Mathematics Grade 12 P1 North West Mock 2025 Question Paper

education Department: Education North West Provincial Government REPUBLIC OF SOUTH AFRICA fi NATIONAL SENIOR CERTIFICATE | GRADE 12 MATHEMATICS P1 SEPTEMBER 2025 MARKS: 150 TIME: 3 hours This question paper consists of 10 pages and 1 information sheet. Copyright reserved Please turn over

Mathematics/P1 3 NW/September 2025 NSC QUESTION 1 11 Solve for x: LLL (w¥-3)3x+15)=0 (2) 1.1.2 7x? — 4x —5=0 (correct to TWO decimal places) (3) 1.13. x*°+4)<0 (2) 1.1.4 Sie — Ot 8 (6) 1.2 Solve for x and y simultaneously: 2y —x =3 and y?—2x?-x-1=0 (6) 19 — 3x? 13 Show that the roots of p = are real for all values ofp € R. x Show ALL calculations. (4) [23] QUESTION 2 2.1 Consider the following geometric series: p + 21+ 63 +... +137 781 2.1.1 Determine the value of p. (2) 2.1.2 Determine the number of terms in the series. (3) 2.1.3. Calculate the sum of this series. (2) 22 A school hall is filling up at a rate of 10 learners in the first minute, 14 learners in the second minute, 18 learners in the third minute, and so on. 2.2.1. How many learners will enter the school hall during the 8" minute? (3) 2.2.2 The school hall is a fifth full after 8 minutes. After how many minutes will the school hall be full? (6) [16] Copyright reserved Please turn over

NW/September 2025 Mathematics/P 1 & NSC QUESTION 3 Consider the following quadratic sequence: 10; 21; 38... 3.1 Determine the general term of the quadratic sequence. ” 32 Determine the tenth term of the quadratic sequence. (2) : i ith95. (3 3.3 Determine which two consecutive terms of the quadratic sequence differ with 95. (3) 19] QUESTION 4 Given: f(x) = log, x 2 4.1 Write down the equation of the asymptote of f. (1) 4.2 Determine the equation of f7' inthe formy=... (2) 43 If g(x) = f "(x —3) -2, determine the x-intercept of g. (3) 4.4 Write down the equation of the asymptote of g . (1) 4.5 Sketch the graph of g. Clearly show ALL the intercepts with the axes and the asymptote. (4) (11) Copyright reserv ed Please turn over

Mathematics/P 1 5 NW/ NSC ‘September 2025 QUESTION 5 Sketched below are the graphs of f(x) = ae: a 5° + bx +c and g(x) = x+ +q. The axis f symmeti es a : : s ~ og é x 4 is the vertical asymptote of g. The line h is an axis of ty of g. Ais the y-intercept of f and g. B(2 ; 0) isa x-intercept of f and h. y 5.1 32 53 5.4 3.5 5.6 5.7 5.8 Show that the equation of f is f(x) =—- * —-x+4. Write down the coordinates of the y-intercept of /. Determine the coordinates of the turning point of /. Determine the equation of h. Determine the equation of g. Determine the coordinates of the x-intercept of g. For which values of x will it be: g(x) .f (x) <0? Determine the equation of k(x) if & is the reflection of g about the line x = 4. -£ ft.N1 lh as os 2”

Mathematics/P1 6 NW/September 2025 NSC QUESTION 6 Mathew’s dad died and he inherited the farm. His dad planned to install solar panels and already paid a deposit of R202 500 which is 15% of the cost of the solar panels. 6.1 Determine the cost of the solar panels. 6.2 The bank grants Mathew a loan at an interest rate of 9,8% per annum, compounded monthly, to pay off the balance of the cost of the panels. Mathew agreed to pay monthly instalments of R20 000. How many monthly instalments are required to pay off the loan? 6.3 After 2 years Mathew decided to pay off the loan. Determine the balance of the loan after 2 years. 6.4 — Calculate the total amount paid for the panels, QUESTION 7 7.10 Given: f(x) =x? —x+3 Determine / ‘(x) from first principles. 7.2 Determine f' (x) if: T2sl (x)= 58-784 2 122 fQx)= = x (2) (6) (3) G) [14] (5) (2) (4) (11)

