Blog

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: 

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

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]

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]

What accounts for a demand for nutritious menu choices?

What is the employment market for private chefs?

How can restaurants meet the growing demand for nutritious menu choices?

TRIGONOMETRY Question 8 8.1    A container ABCDEFGH has dimensions: length = 10m; breadth = 5m and depth = 6m as shown in the sketch below. Right click to open diagram in a new “tab”.   8.1.1 Determine the length of the diagonal AG. (4) 8.1.2 Hence, or otherwise, determine the size of angle θ = CÂG. (2) 8.2   Oblique pyramid, ABCDH, with square base of side 200 m, is shown below.  E is the midpoint of AD and F is a point on AB, 50 m from BC. The perpendicular height of the pyramid is 7 m. The apex of the pyramid is 100 m from side AB and 50 m from side BC. Right click to open diagram in a new “tab”. 8.2.1   Determine the volume of the pyramid given the formula: