8/10/2019 math(t)
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954/1 Hak Cipta Mooi Hoe Yeap 2014
AS-LEVEL MATHEMATICS (T) PAPER 1
Section A (45 marks)
Answer allthe question in this section.
1. Given thatf(x) =x3+px2+ 7x+ q, wherep, qare
constants. Whenx= 1,f (x) = 0. Whenf(x) isdivided by (x+ 1), the
remainder is 16. Find thevalues ofpand q.
(a) Show thatf(x) = 0 has only one real root. Find
the set ofxsuch thatf(x) > 0.
(b) Express(
in partial fractions.
2. (a) Given a= * ()
+and b = 14, find the set ofvalues ofxsuch that the difference
between aand bis less than 0.01, giving your answer correct to
twodecimal places.
(b) Find the roots of the equation e2-2x = 2e-x, giving your
answer in terms of logarithm.
3. (a) Expand (3x2) by using binomial theorem.
(b) Let P= (
)and Q= (
) Find thematrix Rsuch that PR-1= QP.
4. Evaluate
Express as a rational number in its lowest form.
5.Find the value of (
)
6. Given that
6 cos2x8 sinxcosxA + R cos (2x+ ),Find the values of the
constantsA,R, and .
Section B (15 marks)
Answer one question in this section.
7. Lines l1and l2have vector equations r= a+sb and
r= c+ td respectively, wheresand t
,a=j2k, b = i + j k, c = i + 4j+ 6k andd = 3i+j+ k. PointPon l1
and point Q on l2 aresuch thatPQis perpendicular to both l1and
l2.
(a) Find the vector parallel to .
(b) Obtain the positions vectorsPand Q.
(c) Show that the plane throughPQperpendicular
to l1 has vector equation r = (1 ++)i +
()j + (12)kwhereand.
8. During the school holidays, a supermarket offers three
sales
of packagesA,B, andCfor shirts, long pants and shoes withthe
name Tampan.The number of each item and the offer
price for each packages are shown in the following table.
Sales
package
Number of
shirts
Number of
long pants
(pairs)
Number of
shows
(pairs)
Offer
price
(RM)
A 4 2 2 190
B 3 4 3 295
C 2 4 2 250
By representing the prices of shirts, a pair of long pants
and
a pair of shoes asx,y, andzrespectively, obtain a matrixequation
representing the information above.
Solve the matrix equation you have obtained to determine
the price of each item.
END OF QUESTION PAPER
