E
PAGE
NURTURE WORKSHOPADDITIONAL MATHEMATICS SPM
CHECK LISTS3472/1 (Paper 1)TopicsPage
1. Functions1
2. Quadratic Equations (QE)4
3. Quadratic Functions (QF)9
4. Quadratic Inequality (QI)11
5. Indices12
6. Logarithms14
7. Trigonometric Functions17
8. Statistics21
9. Linear Law23
10. Coordinate Geometry25
11. Application of Differentiation26
12. Application of Integration31
13. Probability Distribution 32
14. Arithmetic Progression (AP)33
15. Geometric Progression (GP)34
16. Vectors34
17. Permutation nPr35
18. Combination nCr35
19. Probability36
20.
Working and Answers
Provided by
.
Hj. Busrah Bin Md.SehSMK Jasin,
Melaka.April 2014
1. Diagram shows the relation between set X and set Y
in the graph form.
State
a. the relation in the form of ordered pairs.
b. the type of relation.
c. the range of the relation.
Format SPM 2010 / (3 marks)2. Given the functions and ,
Find
a. h-1(x)
b. gh-1(5)
Format SPM 2010 / (3 marks)3.
Given that f(x) = 3x + 4 and gf(x) = 6x + 7, Find
a. gf(2)
b. g(x)
Format SPM 2012 / (4 marks)
4.
Given that f(x) = 3x + 4 and fg(x) = 6x + 7, Find
a. fg(2)
b. g(x)
Format SPM 2012 / (4 marks)
5. Quadratic equation (1 p)x 2 6x + 5 = 0, where p is a constant, has two different roots. Find the range of values of p
Format SPM 2010 / (3 marks)
6. Quadratic equation x(3x p) = 2x 3, where p is a constant, has real roots.
Find the range of values of p
7. It is given that 3 and m are the roots of the quadratic equation x2 + (n 1)x + 6 = 0 ,
where m and n are constants.
a. Find the value of m and of n.
b. Form new quadratic equation whose roots 2m and n + 1
Format SPM 2012 / (4 marks)
8.
The quadratic function f(x) = 2x2 5x + 7 can be expressed in the form of
f(x) = 2(x m)2 + n where m and n are constants. Find the value of m and of n.
Format SPM 2007 / (3 marks)
9. Diagram shows the graph of quadratic function f(x) = 3(x 4)2 + 2k, where k is a constant.
The curve y = f(x) has the minimum point (q, 6), where q is a constant.
State
a. the value of qb. the value of kc. the equation of the axis of symmetry.
Format SPM 2005 / (3 marks)
10. Given that f(x) = 3x2 2x 13, find the range of values of x for f(x) 5.
Format SPM 2012 / (3 marks)11. Given that f(x) = 3x2 2x 13, find the range of values of x for f(x) > 5.
Format SPM 2012 / (3 marks)12. Given that , find the value of n
Format SPM 2007 / ( 3 marks)
13. Solve the equation Format SPM 2010 / (3 marks)
14. Solve the equation
Format SPM 2010 / (3 marks)15. Solve the equation log 9 (x + 6) = log 3 x
Format SPM 2008 / (3 marks)
16. Solve the equation 3 + log 2 (x 2) = log 2 x
Format SPM 2008 / (3 marks)17. Simplify 2 3 log 25 x2 + log 5 (2x + 1)
Format SPM 2011 / (3 marks)
18. Given that log 2 5 = m and log 2 7 = p, express in terms of m and p
i. log 2 4.9ii. log 4 35
Format SPM 2010 / (4 marks)19. Given that sin = , where is an obtuse angle.
Find a. cot b. sin 2
Format SPM 2009 / (3 marks)20. Given that sin A = and cos B = where A is an obtuse angle and B is a reflex angle.
Find c. tan Ad. sin (A + B)
Format SPM 2009 / (3 marks)
21. Solve the equation 3 sin 2 sin = 0 for
Format SPM 2011 / (3 marks)22. Solve the equation 4 cos 2 + sin = 3 for
Format SPM 2011 / (4 marks)Note.
1.2.
3.
23.
