Mathematics C Mid‐Term Term 1 Examination SAMPLE CPython

Java Python 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