ZIMBABWE SCHOOL EXAMINATIONS COUNCIL <br> General Certificate of Education Ordinary Level
**MATHEMATICS <br> PAPER I**
4004/1
JUNE 2020 SESSION 2 hours 30 minutes
Candidates answer on the question paper Additional materials: Mathematical Instruments
Allow candidates 5 minutes to count pages before the examination. This booklet should not be punched or stapled and pages should not be removed. Time 2 hours 30 minutes
INSTRUCTIONS TO CANDIDATES
Write your Name, Centre number and Candidate number in the spaces at the top of this page. Write your centre and candidate number in the box on the top right corner of every page of this paper. Check that all the pages are in the booklet and ask the invigilator for a replacement if there are duplicate or missing pages. Answer all questions. Write your answers in the spaces provided on the question paper using black or blue pens. If working is needed for any question, it must be shown in the space below that question. Omission of essential working will result in loss of marks. Decimal answers which are not exact should be given to three significant figures unless stated otherwise. Mathematical tables, slide rules and calculators should not be brought into the examination room.
INFORMATION FOR CANDIDATES
The number of marks is given in brackets [ ] at the end of each question or part question.
Answer all questions
**NEITHER MATHEMATICAL TABLES NOR SLIDE RULES NOR CALCULATORS MAY BE USED IN THIS PAPER**
Question 1
Express 208,9
(a)
in standard form,
Answer (a) $\_\_\_\_$ [1]
(b)
correct to 3 significant figures.
Answer (b) $\_\_\_\_$ [1]
(c)
correct to the nearest hundred.
Answer (c) $\_\_\_\_$ [1]
Question 2
Evaluate
(a)
\(-10^{\circ}\),
Answer (a) $\_\_\_\_$ [1]
(b)
\(\left(\frac{4}{9}\right)^{\frac{3}{2}}\).
Answer (b) $\_\_\_\_$ [2]
Question 3
The Venn diagram shows three sets A, B and C with their respective elements.
(a)
List all elements of
#### (i)
\(A \cap C\),
Answer (a)(i) $\_\_\_\_$ [1]
#### (ii)
\((A \cup B)^{\prime} \cap C\).
Answer (a)(ii) $\_\_\_\_$ [1]
(b)
Find \(n(A \cup C)\).
Answer (b) $\_\_\_\_$
Question 4
(a)
Solve the inequality \(2-y<3y-10\).
Answer (a) $\_\_\_\_$
(b)
The perfect square, \(y\), satisfies both \(2-y<3y-10\) and \(y \leq 9\).
Find the possible values of \(y\).
Answer (b) $\_\_\_\_$ [1]
Question 5
Solve the simultaneous equations:
$$ \begin{aligned} & 2x+y=4 \\ & x-y=-2 \end{aligned} $$
Answer $\_\_\_\_$
Question 6
(a)
Convert \(301_{4}\) to a number in base 10.
Answer (a) $\_\_\_\_$ [1]
(b)
Evaluate
#### (i)
\(1101_{2}+111_{2}\), giving the answer in base 2,
Answer (b)(i) $\_\_\_\_$
#### (ii)
\(131_{5}-42_{5}\), giving the answer in base 5.
Answer (b)(ii) $\_\_\_\_$ [1]
Answer $\_\_\_\_$
Question 8
Given that \(m=\frac{1}{2}\) and \(n=-2\), evaluate
(a)
\(m-n\).
Answer (a) $\_\_\_\_$ [1]
(b)
\(\frac{mn}{m+n}\).
Answer (b) $\_\_\_\_$ [2]
Question 9
Express \(\frac{2}{2-3n}-\frac{1}{n}\) as a single fraction in its simplest terms.
Answer $\_\_\_\_$ [3]
Question 10
The matrix \(\begin{pmatrix} (x+2) & 4 \\ 6 & x \end{pmatrix}\) is singular. Find the possible values of \(x\).