The mean of a set of numbers 2, y, 5, (2y 1), 11 and 13 is 7
a. Find the value of y. Hence, state the value of standard deviation.
b. Each number in the set is multiplied by 3 and then 2 is added to it. For this set
of numbers, find
i.. the mean
ii. the standard deviation
Format SPM 2011 / (4 marks)Note;
ValueSetiap data dalam set
Add by a or Subtract by aMultiply by a Divide by aAdd by a and Multiply by b
ModeFollowFollowFollowFollow
Median
Mean
RangeNot FollowFollow multiply only x b
Interquartile Range
Standard Deviation
Variance
Follow by x a2Follow by a2Follow multiply only x b2
24. The mass of a group of 6 students has a mean of 40 kg and a standard deviation of 3 kg.
Find
a. the sum of the mass of the students.
b. the sum of the squares of the mass of the students.
Format SPM 2012 / (3 marks)
25. The variables x and y are related by the equation . A straight line graph is obtained by plotting y against x2 as shown in diagram. Given the gradient of the
straight line is 2.
Find
a. the value of k
b. the value of h.
Format SPM 2010 / (4 marks)
26. The variables x and y are related by the equation y = kx 3 , where k is a constant. a. Convert the equation y = kx 3 to linear form.b. Diagram shows the straight line obtained by plotting log 10 y against log 10 x .
Find the value ofi. h
ii. k
Format SPM 2005 / (4 marks)
27. Diagram shows the straight line AC.
a. a. Find the equation of the straight line which passes through point A and is
perpendicular to AC.
b. b. The point B lies on AC such that AB : BC = 3 : 2. Find the coordinates of B
SPM 2009 / (4 marks)
28. Diagram show the straight line passes through points A(1, 3) and B(6, 7). Point P(x, y) move such that AP : PB = 3 : 2. Find the equation of locus of P.
Format SPM 2010 / (3 marks)
29. Given the function g(x) = 3x2 (2x 5)4. Find g(3)
Format SPM 2004 (3 marks)
30. Given the function g(x) = . Find g(3)
Format SPM 2004 (3 marks)31. Given the function g(x) = . Find g(3)
Format SPM 2004 (3 marks)
32. The gradient of the tangent to the curve y = 2x3 + px2 3 at x = 2 is 4.
Find the value of p.
SPM 2012 / (3 marks)
33. The gradient function of a curve is 3x2 4x. Find the equation of the tangent to the curve at point (1, 3).
SPM 2012 / (3 marks)
34. Given that y = 3x2 + 12x 4, calculate
a. the value of x when y is a minimum
b. the minimum value of y
Format SPM 2003 / (3 marks)
35. It is given that . Find
a. the value of , when x = 4
b.the approximately change in y, in term of p,
when the value of x change from 4 to 4 + p
Format SPM 2011 / (3 marks)36. It is given that . Find
a. the value of , when x = 4
b.the approximately value in y, in term of p,
when the value of x change from 4 to 4 + p
Format SPM 2011 / (3 marks)37.
Two variables, x and y, are related by equation . Given that y increases at a
constant rate 10 unit s-1 . Find the rate of change of x when x = 2.
Format SPM 2005 / (3 marks)
38. The radius of a circle decreases at the rate of 0.5 cm s-1. Find the rate of change of the area when the radius is 4 cm.
39. Given that . Find
a.
b.
c. the value of k if
SMKJ 2013 / (5 marks)
d. the value of h if
40. In a test, 85% of the students have passed. A sample of 10 students is chosen at random.
Find the probability that a. 8 students from the sample passed the test.b.at most 2 students from the sample failed the test
c. at least 1 student from the sample passed the test
Format SPM 2012 / (3 marks)
Jujur Bohong
More then>At least
Less thenNot more
Not less
Max
Min
41. X is a random variable of a normal distribution with a mean 50 and a standard deviation of 18.
Find
a. the z-score when X = 42.8
c. b.
P(42.8 x 50).
Format SPM 2004 / (4 marks)42. It is given that 11, y + 4 and 3y x are three consecutive terms of an arithmetic progression.
a. Express y in term of x
b. Find the common difference if x = 8
Format SPM 2012 / (4 marks) 43. In a geometric progression, the first term is 4 and the common ratio is r. Given that the sum to infinity of this progression is 16. Finda. the value of r.
b. the sum from the second term to fifth term
Format SPM 2008 / (4 marks)
44. Diagram shows two vectors,
a. Express
in the form
b. Find the unit vector in the direction of
Format SPM 2006 (4 marks)
45. Diagram shows four letter cards and three numbered cards.
A code is to be formed using five of these cards.
