ELECTIVE(FURTHER) MATHEMATICS
{For wassce Bece Novdec Nabptex whatsapp 0547316472}
{For wassce Bece Novdec Nabptex whatsapp 0547316472}
*Q 1(c)* If f(x)=2x²+x/2 and g(x)=1/x +4, Find :
*(i)* f(½),
*(ii)* f(¼) × g(½).
*(i)* f(½),
*(ii)* f(¼) × g(½).
*2(a)* Under Mapping h(x)=px²–qx + 2, the image of 3 is 14 and the image of –2 is 24. Find :
*(i)* The value of p and q.
*(ii)* The elements whose image is 4.
3.The function f and g are given as f(x)=x+3/x and g(x)=2x+1.
Evaluate: *(i)* g(–2), *(ii)* f(–½).
Evaluate: *(i)* g(–2), *(ii)* f(–½).
The function f and g are defined as f:x–> x–2 and g(x)–> 2x²–1. Solve :
*(i)* f(x)=g(–½)
*(ii)* f(x) + g(x)=0.
*(ii)* f(x) + g(x)=0.
4.Given that f(x)=2x–1 and g(x)=x² + 1:
*(i)* Find f(1+x):
*(ii)* Find the range of values of x for which f(x)< –3;
*(iii)* Simplify f(x)–g(x).
5.The functions f and g are defined as
f:x–> 3x–2, g(x)=1/x (x≠0).
f:x–> 3x–2, g(x)=1/x (x≠0).
*Evaluate* : *(i)* f(–2), *(ii)* g(½).
*solve*
*(iii)* f(x)=g(½),
*(iv)* f(x)=g(x).
6.If f(x)=4x –2, find :
*(i)* f(2),
*(ii)* f(2t).
*(b)If p= ( 3 ) and q= (–1 )*
*2* *3*
*(i)* Find the vector representing *3p–q*
*2* *3*
*(i)* Find the vector representing *3p–q*
*(ii)Given that :ap + bq =( 3 )
*7(a)* If f(x)=2x²–3x + 4, Simplify f(x)+3x.
*(b)* If g(x)= (x + 3)(x–4)/2.
*(i)* Find the values of x for which g(x)=0.
*(ii)* Evaluate g(–1).
*(iii)* Find the values of C for which g(c)=–3.
8.Two functions, f and g are defined by
f:x—> 2x²–1 and g:x—>3x + 2 Where x is a real number.
f:x—> 2x²–1 and g:x—>3x + 2 Where x is a real number.
*(i)* if f(x–1)–7=0;
*(ii)* Evaluate f(½)g(3)/f(4)–g(5)
*(b)* An Operation (*) is defined on the set R of real numbers by m(*) n=–n/m²+1, Where m,n € R.
QUESTION 10
Using a ruler and a pair of compasses only, construct a triangle ABC such that lABl=7.1cm, lACl=7cm, and <BAC =105°. Construct the bisector of <BAC to meet BC at X and the bisector of AC to meet AX produced at Y. Measure :
*(a)* IXYl,
*(b)* IBCI.
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*(a)* IXYl,
*(b)* IBCI.
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QUESTION 11
(a)* Copy and complete the table of values for y=x²–2 for –3≤x≤4.
*__________________________________*
x –3. –2. –1. 0. 1 . 2. 3. 4.
y. 2. –2. 2. .
*_________________________________*
*(b)* Using a scale of 2cm to 1 unit on the X-axis and a scale of 2units on the y-axis, draw the graph of y=x²–2.
*(c)* Use your graph to find the:
*(i)* root of the equation x²–2=0;
*(ii)* Values of x for which x²–3=0;
*(iii)* gradient of the curve at the point where x=–1.
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(a)* Copy and complete the table of values for y=x²–2 for –3≤x≤4.
*__________________________________*
x –3. –2. –1. 0. 1 . 2. 3. 4.
y. 2. –2. 2. .
*_________________________________*
*(b)* Using a scale of 2cm to 1 unit on the X-axis and a scale of 2units on the y-axis, draw the graph of y=x²–2.
*(c)* Use your graph to find the:
*(i)* root of the equation x²–2=0;
*(ii)* Values of x for which x²–3=0;
*(iii)* gradient of the curve at the point where x=–1.
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*QUESTION 12*
*(a)* Three positive numbers are in Arithmetic progression (AP). The sum of the squares of the three numbers is 155 while the sum of the numbers is 21. If the common difference is positive, find the numbers.
*(b)* If the total surface area of a sphere is 154cm², find its radius.
[ Take π=22/7]
*(b)* If the total surface area of a sphere is 154cm², find its radius.
[ Take π=22/7]
*QUESTION 13*
*(a)* Without using tables or calculator, evaluate √0.14×3.2/0.0028×90.
*(b)* The piolet of an aircraft 2,000 metres above the sea level observes at an instant that the angle of depression of two boats which are in direct straight line are 50° and 72°. Find, correct to the nearest metre, the distance between the two boats.
*(b)* The piolet of an aircraft 2,000 metres above the sea level observes at an instant that the angle of depression of two boats which are in direct straight line are 50° and 72°. Find, correct to the nearest metre, the distance between the two boats.
*QUESTION 14*
*(a)* Using a scale of 2cm to 2units on both axes, draw on the graph sheet two perpendicular axes, Ox and Oy, for the interval –10 ≤x 10, –12 ≤ y ≤ 12.
*(b)* Draw clearly, label the vertices and indicate coordinates as appropriate,
*(i)* triangle ABC with vertices
A(3, 1), B(1,5) and C(5, 7);
*(ii)* image triangle A1 B1 C1 of triangle ABC under an enlargement with scale factor –½ from the origin where A––>A1,
B––>B1, and C––>C1;
*(iii)* image triangle A2 B2 C2 of triangle ABC under an anticlockwise rotation of 90° about the origin where A–– >A2, B–– >B2, and C––>C2.
*(c)* Determine the equation of the line A2C2.
*(b)* Draw clearly, label the vertices and indicate coordinates as appropriate,
*(i)* triangle ABC with vertices
A(3, 1), B(1,5) and C(5, 7);
*(ii)* image triangle A1 B1 C1 of triangle ABC under an enlargement with scale factor –½ from the origin where A––>A1,
B––>B1, and C––>C1;
*(iii)* image triangle A2 B2 C2 of triangle ABC under an anticlockwise rotation of 90° about the origin where A–– >A2, B–– >B2, and C––>C2.
*(c)* Determine the equation of the line A2C2.
*QUESTION 15*
*(a)* Draw the
*(i)* addition (+)
*(ii)* Multiplication (×)
tables for the set x={ 1,2,3,4,5,6} modulo 6.
*(b)* From your tables, solve :
*(i)* (4 (+) n) (+) n =4;
*(ii)* t (+) (t (×) 3)=2.
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*(a)* Draw the
*(i)* addition (+)
*(ii)* Multiplication (×)
tables for the set x={ 1,2,3,4,5,6} modulo 6.
*(b)* From your tables, solve :
*(i)* (4 (+) n) (+) n =4;
*(ii)* t (+) (t (×) 3)=2.
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