WA1 Practice Paper: Weighted Assessment 1 — question paper (print)

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Secondary 4 · Elementary Mathematics (G2 / G3)

WA1 Practice Paper

Weighted Assessment 1

Duration: 50 minutes

Total: 40 marks

Name:

Class:

Date:

READ THESE INSTRUCTIONS FIRST

Write your name, class and register number in the spaces at the top of this page.
Answer all questions.
Show all necessary working. Omission of essential working will result in loss of marks.
Give non-exact numerical answers correct to 3 significant figures, or 1 decimal place for angles in degrees, unless a different level of accuracy is specified in the question.
An approved calculator may be used.
The number of marks is given in brackets [ ] at the end of each question or part question.

Original practice material written for the MOE Elementary Mathematics syllabus. It is not an official MOE or school examination paper. Chapters 1–3 (coordinate geometry, vectors in two dimensions, statistical diagrams).

For Examiner’s Use
Section A	/ 40
Total	/ 40

Section A: Structured questions[40 marks]

Answer all questions in the spaces provided. Show all necessary working — omission of essential working will result in loss of marks. Give non-exact numerical answers correct to 3 significant figures, unless told otherwise.

1
The points A and B have coordinates (−1, 3) and (5, −5) respectively.
1. (a)
  Find the coordinates of the midpoint of AB.
  midpoint =[1]
2. (b)
  Find the length of AB.
  [2]
3. (c)
  Find the gradient of AB.
  [1]
4. (d)
  The point C lies on the line AB and has x-coordinate 11. Find the y-coordinate of C.
  [2]
2
The points C(2, 1), D(6, p) and E(6, 1) are marked on a grid. The gradient of CD is 3.
1. (a)
  Find the value of p.
  [2]
2. (b)
  Find the area of triangle CDE.
  [3]
3
It is given that a = (3, −2) and b = (−1, 4), written as column vectors.
1. (a)
  Find 2a + b as a column vector.
  [2]
2. (b)
  Find the magnitude of a, correct to 3 significant figures.
  [2]
3. (c)
  Given that ma + nb = (5, 0), where m and n are scalars, find the values of m and n.
  [2]
4
In triangle OPQ, the position vectors are OP = p and OQ = q.
1. (a)
  Write PQ in terms of p and q.
  [1]
2. (b)
  R lies on PQ with PR : RQ = 1 : 2. Write PR in terms of p and q.
  [1]
3. (c)
  Hence write OR in terms of p and q, in its simplest form.
  [2]
4. (d)
  The point G has position vector (1/3)(p + q). Using your answer to (c), show that GR is a scalar multiple of p, and state what this tells you about the line GR and the line OP.
  [3]
5
120 commuters were surveyed on how they travel to work. The pie chart sectors are: bus 150°, walk 90°, car 72°, and the rest cycle.
1. (a)
  Find the angle of the cycle sector.
  [1]
2. (b)
  Find the number of commuters who walk.
  [2]
3. (c)
  A stem-and-leaf diagram of eight journey times (minutes) has key 2 | 1 = 21. The rows are: 2 | 1 4 8; 3 | 0 5 5 9; 4 | 2. Find the median time.
  [3]
6
A box plot of 40 journey times shows minimum 14, lower quartile 22, median 28, upper quartile 35 and maximum 46 minutes. The cumulative frequency table for the same data is: t ≤ 10: 4; t ≤ 20: 11; t ≤ 30: 24; t ≤ 40: 36; t ≤ 50: 40.
1. (a)
  Find the interquartile range.
  [1]
2. (b)
  What percentage of the journeys lie between 22 and 35 minutes?
  [1]
3. (c)
  Find the number of journey times t with 20 < t ≤ 30.
  [2]
4. (d)
  State the class that contains the median journey time, with a reason.
  [1]
7
A translation T maps the point P(3, −2) onto P′(7, 1).
1. (a)
  Write T as a column vector.
  [1]
2. (b)
  The point Q′(2, 6) is the image of Q under T. Find the coordinates of Q.
  [2]
3. (c)
  The origin O is mapped onto O′ under T. Find the magnitude of the vector OO′.
  [2]

— End of paper —