Mathematics Grade 12 P1 Northern Cape Mock 2021 QP

Downloaded from hlayiso.com DEPARTMENT OF EDUCATION DEPARTEMENT VAN ONDERWYS LEFAPHA LA THUTO ISEBE LEZEMFUNDO GRADE 12 MATHEMATICS P1 SEPTEMBER 2021 IITA ES ee I -06060000 This question paper consists of 11 pages including an information sheet, Copyright reserved NORTHERN CAPE Please turn over

SU eet os060000 Downloaded from hlayiso.com Mathematics P1/Grade 12 3 QUESTION 1 1.1 Solve for x. ll y2_y-6=0 1.1.2 x(x+6)+1=0(correct to TWO decimal places) 113 6x-257 <0 1.2 Solve simultaneously for x and y: x-y=3 and x°-3y? =13 1.3 If x°=7 and x>0, determine the value of x! without using a calculator. QUESTION 2 2.1 The first four terms of a quadratic number pattern are 171; 282; 387; 486... 2.1.1 Write down the second difference. 2.1.2 Determine the 7“ term of this pattern in the form T, =an +bn+c. September 2021 3) ) (3) (6) © G) [24] 2) (4) 2.1.3 Another pattern, with general term, P, =-60n+2754, is given. Which term of this new pattern will be the same as that of the quadratic pattern 171; 282; 387; 486 ...? a ee 22 tri ies —+—+— +... Study the geometric seri Be ae ae 2.2.1 Calculate the sum of the first 16 terms. 1023 2.2.2 Calculate the value of n such that S,, —7, = : 4096 Copyright reserved (4) GB) (5) [18] Please turn over

Mathematics P1/Grade 12 4 QUESTION 3 n Consider: (6k +13) k=l 3.1. Show that "(6k +13)= 3n? +16n. k=l 3.2 Hence, calculate the difference between the sum of the first 34 terms and the sum of the first 33 terms. 3.3. The first difference of a quadratic number pattern is given by T, =6k+ 13. Pd fifth term of the quadratic number pattern is 120, determine the value of the thir term. Copyright reserved Downloaded from hlayiso.com sestember2021 (3) (2) GB) (3) Please turn over

eTOBOUUU Downloaded from hlayiso.com Mathematics P1/Grade 12 5 September 2021 QUESTION 4 Sketched below are the graphs of f(x)=-x?+4x+5 and g(x)=——+4. B is the x+p turning point of f. The asymptotes of g intersect at B and the point A(3 ; 10) lies on g. Cand D are the x-intercepts of f y & i AG310) Cc D x [e} ot 4.1 Determine the coordinates of B. (3) 4.2 Hence, write down the values of p and q. (2) 4.3 Describe the nature of roots of the graph of ¢, if ¢(x)=—f(x)+10. (2) 44 The graph of h, where h(x) = g(x +m) +n, has asymptotes x=4 and y = 3. Write down the value(s) of m and n. (2) 4.5 The tangent, y=6x+k, touches the graph of at P. Determine the coordinates of P. (4) 46 Determine the values of x for which: 4.6.1 g(x)210 (2) 462 f(x).g/(x)>0 (4) [19] Copyright reserved Please turn over

Mathematics P1/Grade 12 Downloaded from hlayiso.com QUESTION 5 In the diagram below, the graph of f(x) =b" is drawn. AG; 8) i 5.1 Calculate the value of b. 5.2. Determine the equation of f” | the inverse of f, in the form y = ... 5.3 Sketch the graph of f'. Clearly show the intercept(s) with the axes, as well as the coordinates of ONE other point. 5.4 Determine for which values of x, will f Nx) <4. . 1 5.5 Describe the transformation from f to h(x) = q F(x). f Copyright reserved sa point onf- A(3; 8) September 2021 (2) (2) 3) 3) 3) [13] Please turn over } De

en ee “TT REE ee 03060000 Downloaded from hlayiso.com Mathematics P1/Grade 12 7 September 2021 QUESTION 6 6.1 Bonolo Rentsi deposits R4 100 quarterly in a retirement fund for 20 years. The fund earns interest at a rate of 6% p.a. compounded quarterly. The first deposit was made at the end of March of the first year and the last deposit at the end of December of the 20" year. 6.1.1 How much will be in the fund after 20 years? 6.1.2 After 20 years she decides not to withdraw the money, but leave it in the fund for another 5 years without making any further payments. The interest increases to 6,2% p.a. compounded semi-annually. Calculate the total amount in the fund at the end of 25 years. 6.2 A couple is planning to purchase their first home, The bank agrees to a loan of R660 000 at an interest rate of 11% p.a. compounded monthly, The loan is repayable over 15 years, The first payment is due at the end of the first month. 6.2.1 Calculate the monthly payments. 6.2.2 After the 84" payment, the couple decides to increase their monthly payments. Calculate the balance of the loan after the 84 payment. 6.2.3 From the 85 payment they increase the monthly payments to R10 000. Calculate the number of instalments left to settle the loan sooner. QUESTION 7 71 Determine f(x) from first principles if f(x)= 4x? -3. F Determine: Ta “ ify =@x—4\5x+2) 7.2.2 ( * | Gil pease ax x Copyright reserved co) 2) )) 3) (4) {15} 6) @) (4) (11) Please tum over

witness Downloaded from hlayiso.com o™ 12 8 September 202} QUESTION 8 n the diagram below, the eraph of A(x) =(x—1)2(x thee _$y247x—3 is drawn. A andB are aN the x-intercepts and C the minimum turning point of A. ‘ h 0 A B ee Cc 8.1 Calculate the coordinates of: 8.1.1 AandB GB) 8.1.2 C (4) 8.2 Determine the value(s) of x for which: 8.2.1 the graph is concave down. (3) 8.2.2 A(-x)>0 (2) 8.3. Determine the value(s) of p for which h(x)+4 = p has only one solution. (4) [16] Copyright reserved Please turn over Aye od

errr TAT TIE o2060000 Downloaded from hlayiso.com Mathematics P1/Grade 12 9 September 2021 QUESTION 9 The figure below shows a solid brick in the shape of a rectangular prism. The length is 5x units. The width is x units and the height is # units. The total surface area is 720 cm’. 9.1 Show that the volume of the brick is given by: V =300x -32 cubic units. (5) 9.2 Calculate the maximum volume of the brick. (5) [10] QUESTION 10 10.1 Events A and B are given such that P(Aor B)= 3 and P(4)= : : Determine P(B) if: 10.1.1 A and B are mutually exclusive. (2) 10.1.2 A and B are independent events. (3) 10.2 Events S and T are independent such that P(S)= P(T)=y and P(Sor T)=0,84. Determine the numerical value of y. (5) [10] Copyright reserved Please turn over y

Downloaded from hlayiso.com _ sesmber202 Mathematics P1/Grade 12 10 QUESTION 11 A four digit code is created by using the numerals 0 to 6. 2 2 11.1 How many four digit codes can be formed if the numerals can be repeated @) 000, 11.2 Howmany four digit codes can be formed if the code has to be os ee So but less than 3 000 and the code must be an even number? A numeral m @) be used once. [6] GRAND TOTAL: — 150 £ Please turn over Copyright reserved ‘