# Grade 12 Mathematics 2020 Paper 2

## Question 10

In the diagram, a circle passes through D, B and E. Diameter ED of the circle is produced to C and AC is a tangent to the circle at B. M is a point on DE such that AM DE. AM and chord BE intersect at F. 10.1 Prove, giving reasons, that: 10.1.1 FBDM … Read more

## Question 9

9.1 In the diagram, O is the centre of the circle. Points S, T and R lie on the circle. Chords ST, SR and TR are drawn in the circle. QS is a tangent to the circle at S. Use the diagram to prove the theorem which states that QST = R. (5) 9.2 Chord … Read more

## Question 8

8.1 O is the centre of the circle.. KOM bisects chord LN and MNO = 26° K and P are points on the circle with NKP = 32° . OP is drawn. 8.1.1 Determine, giving reasons, the size of: (a) Ô2 (2) (b) Ô1 (4) 8.1.2 Prove, giving reasons, that KN bisects OKP. (3) 8.2 … Read more

## Question 7

A landscape artist plans to plant flowers within two concentric circles around a vertical light pole PQ. R is a point on the inner circle and S is a point on the outer circle. R, Q and S lie in the same horizontal plane. RS is a pipe used for the irrigation system in the … Read more

## Question 6

6.1 In the diagram, P(—5 ; 12) and T lies on the positive x-axis. PÔT = 0 Answer the following without using a calculator: 6.1.1 Write down the value of tan0 (1) 6.1.2 Calculate the value of cos0 (3) 6.1.3 S(a, b) is a point in the third quadrant such that TÔS = 0 + … Read more

## Question 5

The graphs of f(x)1/2 cos x and g(x) = sin(x + 30°) , for the interval x E [0°; 180°], are drawn below. A(130,9° ; 0,33) is the approximate point of intersection of the two graphs. 5.1 Write down the period of g. (1) 5.2 Write down the amplitude of f (1) 5.3 Determine the value of … Read more

## Question 4

M(—3 ; 4) is the centre of the large circle and a point on the small circle having centre O(0; 0). From N(—11 ; p), a tangent is drawn to touch the large circle at T with NT is parallel to the y-axis. NM is a tangent to the smaller circle at M with MOS … Read more

## Question 3

fiTSK is drawn. The equation of ST is y =1/2 x + 6 and ST cuts the x-axis at M. W(-4 ; 4) lies on ST and R lies on SK such that WR is parallel to the J-axis. WK cuts the x-axis at V and the y-axis at P(0 ; -4). KS produced cuts … Read more

## Question 2

The number of aircraft landing at the King Shaka International Airport and the Port Elizabeth Airport for the period starting in April 2017 and ending in March 2018, is shown in the double bar graph below. 2.1 The number of aircraft landing at the Port Elizabeth Airport exceeds the number of aircraft landing at the … Read more