Mathematics Grade 10 P2 Gauteng June 2024 QP (Eng)

Downloaded from hlayiso.com PROVINCIAL EXAMINATION JUNE 2024 GRADE 10 MATHEMATICS (PAPER 2) TIME: 1 hour MARKS: 50 6 pages P.T.O.

Downloaded from hlayiso.com MATHEMATICS 2 (PAPER 2) GRADE 10 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 5 questions. 2. Answer ALL the questions. 3. Clearly show ALL calculations, diagrams, graphs etc. that you have used to determine the answers. 4. Answers only will NOT necessarily be awarded full marks. 5. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 6. If necessary, round-off answers to TWO decimal places, unless stated otherwise. 7. Diagrams are NOT necessarily drawn to scale. 8. Write neatly and legibly. P.T.O.

Downloaded from hlayiso.com MATHEMATICS 3 (PAPER 2) GRADE 10 QUESTION 1 In the figure below, A(−5 ; 2) and B(4 ; –2) are points on a line segment AB. y A(–5 ; 2) x B(4 ; –2) 1.1 Determine the length of AB. (3) 1.2 Determine the coordinates of the midpoint of AB. (3) 1.3 Determine the gradient of line AB. (3) 1.4 Point A undergoes a certain transformation to a point A' such that the gradient of the line A'B becomes undefined. Describe the transformation that maps point A to A'. (2) [11] QUESTION 2 2.1 If A = 78° and B = 34°, calculate the values of the following expressions, correct to two decimal places. 2.1.1 𝑠𝑖𝑛 𝐴 − 𝑠𝑖𝑛 𝐵 (2) 3 2.1.2 √𝑠𝑒𝑐 𝐴 (2) P.T.O.

Downloaded from hlayiso.com MATHEMATICS 4 (PAPER 2) GRADE 10 2.2 In the diagram below, point P(−2; −1) lies in the third quadrant. OP = 𝑟 𝑐𝑚. The axes intersect at O, which represents the origin on the sketch. y θ x r P(–2 ; –1) Using the sketch and without using a calculator, calculate the: 2.2.1 Length of OP. (2) 2.2.2 Value of √5 𝑐𝑜𝑠 𝜃 + 4 𝑐𝑜𝑠𝑒𝑐 2 𝜃 (4) 2.3 Evaluate without using a calculator: sin 45° √2 2 2 . tan 30° (3) [13] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 5 (PAPER 2) GRADE 10 QUESTION 3 The sketch below shows the graph of f(x) = 𝑐𝑜𝑠 𝑥 and g(x) = 2 𝑠𝑖𝑛 𝑥 for the interval 𝑥 ∈ [0°; 360°]. y 2 1 f O x 90° 180° 270° 360° –1 g –2 3.1 Write down the period of 𝑔. (1) 3.2 For which value(s) of x will f (x) ≥ 0 ? (2) 3.3 Determine the range of m(x) if m = −4 f(x) + 1. (3) [6] QUESTION 4 ̂ = 𝜃 and AB In the diagram below, A ̂ D = 90°. BC = 𝑥 𝑚, Ĉ = 𝛽 and BD ̂ C = 90°. . A θ D B x β C 𝑥 sin 𝛽 4.1 Show that AB = (4) tan 𝜃 4.2 Hence, or otherwise, calculate the length of AB, correct to two decimal places, if 𝜃 = 52°; 𝛽 = 40° and 𝑥 = 12 𝑚. Write your answer to the nearest whole number. (2) [6] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 6 (PAPER 2) GRADE 10 QUESTION 5 5.1 Complete the theorem: The line segment joining the midpoints of two sides of a triangle is … and … (Write down the missing words only.) (2) 5.2 ABCD is a rhombus with the diagonals AC = 16 cm and DB = 30 cm. B A 2 1 F 2 O 1 C D 5.2.1 Calculate the length of BC. (4) 5.2.2 Calculate OF, if OF is parallel to DC with F on BC. (3) 5.2.3 ̂ F if OF̂C = 64°. Determine the size of OB (3) 5.3 Determine the area of the rhombus ABCD (2) [14] TOTAL: 50 END