Find
a. the number of different codes that can formed if there is no restriction..
b. the number of different codes that can formed which begin with a number and
end with a letter..
SMKJ 2014 / (4 marks)
46. A student would like to borrow 5 books from school library. These 5 books are chosen from 4 mathematics books, 3 chemistry books and 2 stories books. Calculate the number of different ways in which the five books can be chosen if two mathematics books and one stories book must be borrowed.
47. In how many ways can the word BUSRAH be arranged if the vowel are arranged
side by side.
48. A box contains 20 chocolates. 5 of the chocolates are black chocolates flavour and the other 15 are white chocolates flavour. Two chocolates are taken at random from the box.
Find the probability that
a. both chocolates are black chocolates
b. the chocolates taken are different flavour
Format SPM 2012 / (4 marks)
49. The probability of student A being chosen as school librarian is , while the probability of
student B being chosen is . Find the probability that
a. both of the students are chosen as the school librarian.
b. only one student is chosen as a school librarian.
(4 marks) / SPM 2013
Note; Gradient function = EMBED Equation.3
EMBED Equation.3
Note; Gradient tangent = 4
EMBED Equation.3
-1
x
0
900
1
y
3600
2700
1800
-1
x
0
900
1
y
3600
2700
1800
-1
x
T
x2
S
R
0
y
x
A(4, 3)
0
B
-5
(0, 5)
y
x
0
0
B(6, 7)
C(6, 0)
A(-4, 5)
y
B(x, y)
x
0
(5, h)
900
1
y
3600
2700
1800
Note: Same base Method
If log 9 x = log 3 4
Therefore
log 9 x = EMBED Equation.3
log 9 x = EMBED Equation.3
x = 16
Note: Factorice method
log 10 x
Note: ax2 + bx + c = 0
a(x + bota)2 (bota)2 ma + c = 0
(q, 6)
Note: f(x) = a(x + b)2 + c
therefore
Min/Max point = (b, c)
Note: Index Laws method
If an = am , therefore n = m
If xn = yn , therefore x = y
0
Note: Roots = Answers
If roots are 3 and 5,
therefore x = 3 , x = 5
and (x 3)(x + 5) = 0
Note: Distinct Roots/Two Different Roots
b2 4ac > 0
Note: Real Roots
b2 4ac 0
Note:
Inside ---- Comparison
Method
Note:
Outside ---- Substitution
Method
E
4
y = f(x)
2
(1, 2)
x
y
log 10 y
Set y
y
0
A(1, 3)
3
Set X
4
3
2
1
p
q
r
s
Note: If f(x) = EMBED Equation.3
Than f(x) = EMBED Equation.3
Note: If f(x) = EMBED Equation.3
Than f(x) = EMBED Equation.3
Note: If f(x) = DB
Than f(x) = DB + BD
Note: Seen word Locus
Therefore use Distance Formula
Note: No word Locus
Therefore use Cross Formula
Note: Use comparison method or substitution method
Note: Use comparison method or substitution method
Note: Change sentence to statistics symbol and formula
Note; Seen word Min. / Max.
Find EMBED Equation.3 and EMBED Equation.3 and x when EMBED Equation.3 = 0
Note; Seen word
Approximately value in x = x + EMBED Equation.3
Approximately value in y = y + EMBED Equation.3
Note; Seen word
Approximately change in x = EMBED Equation.3
Approximately change in y = EMBED Equation.3
Note;
Seen word Rate of change
Use Chain Law EMBED Equation.3 EMBED Equation.3 EMBED Equation.3 EMBED Equation.3
Note;
Use Number Line
Note; Binomial; Only has two possible outcomes Success = r and Failure = r
Note:
AB = OB OA
PQ = OQ OP
MN = ON OM
Note; Combination nCr
Key-word; Divided
Select
Choose
Chosen
Note: Permutation nPr
Key-word; Formed
Arrange
Note;
Side by side = Next to each other = Together
Note; ..or.. = +
.. and .. = x
Note; ..or.. = +
.. and .. = x
Note; EMBED Equation.3
PAGE 2
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