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.