Mathematics Grade 12 Limpopo March 2022 Question Paper

Downloaded from hlayiso.com VHEMBE WEST DISTRICT GRADE 12 MATHEMATICS CONTROL TEST 1 – 2022 DD DATE: 11 MARCH 2022 MARKS: 50 DURATION: 1 HOUR This question paper consists of 09 pages including formula and diagram sheet. Copyright reserved Please turn over Page 0 of 9

Downloaded from hlayiso.com INSTRUCTIONS 1. Read and answer all questions carefully. 2. It is in your own interest to write legibly and to present your work neatly. 3. All necessary working which you have used in determining your answers must be clearly shown. 4. Approved non-programmable calculators may be used except where otherwise stated. Where necessary give answers correct to 2 decimal places unless otherwise stated. 5. Ensure that your calculator is in DEGREE mode. 6. Diagrams have not necessarily been drawn to scale. 7. Use spaces provided on the question paper to answer Question 4 and 5. Page 1 of 9

Downloaded from hlayiso.com Question 1 1.1. Given : 0; 5; 16; 33 are the first four terms of the quadratic sequence. 1.1.1. Show that the n th term is given by, Tn  3n 2  4n  1 . (4) 1.1.2. Determine which term in the sequence is equal to 5896? (2) [06] Question 2 2.1 The first three terms of an arithmetic sequence are 2𝑝 − 3 ; 𝑝 + 5 ; 2𝑝 + 7. 2.1.1. Determine the value(s) of p. . (2) 2.1.2. Calculate the sum of the first 120 terms. (2) 2.2 The following pattern is true for above arithmetic sequence: T1  T4  T2  T3 T5  T8  T6  T7 T9  T12  T10  T11 Tk  Tk 3  Tx  Ty 2.2.1. Write the value of x and y in terms of k . (2) 2.2.2. Hence, calculate the value of Tx  Ty in terms of k in simplest form. (4) [10] Question 3 3.1. Consider the following geometric sequence: 3 81 3 sin 30 0 ; cos30 0 ; ;…. 2 2 Determine the number of terms in the sequence. (4) Page 2 of 9

Downloaded from hlayiso.com 3.2. Rectangles of width 2 cm are drawn from the edge of a sheet of paper that is 40 cm long such that there is a 2 cm gap between on rectangle and the next. The length of the first rectangle is 27 cm and the length of each successive rectangle is 85% of the length of the previous rectangle until there are rectangles drawn along the entire length of PS. Each rectangle is coloured dark grey. 3.3.1. Calculate the length of 12th rectangle. (3) 3.3.3. Calculate the percentage of paper is coloured dark grey. (4) [11] Page 3 of 9

Downloaded from hlayiso.com Question 4 4.1. In the figure below below, O is the centre of the circle with P , Q and R on the circumference. SR is the tangent to circle centre O at R. ^ ^ (5) Prove that PRS  Q Page 4 of 9

Downloaded from hlayiso.com 4.2 In the figure below, E is the centre of the circle and DE is perpendicular to AB . AC and DE intersect at F and DF  DC . 4.2.1. Prove that BEFC is a cyclic quadrilateral. (3) 4.2.2. Prove that DC is a tangent at C (3) Page 5 of 9

Downloaded from hlayiso.com Question 5 In the diagram, circle ABSR is drawn. Chords RA and SB produced to meet at P . PA  RS and QT // AB . 5.1. Prove that PSR /// PAB (3) Page 6 of 9

Downloaded from hlayiso.com 5.2. PS  BA  SR 2 (3) 5.3. PT 2 (3) If RS  10cm and  calculate the length of PQ . TB 3 5.4. area of PAB Calculate area of PTQ Page 7 of 9

Downloaded from hlayiso.com INFORMATION SHEET: MATHEMATICS  b  b 2  4ac x A  P(1  ni) A  P(1  ni) A  P(1  i ) n 2a n n n(n  1) A  P(1  i ) n 1  n i  Tn  a  (n  1)d i 1 i 1 2 Sn  n  2a  (n  1)d  Tn  ar n1 S n  a r  1 n  ; r 1 S  a ; 1  r  1 2 r 1 1 r F  x 1  i   1 n  P x[1  (1  i)n ] f ' ( x)  lim f ( x  h)  f ( x) i i h 0 h  x  x 2 y1  y 2  d  ( x 2  x1 ) 2  ( y 2  y1 ) 2 M  1 ;   2 2  y 2  y1 y  mx  c y  y1  m( x  x1 ) m m  tan  x 2  x1 x  a 2   y  b2  r 2 In ABC: a  b  c a 2  b 2  c 2  2bc. cos A sin A sin B sin C 1 area ABC  ab. sin C 2 sin      sin . cos   cos.sin  sin      sin . cos   cos.sin  cos     cos. cos   sin .sin  cos     cos. cos   sin .sin  cos2   sin 2   cos 2  1  2 sin 2  sin 2  2 sin  . cos 2 cos2   1  n 2  fx  x  x  i x   2 i 1 n n n( A) P( A)  P(A or B) = P(A) + P(B) – P(A and B) nS  yˆ  a  bx b  x  x ( y  y )  (x  x) 2 Page 8 of 9