Grade 11 Mathematics (MATH) November Paper 2 and memo - 2023 (2)
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Course
Mathematics
Institution
11th Grade
Grade 11 Math November Paper 2 and Memo:
Total: 150 Marks.
This exam covers the following work:
Statistics | Euclidean and Analytical Geometry | Trigonometry
This is a practice paper with memorandum meant to test the student's knowledge, and will not be the same paper written for the exam...
QUESTION 1
1.1 Solve for x :
1.1.1 x 2−5 x−6=0 (2)
1.1.2 ( 2 x−3 ) ( x+1 ) =9 (3)
1.1.3 x−√ x−1=3 (4)
1.1.4 x ( x +10 ) >−25 (4)
2
1.1.5 x 3 =4 (3)
1.1.6 22 x −4 x−1=12 (4)
1.2 Simultaneously solve x and y :
2 x− y=1 and 3 x 2−4 xy + y 2=0 (5)
1.3 Solve the following inequalities:
1.3.1 x 2+ 5 x−6>0 (3)
1.3.2 −3 ( x+ 1 )( x−2 )< 0 (3)
[31]
QUESTION 2
2.1 x=−3 ± 2 √2 are the roots of a quadratic function, f (x), of which the y-intercept is 4.
Determine f ( x). (5)
2
x −2 x +2
2.2 Given: g( x )=
3−x
2.2.1 For which values of x will g(x ) be undefined. (2)
2.2.2 Explain why g( x ) will never equal zero. (Show all your calculations). (3)
2−x
2.3 Solve x if : < 0. Graphically represent your answer. (5)
x+5
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Grade 11 November Paper 1
,2.4 Simplify and leave an answer with positive exponents only:
√
x x+1
4 3 .9
(4)
27 x+2
2.5 Without solving the equation, determine the nature of the roots of: 4 x2 =2 x +1. (5)
[24]
QUESTION 3
3.1 The first three terms of a linear series, is given as: 3 x−2 ; x+ 9; 2 x +5
3.1.1 Determine the value of x . (3)
3.1.2 Determine the numerical value of T3. (2)
3.2 Given the quadratic series: −128 ;−84 ;−48 ;−20 ; ...
3.2.1 Determine the next two terms of the series. (2)
3.2.1 Determine T n, the general term of the pattern. (3)
3.2.3 Given that T n=−4 n2 +56 n−180 , determine the largest possible
numerical value for T n . (4)
3.3 Given T n=13−3 n :
3.3.1 Which term in the series would be equal to -179. (3)
3.3.2 Determine the numerical value for the 11th term. (2)
3.4 James and John look at the following patterns:
Pattern 1 Pattern 2 Pattern 3
James says if he increases the pattern number by one, square that number and then
subtract the pattern number increased by one he will get the general formula.
John says he can derive the general formula for the number of blocks by taking the number
of columns in each pattern and multiplying if by the number of rows.
Who is correct between James and John? Prove your answer. (5)
[24]
QUESTION 4
−3
Given: f ( x)= −1 and g( x )=−a x . The point (1 ;−3) lies on g .
x +3
4.1 Determine the value of a . (2)
4.2 Draw a neat sketch of the two graphs on the same axis. Show all intercepts
with the axes and asymptote clearly. (5)
4.3 Determine the axis of simmetry of f that has a positive gradient. (2)
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Grade 11 November Paper 1
, [9]
QUESTION 5
R(−1 ; 9) is the turning point of : f ( x )=a x2 +bx +c . P and Q are the x -intercepts of f .
TV is a straight line parallel to the y -axis. For g ( x )=x+ 4 , the x -intercept is at point P.
S is one of the intercept points between f and g .
5.1 Calculate the coordinates of P. (2)
5.2 Show that for f ,a=−1 , b=−2∧c=8. Show all your calculations. (5)
5.3 Calculate the coordinates of S, the intercept point of the two graphs f and g. (4)
5.4 Determine the maximum length of TV between the points P and S. (5)
[16]
QUESTION 6
4 1
In the figure below, where f ( x )= +3 and g ( x )= x+5 .
x +2 2
Determine the following:
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Grade 11 November Paper 1
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