Mathematics Grade 10 Paper 1 KZN June 2024 Memo

Downloaded from hlayiso.com Downloaded f rom St anmorephysics. com NATIONAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS P1 COMMON TEST JUNE 2024 MARKS: 50 TIME: 1 hour This question paper consists of 5 pages. Copyright Reserved Please Turn Over

Downloaded from hlayiso.com Mathematics P1 2 June 2024 Common Test Downloaded f rom St anmorephysics. NSC –Grade 10 com INSTRUCTIONS AND INFORMATION Read the following instructions carefully before answering the questions. 1. This question paper consists of 3 questions. 2. Answer ALL the questions. 3. Number the answers correctly according to the numbering system used in this question paper. 4. Clearly show ALL calculations, diagrams, graphs, etc. which you have used in determining your answers. 5. Answers only will NOT necessarily be awarded full marks. 6. You may use an approved scientific calculator (non-programmable and non-graphical), unless stated otherwise. 7. If necessary, round off answers correct to TWO decimal places, unless stated otherwise. 8. Diagrams are NOT necessarily drawn to scale. 9. Write neatly and legibly. Copyright Reserved Please Turn Over

Downloaded from hlayiso.com Mathematics P1 3 June 2024 Common Test Downloaded f rom St anmorephysics. NSC –Grade 10 com QUESTION 1 1.1 Simplify fully: 1.1.1 ( 3x − 2 ) ( 2 x 2 − 4 x + 1) (2) 1.1.2 4 x.8 x +1 32 x +1 (3) 1.1.3 x+7 3 2 − + x −x − 6 x − 3 2x + 4 2 (5) 1.2 Factorise fully: 1.2.1 5x2 − 2 x − 3 (2) 1 1.2.2 x3 + 125 (2) [14] QUESTION 2 2.1 Solve for x: 2.1.1 x ( x − 1) = 6 (3) 2.1.2 3x + 3x−1 = 36 (3) x 2.1.3 −2  −1  1 3 (3) 2.2 A shop sells bicycles and tricycles. In total there are 7 cycles (cycles include both bicycles and tricycles) and 19 wheels. Determine how many of each there are, if a bicycle has two (5) wheels and a tricycle has three wheels. [14] Copyright Reserved Please Turn Over

Downloaded from hlayiso.com Mathematics P1 4 June 2024 Common Test Downloaded f rom St anmorephysics. NSC –Grade 10 com QUESTION 3 3 3.1 Given: f ( x ) = x − 2 and g ( x ) = , which are not drawn to scale. A and B are points of x intersection of the graphs. DF is perpendicular to the x-axis, with points E and F on the graphs of g and f respectively. Determine: 3.1.1 The coordinates of point C. (1) 3.1.2 The x-coordinates of A and B. (4) 3.1.3 The length of EF if OD = 6 units . (3) 3.1.4 The equation of j if j ( x ) = g ( x ) + 2 . (1) 3.1.5 The value(s) of x for which f ( x )  g ( x ) where x  0 . (2) Copyright Reserved Please Turn Over

Downloaded from hlayiso.com Mathematics P1 5 June 2024 Common Test Downloaded f rom St anmorephysics. NSC –Grade 10 com 3.2 Sketch the graph of h( x) = ax 2 + q if it is given that: • The range of h is  −4;  ) • a0;a0 • q0 • One root of h is positive and one root of h is negative. (3) 3.3 Given: g ( x ) = 3.2x − 12 3.3.1 Write down the equation of the asymptote of g . (1) 3.3.2 Determine the y intercept of g . (2) 3.3.3 Determine the x intercept of g . (2) 3.3.4 Sketch the graph of g, clearly showing the asymptote and the intercepts with the (3) axes. [22] TOTAL: [50] Copyright Reserved Please Turn Over

Downloaded from hlayiso.com Downloaded f rom St anmorephysics. com NATIONAL SENIOR CERTIFICATE GRADE 10 MATHEMATICS P1 COMMON TEST JUNE 2024 MARKING GUIDELINE MARKS: 50 This marking guideline consists of 5 pages. Copyright Reserved Please Turn Over

