Mathematics Grade 10 P1 Gauteng June 2024 QP (Eng)

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

Downloaded from hlayiso.com MATHEMATICS 2 (PAPER 1) GRADE 10 INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. Answer ALL the questions. 2. This question paper consists of FIVE questions. 3. Present your answers according to the instructions of each question. 4. Clearly show ALL calculations, diagrams, graphs et cetera, which were used in determining the answers. 5. Answers only will NOT necessarily be awarded full marks. 6. Use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 7. Where necessary, answers should be rounded-off to TWO decimal places, unless stated otherwise. 8. Diagrams are NOT necessarily drawn to scale. 9. Number the questions correctly according to the numbering system used in the question paper. 10. Write neatly and legibly. P.T.O.

Downloaded from hlayiso.com MATHEMATICS 3 (PAPER 1) GRADE 10 QUESTION 1 9 If x {0;1;2;3;4} , write down a value of x such that 𝐾 = √4−𝑥 is: 1.1 Undefined (1) 1.2 Rational (1) 1.3 Irrational (1) [3] QUESTION 2 2.1 Simplify the following: 2.1.1 2b(b – 5c)2 (2) 3x − 2.3x −1 2.1.2 (3) 3x + 2 + 2.3x +1 2.2 Factorise completely: a2 – ax – 1 + x (3) [8] QUESTION 3 3.1 Solve for x: 3.1.1 3x2 = 2x (2) 3.1.2 7 5 4 = + 2 (4) 3− x x +3 x −9 3.1.3 16,2 x−1 = (0,5) x−4 (4) 3x 3.2 Given: 2 −  14 4 3.2.1 Solve the inequality. (2) 3.2.2 Write down the first natural number that will satisfy the inequality. (1) 3.3 Solve simultaneously: 2𝑥 + 𝑦 = 8 and 2𝑦 + 3𝑥 = −2 (4) [17] P.T.O.

Downloaded from hlayiso.com MATHEMATICS 4 (PAPER 1) GRADE 10 QUESTION 4 Consider the functions f (𝑥) = 𝑎𝑥 2 + 𝑐 and 𝑔(𝑥) = 𝑏𝑥 + 𝑞. 𝑓 ang 𝑔 intersect at points A(–1 ;–3) and B (2; 0). 4.1 Calculate the values of 𝑎 and 𝑐. (4) 4.2 Calculate the values of b and 𝑞. (3) 4.3 Use the ANSWER SHEET provided to sketch the graphs 𝑓 𝑎𝑛𝑑 𝑔 on the same set of axis. (6) 4.4 Determine the value of 𝑔(𝑥) − 𝑓(𝑥). (2) 4.5 For which values of 𝑥 is 𝑔(𝑥) ≥ 𝑓(𝑥). (2) [17] QUESTION 5 The graph of f ( x) = 2 x + 2 + k is drawn below. 5.1 Use the laws of indices to show that 2 x + 2 + k is the same as 4.2 x + k. (2) 5.2 Determine the value of k. (2) 5.3 Write down the equation of the asymptote of 𝑓. (1) [5] TOTAL: 50 END

Downloaded from hlayiso.com MATHEMATICS 5 (PAPER 1) GRADE 10 NAME: ________________________________________________ ANSWER SHEET QUESTION 4.3

Downloaded from hlayiso.com MATHEMATICS 6 (PAPER 1) GRADE 10 INFORMATION SHEET − b  b 2 − 4ac x= 2a A = P(1 + ni) A = P(1 − ni) A = P(1 − i) n A = P(1 + i) n Tn = a + (n − 1)d Sn = n 2a + (n − 1)d  2 Tn = ar n −1 Sn = ( a r n −1 ) ;r 1 S = a ; −1  r  1 r −1 1− r F=  x (1 + i )n − 1  P=  x 1 − (1 + i )− n  i i f ( x + h) − f ( x) f ' ( x) = lim h→ 0 h  x + x2 y1 + y 2  d = ( x2 − x1 ) 2 + ( y 2 − y1 ) 2 M  1 ;   2 2  y − y1 y = mx + c y − y1 = m( x − x1 ) m= 2 m = tan  x 2 − x1 (x − a )2 + ( y − b)2 = r 2 a b c In ABC: = = a 2 = b 2 + c 2 − 2bc. cos A sin A sin B sin C 1 area ΔABC = ab. sin C 2 sin (α + β ) = sin α.cos β + cosα.sin β sin (α − β ) = sin α.cos β − cosα.sin β cos(α + β ) = cosα.cos β − sin α.sin β cos(α − β ) = cosα.cos β + sin α.sin β cos2  − sin 2   cos 2 = 1 − 2 sin 2  sin 2 = 2 sin  . cos  2 cos2  − 1  n  fx  (x − x)i 2 x=  2 = i =1 n n n(A) P(A) = P (A or B) = P(A) + P(B) – P(A and B) n(S)  (x − x )(y − y) yˆ = a + bx b= 2  (x − x )