANALYTICAL GEOMETRY Question 1   The sketch shows triangle PQR in the Cartesian plane. The coordinates of point P are (5; 0). The angle of inclination of line PQ is 116,57°. S is the midpoint of line PQ. The length ratio OR : OP is 3 : 2.      Right click to open diagram in a new “tab”.   1.1 Determine: 1.1.1 the gradient of PQ, to the nearest integer value. (2) 1.1.2 the equation of PQ in the form . (2) 1.1.3 the distance PS in surd form. (3) 1.1.4 the coordinates of Q. (2) 1.2 Determine the coordinates of R. (2) 1.3 Calculate the area of ΔPQR. (4)   TOTAL [15]

ANALYTICAL GEOMETRY Question 2  Rectangle ABCD has vertices A(4 ; 0), B(–4 ; a), C(–6 ; 0) and D.B lies in the second quadrant. Right click to open diagram in a new “tab”.   2.1 Show that a = 4. (4) 2.2 Determine the equation of the straight line CD in the form . (4) 2.3 Calculate the coordinates of D. (4) 2.4 Calculate the length of AC. (2)   TOTAL [14]

 TRIGONOMETRY Question 6  6.1 Prove the identity: 

ANALYTICAL GEOMETRY Question 3 A trapezium with vertices P (1; 2), Q (2; –3), R (0; –5) and S (–4; p) is shown in the sketch below.  In addition, QR // PS. Right click to open diagram in a new “tab”.   3.1 Show that p = –3. (4) 3.2 Calculate PS : QR in the simplest form.  (5) 3.3 T (x; y) on PS is such that PTRQ is a parallelogram. Determine the co-ordinates of T.  (5)   TOTAL [14]

ANALYTICAL GEOMETRY Question 4     4.1 ΔPQR with vertices P(–9; 9), Q(9; 12) and R(3; –9) is shown in the sketch. The straight–line ST is parallel to QR and passes through the origin. M is a point on the line ST with coordinates (a ; 7). PK̂L = α. The angle of inclination of the straight line QR is β. PR̂Q = θ.     Right click to open diagram in a new “tab”.     4.1.1 Calculate the gradient of the line QR. (3) 4.1.2 Determine the equation of line ST in the form . (2) 4.1.3 Calculate the length of line PM in simplified surd form. (4) 4.1.4 Calculate the value of angle θ. (4)    4.2 The rhombus, PQRS, has vertices P (–3; 9), Q(8; 6), R(1; a) and S. The diagonals of the rhombus intersect at point T with coordinates (b; c). PT has length .      Right click to open diagram in a new “tab”.     4.2.1 Calculate the perimeter of the rhombus. (2) 4.2.2 Determine the length of QT. (3) 4.2.3 Determine the equation of the straight line PR. (3) 4.2.4 Determine the coordinates (b; c) of point T (6) 4.2.5 Determine, showing ALL your calculations, whether rhombus ABCD is a square or not. (5)   TOTAL [32]

What is the outcome when people do not have access to adequate amounts of nutritious food?

What accounts for a demand for nutritious menu choices?