# Maths Paper 1, November 2024 > Practise 49 questions (150 marks) from Grade 12 Maths Paper 1 November 2024. Answer any one and see it marked mark by mark, like the exam. Canonical: https://sharpkop.co.za/maths/2024-nov-p1/ Last updated: 2026-11-12 49 questions in this paper. Answer any one and see it marked mark by mark. ## Every question - [1.1.1 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q1-1-1/): Solve for x: x(x + 5) = 0 - [1.1.2 (4 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q1-1-2/): Solve for x: 3x^2 + 2 = 7x. Round your answers to TWO decimal places. - [1.1.3 (4 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q1-1-3/): Solve for x: x^2 - 4x - 5 > 0 - [1.1.4 (5 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q1-1-4/): Solve for x: 3^(2x) - 3^(x+2) + 8 = 0. Hint: leave your answers in exact form if needed. - [1.1.5 (4 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q1-1-5/): Solve for x: √(3x+10)-x=2 - [1.2 (5 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q1-2/): Solve for x and y simultaneously: 2x + y = 5 y^2 + xy = 3 - [1.3 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q1-3/): Look at the product (1+1/3)(1+1/4)(1+1/5)…(1+1/n), where n ≥ 3 and the last factor is 1+1/n. - [2.1.1 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q2-1-1/): An arithmetic series has a first term of 4 and a common difference of 3. The series has 30 terms. Calculate the sum of all 30 terms. - [2.1.2 (4 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q2-1-2/): The first term of an arithmetic series is 6 and the common difference is 4. The series has 15 terms. - [2.2.1 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q2-2-1/): The first differences of a quadratic number pattern are 4; 6; 8; … Given that T_(60) = 3 500, calculate the value of T_(59). - [2.2.2 (5 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q2-2-2/): The first differences of a quadratic number pattern are: 4; 6; 8; … The third term of the pattern is 22. - [3.1 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q3-1/): A circle with radius 20 cm is drawn. A second, smaller circle is drawn so that it passes through the centre of the first circle and... - [3.2 (4 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q3-2/): A circle of radius 8 cm is drawn. A second, smaller circle is drawn so that it passes through the centre of the first circle and touches... - [3.3 (4 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q3-3/): A circle of radius 20 cm is drawn. A second circle is drawn so that it passes through the centre of the first circle and touches the... - [4.1 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q4-1/): The function g is defined by g(x) = b^x + 2, where b > 0. The point P(3; 43/8) lies on the graph of g. Calculate the value of b. - [4.2 (1 mark)](https://sharpkop.co.za/maths/2024-nov-p1/q4-2/): The function g(x) = b^x + 3 is defined for b > 0, and the point P(2; 37/4) lies on g. - [4.3 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q4-3/): The function g is defined by g(x) = b^x - 2 where b > 0. The point P(2; -7/4) lies on g. - [4.4 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q4-4/): The function f(x)=(1/2)^x-1 is given. C is the point on the graph of f where y=7. - [5.1 (1 mark)](https://sharpkop.co.za/maths/2024-nov-p1/q5-1/): The diagram below shows the graph of f(x) = a/(x + p) + q with domain x ∈ R, x ≠ 2. Write down the value of p. - [5.2 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q5-2/): The diagram below shows the graph of f(x)=a/(x+p)+q with domain (-∞;2)cup(2;∞). The graph of f cuts the y-axis at (0;2). - [5.3 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q5-3/): The diagram below shows the graph of f(x)=a/(x+p)+q, with domain xinR, x ≠ 2. The vertical asymptote is x=2 and the horizontal asymptote... - [5.4 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q5-4/): The graph of f(x)=(-6)/(x-2)-2 is drawn in the diagram below. Its domain is x ∈ (-∞;2)cup(2;∞). - [5.5 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q5-5/): The function f is given in the information above. Graph f is transformed to a new graph h so that: • h has the same domain and the same... - [6.1 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q6-1/): The diagram below shows the graph of f(x) = -x^2 + 6x + 7, a parabola with turning point B. Calculate the coordinates of B. - [6.2 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q6-2/): The diagram below shows the parabola f(x) = -x^2 + 2x + 8 