Placement Test for New Syllabus Mathematics 4
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1.	The table shows the number of minutes a retail salesperson spent on each of the 80 customers he served in a particular week. Time (t minutes) No. of Customers 6 8 14 32 14 6
	(a)	What is the modal class?
	(b)	Estimate the mean length of time the salesperson spent per customer.
	(c)	Draw a cumulative frequency diagram for the distribution. Use a scale of 2 cm to represent 5 minutes on the time axis and 2 cm to represent 10 customers on the cumulative frequency axis. Use the diagram to estimate the interquartile range.

 

2.	The vertices of the ABC are A(1, 1), B(3, 1) and C(1, 2). ABC is transformed to A1B1C1 by a shear with y axis invariant and factor 2. Give the vertices of A1B1C1.

 

3.	Hotels A and B are 40 km apart such that A is due north of B. The amusement park P is halfway between A and B. A man intends to build two motels M and N such that M is east and N is west of the road between A and B. Both motels will be more than 12 km from A but nearer to A than to B.
	(a)	Draw a scale map showing the possible sites of motel M if the distance between the amusement park and M is 20 km.
	(b)	Draw a scale map showing the possible sites of motel N if the distance between the amusement park and M is less than 20 km.

 

 

4.

A dog's lead is 4 m long. It is attached to a fixed point A on the corner of his dog house, which has a width and breadth of 2 m. Calculate the area the dog can cover. (= 3.14)

 

 

5.	Two points P and Q have position vectors p and q respectively, relative to the origin. Given that p = and = find
	(a)	p
	(b)

 

 

6.	OABC is a rectangle whose diagonals intersect at M. If = a and = c, express in terms of a and c.
	(a)
	(b)
	(c)	If |a| = 14 and |c| = 25, find BOC

 

 

7.	A general point (x, y) is mapped onto (x', y'). Write down two equations in the form x' = ax + by and y' = cx + dy which define the following transformations.
	(a)	An enlargement E with factor 4 and origin as center.
	(b)	A stretch S with factor and the y-axis as the invariant line.
	(c)	A shear H with factor 1 and x-axis as the invariant line.

 

 

8.	Under and enlargement, the points A(1, 0) and B(2, 2) are mapped on to the points A', B' under the transformation M: (x, y) (3x, 3y - 2). Determine
	(a)	The center and scale factor of the enlargement.
	(b)	the image of the line y = 2x - 2 under the enlargement.

 

 

9.	John either rides his bike or takes the bus to school. The probability that it rains is 0.6. If it is raining, the probability that he rides his bike is 0.2. If it is not raining, the probability that he takes the bus is 0.3. Calculate the probability that
	(a)	on any particular day, he does not ride his bike.
	(b)	he rides his three days in a row.

 

 

10.	A bag contains 10 marbles, of which 3 are red and 7 are blue.
	(a)	What is the probability of picking a red marble, at random, from the bag?
	(b)	When n blue marbles are removed from the bag, and the probability of picking a red marble becomes , find n.

 

 

11.	Find the nth term of the sequence 1, 2, 5, 10, 17 ... in terms of n.

 

 

12.	An animal feed is to be made from three ingredients, oats, corn, and barley. The mix must include 60% of oats and corn. The corn and barley must be in the ratio of 4 to 3 by weight. How much of each ingredient is needed to make 750 kg of the animal feed?

1.	(a) (b) 26.1 min (c) 7.9 min			2.	A1(1, 3), B1(3, 7), C1(1, 4)
3.	(a)		The thick line, excluding the small circles, represents possible sites for M.	(b)		The shaded region, excluding the dotted boundaries, represents the possible sites for N.
4.	43.96 m2			5.	(a) (b) 5
6.	(a) -c (b) (a - c) (c) 29.2o			7.	(a) x' = 4x, y' = 4y (b) x' = x, y' = y (c) x' = x + y, y' = y
8.	(a) (0, 1), 3 (b) y = 2x - 8			9.	(a) 0.6 (b) 0.064
10.	(a) (b) 5			11.	(a) n2 - 2n + 2
12.	50 kg oats, 400 kg corn, 300 kg barley.

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