School of Technology & Mathematics

Department of Mathematics

CORE MATHEMATICS TEST 3 [25 Marks] Answer all questions and show necessary working.

Please Write both your name and ID number on your answer sheets

1. A mother bought 3 packs of Supligen and 4 packs of Orange Juice for $13.40. If she had bought 4 packs of Supligen and 3 packs of Orange Juice at the same grocery, then the cost would have been $14.95.

(a) Using s to represent the cost in dollars per pack of Supligen, and j to represent the cost in dollars per pack

of Orange Juice, write down a pair of simultaneous equations to represent the information given above.

[2 mrks]

(b) Hence, determine the cost per pack of Supligen and the cost per pack of Orange Juice.[4 mrks]2. (a) Use the method of factorization to solve the following quadratic equation:

[3 mrks]

(b) Use the quadratic formula to solve the following quadratic equation:

[4 mrks] Recall that if , then

3. (a) If {2, 4, 6, 8, 10, 12, 14, 16}, determine the exact number of subsets which can be formed from it.

[2 mrks]

(b)

The figure above shows the universal set U , and the two subsets A and B. List the members of each of

each of the following sets:

(i) A = { }

[1 mrk]

(ii) B = { }

[1 mrk]

(iii) = { }

[2 mrks]

(iv) = { }

[1 mrk] (v) = { }

[1 mrk]4. In a class of 30 pupils, 18 take French and 17 take German. 3 take neither. How many take both French and

German?

[4 mrks]Page 2 of 2

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