ADP MATH Gr12 Term 1 Summative Test 2024-2025 PDF

**Question No:** **Marks in Number** **Corrected by** **Revised by** **Maximum Mark** **Student's Mark** **Question 1** **20** **Question 2** **5** **Question 3** **6** **Question 4** **9** **Question 5** **9** **Question 6** **5** **Question 7** **6** **Total** **60** **Revise...

**Question No:** **Marks in Number** **Corrected by** **Revised by** **Maximum Mark** **Student's Mark** **Question 1** **20** **Question 2** **5** **Question 3** **6** **Question 4** **9** **Question 5** **9** **Question 6** **5** **Question 7** **6** **Total** **60** **Revised by** **Added by** ------------- ------------- ------------------- ---------------- **Subject** **MATH** **NO: of Pages** **9** **Grade** **G12 A/B** **Date** **7/10/2024** **Term** **1** **Time Allotted** **50 minutes** ------------- ------------- ------------------- ---------------- --------------------- ---------- **Final Moderator** **Signature** **Name** --------------------- ---------- **[Examination Room Rules]** \* You **must **enter an exam room without any bags and water bottles. \* Switch off your phones and smartwatches and hand them to the proctor. \* Start the test only at the teacher's instruction. \* Use only blue pens, and refrain from using correctors. \* Read all the questions carefully and answer them all according to the instructions on the exam paper. \* Revise your answers before submitting your exam paper. \* Submit the papers and leave the exam room after half of the assigned time passes.   **SECTION A:** **Question 1: Multiple choice questions (2 marks each)** **Various options are provided as possible answers to the following questions. Choose the correct answer by [drawing a circle] around the [letter] of your choice.** --------- ---------------------------------------------------------------------------------------------------------------------------------------- ------------------ **1.1** **The graph of a function f is shown below. For which of the following values of c does?** [lim~*x* → *c*~*f*(*x*) = 2]{.math.inline} **A** **0 only** **B** **0 and 4 only** **C** **-3** **D** **-3 and 0** --------- ---------------------------------------------------------------------------------------------------------------------------------------- ------------------ --------- ------- ------------------------------------------------------------------------------- **1.2** **A** \ [*f*(*x*) = *x* − 2]{.math.display}\ **B** \ [\$\$f\\left( x \\right) = \\ \\frac{x\^{2} - 4}{x - 2}\$\$]{.math.display}\ **C** \ [\$\$f\\left( x \\right) = \\ \\sqrt{x - 1}\$\$]{.math.display}\ **D** \ [*f*(*x*) = *sin*(*x* − 2)]{.math.display}\ --------- ------- ------------------------------------------------------------------------------- --------- ----------------------------------------------------------------------------------------------------------------------- --------------- **1.3** **Find the limit of** [\$\\frac{x\^{2} - 1}{x - 1}\$]{.math.inline} **as** [*x*]{.math.inline} **approaches to 1?** **A** **0** **B** **1** **C** **2** **D** **Undefined** --------- ----------------------------------------------------------------------------------------------------------------------- --------------- +-----------------------+-----------------------+-----------------------+ | **Use the graph below | | | | to answer the | | | | following 3 | | | | questions: | | | | (1.4,1.5,1.6)** | | | +-----------------------+-----------------------+-----------------------+ | **1.4** | **Find the limit as x | | | | approaches 2^+^** | | +-----------------------+-----------------------+-----------------------+ | | **A** | **1** | +-----------------------+-----------------------+-----------------------+ | | **B** | **2** | +-----------------------+-----------------------+-----------------------+ | | **C** | **3** | +-----------------------+-----------------------+-----------------------+ | | **D** | **Undefined** | +-----------------------+-----------------------+-----------------------+ | | | | +-----------------------+-----------------------+-----------------------+ | **1.5** | **Find the limit as x | | | | approaches 2^-^** | | +-----------------------+-----------------------+-----------------------+ | | **A** | **1** | +-----------------------+-----------------------+-----------------------+ | | **B** | **2** | +-----------------------+-----------------------+-----------------------+ | | **C** | **3** | +-----------------------+-----------------------+-----------------------+ | | **D** | **Undefined** | +-----------------------+-----------------------+-----------------------+ | | | | +-----------------------+-----------------------+-----------------------+ | **1.6** | **Find the limit as x | | | | approaches 2** | | +-----------------------+-----------------------+-----------------------+ | | **A** | **1** | +-----------------------+-----------------------+-----------------------+ | | **B** | **2** | +-----------------------+-----------------------+-----------------------+ | | **C** | **3** | +-----------------------+-----------------------+-----------------------+ | | **D** | **Undefined** | +-----------------------+-----------------------+-----------------------+ +-----------------------+-----------------------+-----------------------+ | **1.7** | **Use the figure | | | | shown below , and | | | | choose the correct | | | | statement:** | | | | | | | |  | | +-----------------------+-----------------------+-----------------------+ | | **A** | **The function is | | | | continuous for all | | | | real numbers.** | +-----------------------+-----------------------+-----------------------+ | | **B** | **The function is | | | | discontinuous | | | | at**[ *x* = 2]{.math | | | |.inline} | +-----------------------+-----------------------+-----------------------+ | | **C** | **The function is | | | | discontinuous at** | | | | [*x* = 1]{.math | | | |.inline} | +-----------------------+-----------------------+-----------------------+ | | **D** | **None of the above** | +-----------------------+-----------------------+-----------------------+ --------- ---------------------------------------------------------------------------------------------------------------- -------- **1.8** **The slope of the tangent line to** [*f*(*x*)= *x*^2^]{.math.inline} **at** [*x* = 3]{.math.inline} **is:** **A** **3** **B** **6** **C** **9** **D** **12** --------- ---------------------------------------------------------------------------------------------------------------- -------- --------- ----------------------------------------------------------------------------------------------------------------- ----------------------------------------------------------------- **1.9** **A function** [*f*(*x*)]{.math.inline} **is [discontinuous] at** [*x* = 2]{.math.inline} **if:** **A** \ [lim~*x* → 2−~*f*(*x*)= lim~*x* → 2+~*f*(*x*)]{.math.display}\ **B** \ [lim~*x* → 2~*f*(*x*)= 2]{.math.display}\ **C** \ [lim~*x* → 2~*f*(*x*) is exist]{.math.display}\ **D** \ [*f*(2) is undefined]{.math.display}\ --------- ----------------------------------------------------------------------------------------------------------------- ----------------------------------------------------------------- ---------- ------------------------------------------------------------------------- --------------------------------------------------------------- **1.10** **Which of the following functions is continuous at all real numbers?