Foundation Program

SAMPLE C

Mathematics C

Mid-Term Term 1 Examination

MID-TERM?1?EXAMINATION

Question 1 ?????????????????Use a SEPARATE book clearly marked Question 1

(i) ????Find the gradient of?the straight line passing through the points ??(a -?2b,?2a - b) ?and?(b -?2a, b)?in?simplest?form.

Find?the?domain?of?the?function y = x2 - 5x .

(iii) ?????Given?that?the?point??(-2,1) ?is?on?the?curve y = f (x)?.??By?moving?this?point,?find?a?point?on?the?graph?of f (x +?1)?-?2 ?.

(vi)??????Write x2 ?-?6x -?2?in?the?form. a(x - p)2 ?+ q .

(v) ??????If A = {x :0 ≤ x ≤ 3}?, B = {x : -2 < x < 1} graph on separate number lines the following sets:

(a) A ∩ B .

(b) A B .

(vi) ?????On separate number planes sketch the graphs?of?each?of?the?following?showing their essential features.

(a)? ? ? ? y = - x+1/2?.

(b) y = |4?- |x||.

Question 2 ?????????????????Use a SEPARATE book clearly marked Question 2

(i) ???????Solve?the?inequality ??2 ≤ |x + 4| ≤ 6 .

(ii) ??????If??log10 x = m and?log10y = n , ?express the?following?in terms?of m and n:

(a)????????log10 y/x.

(b) ???????logxy 10 ?.

(c)????????log10 xy .

(iii) ?????The remainder when the polynomial P(x)?is divided by??(x -?2)?is ?7 , ?and the?remainder when P(x)?is divided by??(x +?3)?is ?2?. ?Find the remainder when the P(x)?is divided by x 2?+ x -?6 ?.

(iv) ?????When students in a tutorial group?of?18?were?asked?if?they?spoke?Chinese?or

Indonesian,?10 said they spoke Chinese, 7?said they?spoke Indonesian?and?6?said?they?spoke?neither?of?these?languages.

(a) ???????Show this information on a Venn?diagram.

(b) ??????Find how many students?spoke?both?Chinese?and?Indonesian.

Question 3 ?????????????????Use a SEPARATE book clearly marked Question 3

(i) ???????(a) ??????Factorise x6?—?5x4?+?4x2?.

(b) ??????Hence sketch the graph?of y = x6??—?5x4 ?+?4x2?.

(c) ??????Find the values?of x for which x6 ?—?5x4?+?4x2 ?< 0 .

(ii) ??????A bin is being loaded with sand and?after?one hour?is?filled to?capacity.

The volume V cubic metres of?sand in the bin at time t minutes is?given by the equation V = 5/t - 800/t2? for??0 ≤ t ≤ 60 .

(a)???????Find?the?capacity?of?the?bin.

(b) ??????Find the time taken to load ??3?.?5 m3 ????of?sand into the bin.

(c)???????Sketch the graph of?the function V = 5/t - 800/t2 for??0 ≤ t ≤ 60 .

(iii)?????The barometric pressure at any point h km above sea level is?given?by p = 1030e— 0.124h . ?Find

(a)???????the barometric pressure at a height of ?12 km.

(b)???????the barometric pressure at sea level.

(c) ??????the height?at which the barometric pressure?is half?that?at?sea?level.