Mathematics Grade 12 P1 Western Cape Mock 2025 QP (Eng)

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34,| Western Cape /} Government PLC TRIAL EXAMINATION SEPTEMBER 2025 MATHEMATICS PAPER 1 GRADE 12 TOTAL: 150 DURATION: 3 hours This question paper consists of 11 pages and a formula page SA EXAM PAPERS Proudly South African

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This Paper was downloaded from SAEXAMPAPERS QUESTION 6 6.1 6.2 6.3 6.4 The graph of p(x) = 2* + q passes through the points A(0; 3) and B(2; 6). » ¥y Calculate the value of q. The graph of p is translated 2 units down to obtain k(x). Determine the equation of k7+(x) in the form y =........ > For which values of x is: 6.3.1 k(x) <0 63.2 p(x+3).k+4(«-5)>0 If p is reflected about the horizontal asymptote and translated 3 units to the left to form h(x), determine the equation of h(x). SA EXAM PAPERS Proudly South African (2) (3) 2) (2) (2) (11]

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This Paper was downloaded from SAEXAMPAPERS 8.3. The graph of f(x) = ax? + bx? — 2 has a local maximum at (—1;—1) yt f > (—1;-1) 0 x f 8.3.1 Show that a = 2 and b = 3. (4) 8.3.2 For which values of x will the graph be concave up? (3) 8.3.3. For which values of x will x. f’(x) > 0? (2) SA EXAM PAPERS Proudly South African

This Paper was downloaded from SAEXAMPAPERS 8.4 A tangent at A(3; —10) to a curve y = —x? — 1, intersects the x-axis at B. AT is perpendicular to the x —axis with T on the x —axis. \ y B T [e) x A(3;—10) Determine the length of AB. (6) [28] QUESTION 9 A ball is thrown vertically upwards. The height of the ball in meters, after t seconds is given by the equation h(t) = 9t — 2t?. 9.1 Determine the height of the ball after 2 seconds. qd) 9.2 Determine the speed of the ball after 2 seconds. (3) 9.3 After how many seconds will the ball reach the ground again? (2) [6] SA FXAM PAPERS Proudly South African

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10.3 When creating an online profile with Titus Holdings, a unique login code is generated. The code is to be alphanumeric (include digits and letters) and to be 5 characters long. The first two characters are letters and the remaining characters are digits. 10.3.1 If letters may be repeated, but the digits may not, determine how many unique login codes can be created. (2) 10.3.2 A security alert is that the codes are not safe enough and implements new restrictions on the codes. If Titus Holdings project they will have 1600 people create profiles, determine if they will have enough unique codes considering they need to meet the updated restrictions below: @ No repetition allowed (letters and digits) e All codes to begin with the letter “T” e All digits to be € {0; 2; 3; 5; 6; 8; 9} G) e The 3-digit numeric portion to be divisible by 5. [14] TOTAL 150 SA EXAM PAPERS Proudly South African

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