Mathematics/P 1 NW/September 2025 NSC QUESTION 8 a =; 2 a The graph of f(x) =x" + bx’ + ex +d is sketched below. A and Bare the turning points of f. f(x) >0 for x>2. The line y=20 isa tangent to f atx=1. 4 y A f ya B < Se v 8.1 Show that b=—6, c =9 and d= 16. (5) 8.2 For which values of x is f strictly decreasing? (2) 8.3 g(x) = mx — 16 isa tangent to f. Determine the value of m. (6) [13] Copyright reserved Please turn over

NW/September 2025 Mathematics/P1 NSC QUESTION 9 ; three The rough sketch graphs below represent the distance covered by each A pil pea athletes: Ben, John and Chris, in a marathon race of 80 km at different a bee: start of the race. The y-axis represents the distance in km and x-axis the time 1 - The following equations represents roughly the movements of the three athletes: Ben: f(x)=mx +c; John: g(x) =2,6x? Chris: k(x) = x° - 10,5x” + 37x 9.1 Which athlete was leading after the first hour? (1) 9.2 Which athlete completed the race in the shortest time? () 9.3. During the race, Chris slowed down to drink water. Determine after how many kilometres Chris run at his slowest speed. (NOTE: Chris never actually stopped during the race.) (5) 9.4 Atwhat time during the first part of the race, were John and Chris the furthest apart from one another? Show ALL calculations. Give your answer in hours and minutes. (4) (11)

Mathematics/P | 9 NSC QUESTION 10 Three events A, B and C are represented on the Venn-diagram below. e A and B are independent events. e Aand C are mutually exclusive events. e P(A) = 0,25. e P(A or B) = 0,55. e x lies outside the P(A), P(B) or P(C), but inside the sample space. 10.1 Show that P(B) = 0,4. 10.2 Calculate P(A and B). 10.3. If P (only C) = 0,25. Calculate x. 10.4 If it is further given that P[(NOT A) and (NOT C)] = 0,38. Calculate P(only B). NW/September 2025 (3) (2) (2)

pee eer a cre NRE TE NW /September 2025 10 Mathematics/P | NSC QUESTION 11 Examination numbers for the grade 12 final examination are determined in the following way: «The first digit is the province number. Northwest is number 9. The 2nd and 3rd digits are the year. For this year it will be 25. The 4th digit is the district number. ¢ Digits 5 to 8 are the centre or school number. © The last 4 digits are the candidate’s number in his/her school. d the digits may repeat. j The examination number may contain digits 0 to 9 an district Consider only examination numbers for the year 2025 of Northwest and distric _ number 4, An example of an examination number: S'(o)= | 9 [25] 4 | 4085 | oor a province | year | district | centre [ candidate number al} d=; | 11.1 Determine the number of different examination numbers (for the year 2025 of -—_ Northwest and district 4) that can be formed by using this system. (2) aw 11.2. An examination number (for the year 2025 of Northwest and district 4) is (r-a}’+(y- randomly selected. In ABC: _A SIN « Calculate the probability that this examination number will have a centre number: 5 a~ = that is an even number between 1000 and 5000 ¢ where the digits may not repeat (5) areaAs (7 : , sin(a + 8) = sin a.cos TOTAL: 150 cos(a + )=cosa.coss ‘cos*a@-sin’a@ cos2a ={1-2sin?a 2cos*a-1

NW/September 2025 Mathematics/P1 10 NSC QUESTION 11 inati ined i lowin, Examination numbers for the grade 12 final examination are determined in the fol g way: The first digit is the province number. Northwest is number 9. The 2nd and 3rd digits are the year. For this year it will be 25. The 4th digit is the district number. Digits 5 to 8 are the centre or school number. The last 4 digits are the candidate’s number in his/her school. The examination number may contain digits 0 to 9 and the digits may repeat. ae Consider only examination numbers for the year 2025 of Northwest and district number 4. An example of an examination number: 9 25 4 4085 0001 rovince | year | district | centre | candidate number 11.1 Determine the number of different examination numbers (for the year 2025 of Northwest and district 4) that can be formed by using this system. (2) 11.2. An examination number (for the year 2025 of Northwest and district 4) is randomly selected. Calculate the probability that this examination number will have a centre number: e that is an even number between 1000 and 5000 e where the digits may not repeat (5) (7] TOTAL: 150