5.1 In the diagram below, P(1;3) is a point on the Cartesian plane, OP = r and XÔP= θ. 5.1.1 Make use of the diagram to calculate the value of θ. (2) 5.1.2 Calculate the length of OP. Leave the answer in surd form. (2) 5.1.3 Determine the values of the following, without using a … Read more
4.1 Calculate the gradient of NQ. (1) 4.2 Calculate the gradient of MP. (1) 4.3 Calculate the angle of inclination of MP. (3) 4.4 Hence, determine the equation of the line MP. (4) 4.5 Hence, determine the coordinates of P. (4) 4.6 Determine the co-ordinates of R. (3) [16]
6.1 Complete: ···= a2 + b2 – 2ab cosĈ .(1) 6.2 TRS is a secant of the circle, and SU is a tangent at U. TU = 16 cm, TR = 12 cm and T̂ = 41°. Calculate the: 6.2.1 Length of UR, correct to two decimals. (3) 6.2.2 Size of Û2 (3) 6.2.3 Length … Read more
The points A(2a – 11; a +2), C(4; -1) and D(4p; p – 7) are the vertices of ∆ACD with B(-2; 3)on AC. 3.1 If points A, B and C are collinear, find the value of a. (4) 3.2 Determine the equation of the line AC. (3) 3.3 Hence, determine the co-ordinates of midpoint M … Read more
The following is a sample of weekly wages earned by ten people working for a smallprinting and design company. 2.1 Calculate the mean weekly wage. (2) 2.2 Calculate the standard deviation of the weekly wage. (1) 2.3 Determine the percentage of workers which lie within ONE standard deviation of the mean. (4) [7]
5.1 On the same set of axes draw ƒ(𝑥) = -cos(45° – 𝑥) and g(𝑥) = tan(-𝑥) in the interval of -90° ≤ 𝑥 ≤ -180°. Make use of the grid provided in the SPECIAL ANSWER BOOK. 5.2 For which values of 𝑥 is ƒ(𝑥) – g(𝑥) ≤ 0 for 𝑥 ∈ [−90°; 90°] (2) … Read more
The following table represents the heights, in centimetres, of 120 boys in a school. 1.1 Complete the cumulative frequency table in the SPECIAL ANSWER BOOK. (2) 1.2 Draw an ogive, using the diagram in the SPECIAL ANSWER BOOK, to representthe information in the table. (4) 1.3 Determine, using the ogive, the five number summary. (5) … Read more
4.1 Given: 𝑝.sin 𝛽 – 4 = 0 and 𝑝.cos 𝛽 + 3 = 0 where 𝑝 > 0 4.1.1 Explain why 𝛽 ∈ [900;1800] (3) 4.1.3 Determine the numerical value of 𝑝. 4.2 Simplify without using a calculator: sin1430.cos1270 – sin530.cos370 [24]
In the diagram below, ∆ PQS is drawn with vertices P (-2 ; 3), Q (3 ; 6) and S in a Cartesian plane. Line QS passes through the origin at O. PS║QR. PŜQ 20,230. 3.1 Calculate the gradient of QS. (2) 3.2 Calculate the size of 𝜃. (2) 3.3 Determine the: 3.3.1 gradient of … Read more
SECTION D: POETRY 5.1 Read the poem carefully and then answer the questions which follow. Thenumber of marks allocated to each question serves as a guide to the expectedlength of you answer. 5.1.1 Refer to Stanza 2: Lines 1–2. (‘There’s little Tom…a lamb’s back;’) (a) Identify the figure of speech in the above lines. (1)(b) … Read more