** **A** \ [\$\$f\\left( x \\right) = \\frac{1}{x}\$\$]{.math.display}\ **B** \ [*g*(*x*) = *x*^2^]{.math.display}\ **C** \ [\$\$h\\left( x \\right) = \\ \\sqrt{x}\$\$]{.math.display}\ **D** **None of the above** **/20** ---------- ------------------------------------------------------------------------- --------------------------------------------------------------- **Question 2: Matching Columns** **Match the letter of the word in [Column B] with the number of the related definition in [Column A]. Write down the corresponding [letter] in the space provided next to the definition in Column A.** -------------- ---------------------------------------------------------------------------------------------------------------------------------------- -- -------------- ------- ----------------------- **Column A** **Answer** **Column B** **2.1** **The graph passes through the point without a break.** **A** **Undetermined** **2.2** **is the value that (** [*f*(*x*) ]{.math.inline}**) gets closer to as** [( *x*]{.math.inline} **) gets closer to a certain value.** **B** **Slope** **2.3** **the process of changing a denominator from a radical (square root) to a rational number (integer)** **C** **Tangent** **D** **Discontinuity** **2.4** **is the straight line that just touches the curve at that point** **E** **Continuity** **F** **The limit of f(x)** **2.5** **It tells how steep the graph is at the point of tangency** **G** **Secant** **H** **Rationalizing** **/ 5** -------------- ---------------------------------------------------------------------------------------------------------------------------------------- -- -------------- ------- ----------------------- **SECTION B: Free Response** +-----------------------------------+-----------------------------------+ | **3.1** | | | ----------------------- ------- | | | -- | | |  **3.2** | | | **/6** | | +-----------------------------------+-----------------------------------+ | | | +-----------------------------------+-----------------------------------+ **Question 4: Find the slope of the tangent to the functions below: (SHOW YOUR WORK)** **(3 marks each)** +-----------------------------------+-----------------------------------+ | \ | **4.1** | | [*f*(*x*) = 3*x* − 1,  *x* = 4]{. | | | math | | |.display}\ | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | +===================================+===================================+ | **............................... | **4.2** | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | +-----------------------------------+-----------------------------------+ |  | **4.3** | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | +-----------------------------------+-----------------------------------+ | **/9** | | +-----------------------------------+-----------------------------------+ **Question 5: Calculate each limit below: (SHOW YOUR WORK) (3 marks each)** +-----------------------------------+-----------------------------------+ | \ | **5.1** | | [\$\$\\lim\_{x \\rightarrow | | | 3}\\frac{x\^{2} + 3x - 18}{x - | | | 3}\$\$]{.math.display}\ | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | +===================================+===================================+ | | | +-----------------------------------+-----------------------------------+ | \ | **5.2** | | [\$\$\\lim\_{x \\rightarrow | | | 0}{\\frac{\\sqrt{x + 9} - 3}{x} | | | =}\$\$]{.math.display}\ | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | +-----------------------------------+-----------------------------------+ | \ | **5.3** | | [\$\$\\underset{x \\rightarrow | | | 1}{lim\\ }\\frac{x\^{3} + x\^{2} | | | - 5x + 3}{x\^{3} - 4x\^{2} + 5x - | | | 2} = \\ \$\$]{.math.display}\ | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | +-----------------------------------+-----------------------------------+ | **/9** | | +-----------------------------------+-----------------------------------+ **SECTION C** +-----------------------------------+-----------------------------------+ | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | +-----------------------------------+-----------------------------------+ | | **/ 3** | +-----------------------------------+-----------------------------------+ **Question 7: Write the type of discontinuity for each function below: (6 marks)** Solved 2. Match the type of discontinuity to its graph. \| Chegg.com  Solved 2. Match the type of discontinuity to its graph. \| Chegg.com --------------------------------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------------------------------------- ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- **\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--** **\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--** **\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\-\--** **Bonus Question** +-----------------------------------+-----------------------------------+ | **7.1** | **Determine the equation of the | | | tangent to the curve of each | | | function at** [*x* = 2]{.math | | |.inline}**.** | | | | | | \ | | | [*y* = *x*^2^ − 4*x* ]{.math | | |.display}\ | | | | | | **............................... | | |................................. | | |................................. | | |.............** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | | | | | | **............................... | | |................................. | | |................................. | | |...........** | +-----------------------------------+-----------------------------------+ | | **/ 3** | +-----------------------------------+-----------------------------------+