Mathematics Grade 10 P1 North West June 2019 Question Paper

Downloaded from hlayiso.com GRADE 10 MATHEMATICS PAPER 1 MID YEAR EXAMINATION 2019 MARKS: 75 TIME: 1 hour 30 minutes This question paper consists of 5 pages Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/P1 2 NW/June 2019 Grade 10 INSTRUCTIONS AND INFORMATION 1. This question paper consists of 6 questions, answer ALL the questions. 2. Clearly show ALL calculations, diagrams, graphs, et cetera that you have used in determining the answers. 3. An approved scientific calculator (non-programmable and non-graphical) may be used, unless stated otherwise. 4. If necessary, answers should be rounded off to TWO decimal places, unless stated otherwise. 5. Number the answers correctly according to the numbering system used in this question paper. 6. It is in your own interest to write legibly and to present the work neatly. Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/P1 3 NW/June 2019 Grade 10 QUESTION 1 2E 1.1 Given that v  . m 1.1.1 If m  12 and E  132, determine the value of v. Leave answer in surd form (2) 1.1.2 State whether v is rational or irrational. (1) 1.1.3 Determine between which two consecutive integers does v lie? (2)  1.2 Write the recurring decimal 0,5 2 as a fraction (4) [9] QUESTION 2 2.1 Factorise fully: 2.1.1 a 2  2a  ax  2 x (3) x 3  27 2.1.2 (3) x 2  3x  9 2.2 Simplify the following: 2.2.1 (2 y  3)(6 y 2  4 y  8) (3) 2 2n  4 n  2 2.2.2 (3) 16 n 3x 3  7 x 2  6 x 3x 2  2 x 2.2.3  (6) x2  9 3x  9 [18] QUESTION 3 3.1 Solve for x: 3.1.1 9 x  4  5(2 x  3) (3) 1 3.1.2 4x  (2) 256 3.2 Solve the following inequality and represent it graphically: 10  x  4  12 (4) 3.3 Make r the subject of the formula if A   R 2   r 2 (2) Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/P1 4 NW/June 2019 Grade 10 3.4 Given: x 2  9 y 2  99 and x  3y  3 3.4.1 Determine the value of x  3 y (2) 3.4.2 Hence, solve for x and y simultaneously (4) [17] QUESTION 4 4.1 Given the number pattern: 4;  1;  6;... 4.1.1 Write down the next two terms of the pattern (2) 4.1.2 Determine the n th term of the sequence. (3) 4.1.3 Calculate T27 , the twenty seventh term of the pattern. (2) 4.1.4 Which term of the pattern is equal to  71 (2) 4.2 Study the following illustration: 1 1  1 11 11  121 111 111  12321 Express 12345654321 as per the illustration above. (1) [10] QUESTION 5 f ( x)  2 x 2  2 and g ( x)  2 x  1 are the defining equations of the graphs of f and g respectively. 5.1 Write down the equation of the asymptote of g. (1) 5.2 Sketch the graphs of f and g on the same set of axes, clearly show the intercepts with the axes, the turning points as well as the asymptotes. (6) 5.3 Write down the range of the graph of g. (1) 5.4 What transformation does the graph of y  f (x) undergo in order to obtain the graph of y  2 x 2  2 (2) [10] Demo NW/JUNE/MATH/ EMIS/6*******

Downloaded from hlayiso.com Mathematics/P1 5 NW/June 2019 Grade 10 QUESTION 6 2 Sketched below are the graphs of: h( x)    1 and p ( x)  ax  q. x A(-2;4) and B(3;-1) are points on the graph of p. 6.1 Show that a  1 and q  2 (4) 6.2 Determine the values of x for which h( x)  p ( x) (4) 6.3 Determine the values of x for which h( x)  p ( x) (3) [11] GRAND TOTAL: 75 MARKS Demo NW/JUNE/MATH/ EMIS/6*******