and a straight line g. - [6.3 (4 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q6-3/): The diagram below shows the parabola f(x) = -x^2 + 6x + 7 and the straight line g(x) = 2x + 2. - [6.4 (5 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q6-4/): The diagram below shows the parabola f(x) = -x^2 + 6x + 7 and a straight line g. - [7.1 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q7-1/): On the day Sipho was born, his aunt invested R10 000 in a savings account. The account earns interest at 4% p.a., compounded quarterly. - [7.2 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q7-2/): A laptop loses value over time using the straight-line method of depreciation. - [7.3.1 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q7-3-1/): Naledi borrowed R80 000 from a bank on 1 July 2023. She agreed to repay the loan over 4 years in equal monthly instalments of R2 000... - [7.3.2 (7 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q7-3-2/): Sipho took out a loan of R80 000 on 1 June 2021 at an interest rate of 12% p.a., compounded monthly. - [8.1.1 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q8-1-1/): Find d/dx[7x^2 - 4x]. - [8.1.2 (4 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q8-1-2/): Determine f’(x) if f(x) = 3/(x^4) - 3√(x^5). - [8.2 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q8-2/): Find the equation of the tangent to the curve g(x) = x^3 - 3x^2 + 4x + 1 at the point where x = 2. - [8.3.1 (5 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q8-3-1/): Given: g(x) = -4x^2. Use first principles to determine g’(x). - [8.3.2 (1 mark)](https://sharpkop.co.za/maths/2024-nov-p1/q8-3-2/): The function g is defined by g(x) = -4x^2. State one way to restrict the domain of g so that its inverse, g^(-1), is a function. - [8.3.3 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q8-3-3/): The function g is defined by g(x) = -4x^2. Find the inverse relation of g and write it as y = …, choosing the branch for which y ≤ 0. - [9.1 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q9-1/): The diagram below shows the graph of a cubic function g with turning points P(1;8) and Q(2;7). The graph cuts the y-axis at R(0;3). - [9.2 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q9-2/): The diagram below shows the graph of a cubic function g with turning points P(1;8) and Q(2;7). The graph cuts the y-axis at R(0;3). - [9.3 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q9-3/): The diagram below shows the graph of a cubic function g with turning points P(1;8) and Q(2;7). The graph cuts the y-axis at R(0;3). - [9.4 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q9-4/): The diagram below shows the graph of a cubic function g with turning points P(1;8) and Q(2;7). The graph cuts the y-axis at R(0;3). - [10.1 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q10-1/): A delivery drone flies from a depot and lands at a warehouse. Its speed, in km/h, after t hours of flight is given by v(t) = -2t^2 + 12t. - [10.2 (5 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q10-2/): A runner travels from checkpoint A and stops at checkpoint B. Her speed (in km/h) after t hours is given by s’(t) = -6t^2 + 24t, where... - [11.1 (3 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q11-1/): Draw a Venn diagram with three overlapping circles to show ALL the learners who write these examinations, and fill in the number in... - [11.2 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q11-2/): Calculate the probability that a learner chosen at random writes at least TWO of the three subjects. - [11.3 (4 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q11-3/): Decide whether the events "a learner sits for Mathematics" and "a learner sits for Tourism" are independent. - [12.1 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q12-1/): A school locker uses a 4-character lock code made from the 26 letters of the alphabet and the digits 0 to 9. - [12.2 (4 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q12-2/): Work out how many different passes can be made under these conditions: • No vowel (A, E, I, O, U) may be used • The first letter cannot... - [12.3 (2 marks)](https://sharpkop.co.za/maths/2024-nov-p1/q12-3/): A company makes 4-character codes in the form letter | digit | letter | digit. ## Related - [Grade 12 Maths past papers](https://sharpkop.co.za/maths/) Questions are based on National Senior Certificate papers set by the Department of Basic Education. 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