Downloaded from hlayiso.com Mathematics 2 Common Test June 2024 Downloaded f rom St GRADE anmorephysics. com 10-Marking Guideline QUESTION 1 1.1.1  6 x3  12 x 2  3x  4 x 2  8 x  2 Asimplification  6 x3  16 x 2  11x  2 CAanswer (2) 1.1.2 2 2 x.23 x 3 22 x.23 x 3  A 25 x  5 25 x  5  2 2 CA 22 1 1 (3)  CA 4 4 1.1.3 x7 3 2 A  x  3 x  2  and 2(𝑥 + 2)     x  3 x  2  x  3 2  x  2  x  7  3 x  2  x  3 CA x  7  3 x  2  x  3  x  3 x  2   x  3 x  2  x  7  3x  6  x  3   x  3 x  2  CA  x  2 x  2   x  3 x  2  CA   x  2    x  2   x  3 x  2  1 1 CA  x3 x3 (5) 1.2.1   5 x  3 x  1 A  5 x  3 A  x  1 (2) 1.2.2  1  1 1   1   x    x2  x   A  x    5  5 25   5  1 1  A  x 2  x   (2)  5 25  [14] Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 3 Common Test June 2024 Downloaded f rom St GRADE anmorephysics. com 10-Marking Guideline QUESTION 2 2.1.1 x2  x  6  0 Astandard form CAfactors  x  3 x  2   0 x  3 or x  2 CAboth answers (3) 2.1.2  1  1 3x  1    36 A 3x  1    36  3  3 3  27 x CA 3x  27 x3 CA x  3 (3) 2.1.3 x x 2  1   11 A 2  1   11 3 3 x x 1  2 CA 1  2 3 3 (3) 3  x  6 CA 3  x  6 2.2 Let bicycles  x tricycles  y x  y  7.............  (1) A x  y  7 2 x  3 y  19.........  (2) A 2 x  3 y  19 2 x  2 y  14......  (3) CA 2x  2 y  14 Add (2) and (3) y 5 CA y  5 x2 CA x  2 OR x  y  7.............  (1) 2 x  3 y  19.........  (2) OR A x  y  7 x  7  y..............  (3) A 2 x  3 y  19 subst. (3) into (2) CA x  7  y 2  7  y   3 y  19 14  2 y  3 y  19 y5 CA y  5 x2 (5) CA x  2 [14] Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 4 Common Test June 2024 Downloaded f rom St GRADE anmorephysics. com 10-Marking Guideline QUESTION 3 3.1.1 f  0   2 A C  0; 2  C  0; 2  (1) 3.1.2 3 3 x2 A x  2  x x x  2x  3  0 2 A x  2 x  3  0 2  x  3 x  1  0 CA  x  3 x  1  0 x  3 or x  1 CA x  3 or x  1 A  1; 0  , B  3; 0  (4) 3.1.3 f  6  6  2 A y – value of F 4 3 g 6  6 1 A y – value of E  2 7 7  EF=3,5 or units CA EF=3,5 or units 2 2 (3) 3.1.4 3 3 j ( x)  2 A j ( x)  2 (1) x x 3.1.5 1  x  0 CA 1  x  0 A OR x [1;0) (2) Copyright Reserved Please turn over

Downloaded from hlayiso.com Mathematics 5 Common Test June 2024 Downloaded f rom St GRADE anmorephysics. com 10-Marking Guideline 3.2 Ashape Ax-intercepts on either sides of the y- axis Aturning point /y- intercept at y  4 (3) 3.3.1 y  12 Aanswer (1) 3.3.2 g  0   9 A g (0)  3.20 12 A 9 (2) 3.3.3 3.2 x  12 A 2 x  4 2x  4 A x  2 (2) x2 3.3.4 Ashape CAboth intercepts Aasymptotes (3) [22] TOTAL: [50] Copyright Reserved Please turn over