Answer $\_\_\_\_$ [3]
Question 11
Given that \(f(x)=\frac{k+x}{3x-2}\) and that \(f\left(-\frac{1}{3}\right)=\frac{1}{6}\), find the value of \(k\).
Answer $\_\_\_\_$ [3]
Question 12
It is given that \(\mathbf{p}=\binom{5}{4}, \mathbf{q}=\binom{-3}{2}\) and \(\mathbf{r}=\binom{x}{y}\).
(a)
Find \(|\mathbf{p}|\), leaving the answer in surd form,
Answer (a) $\_\_\_\_$ [1]
(b)
the value of \(x\) and the value of \(y\) if \(\mathbf{p}-\mathbf{q}=2\mathbf{r}\).
Answer (b) $\_\_\_\_$ [2]
Question 13
A salesman's total monthly salary consists of a basic salary of $200 and a 2% commission on his monthly sales. In one month his total salary was $560. Calculate
(a)
his commission for that month,
Answer (a) $\_\_\_\_$ [1]
(b)
the sales he made for that month.
Answer (b) $\_\_\_\_$
Question 14
It is given that \(\sin y=\frac{5}{13}\) and that \(y\) is an acute angle. Find as a common fraction,
(a)
\(\cos(180^{\circ}-y^{\circ})\).
Answer (a) $\_\_\_\_$ [2]
(b)
\(\tan y^{\circ}\).
Answer (b) $\_\_\_\_$ [1]
Question 15
The table shows grades obtained by 150 candidates in a Mathematics test.
| Grade | A | B | C | D | E | U | | :--- | :---: | :---: | :---: | :---: | :---: | :---: | | Frequency | 5 | 25 | 30 | 29 | 21 | 40 |
(a)
Find the median grade.
Answer (a) $\_\_\_\_$ [1]
(b)
Calculate the probability that two candidates chosen at random from the 150 obtained grade A or B.
Answer (b) $\_\_\_\_$ [2]
Question 16
(a)
Point \(R(-3;-2)\) is mapped onto point \(R_1\) by a transformation represented by the matrix \(\begin{pmatrix} 1 & 0 \\ 0 & -1 \end{pmatrix}\). Find the coordinates of \(R_1\).
Answer (a) $\_\_\_\_$ [1]
(b)
In the diagram triangle P is the image of triangle Q under a certain transformation.
Describe fully the single transformation that maps triangle P onto triangle Q.
Answer (b) $\_\_\_\_$ $\_\_\_\_$
Question 17
It is given that \(g \propto \frac{m}{r}\) and \(g=1\) when \(m=2\) and \(r=3\). Find the
(a)
formula connecting \(g, m\) and \(r\),
Answer (a) $\_\_\_\_$ [2]
(b)
numerical value of \(g\) when \(m=10\) and \(r=3\).
Answer (b) $\_\_\_\_$ [1]
Question 18
In the diagram A, B, C and D are points on the circumference of a circle centre O.
PD is a tangent to the circle at D, \(A\hat{D}B=28^{\circ}\) and \(C\hat{B}D=47^{\circ}\). Calculate
(a)
\(B\hat{A}D\).
Answer (a) $\_\_\_\_$
(b)
\(C\hat{D}P\),
Answer (b) $\_\_\_\_$
(c)
\(C\hat{A}B\),
Answer (c) $\_\_\_\_$
(d)
\(B\hat{C}D\).
Answer (d) $\_\_\_\_$
Question 19
(a)
Simplify \(4b-3(4-2b)\).
Answer (a) $\_\_\_\_$ [2]
(b)
Factorise completely \(x-y-xy+x^{2}\).
Answer (b) $\_\_\_\_$
Question 20
(a)
Name the regular polygon which has rotational symmetry of order 5.
Answer (a) $\_\_\_\_$
(b)
The sum of the interior angles of a hexagon is \(720^{\circ}\). Three of its interior angles are \(140^{\circ}, 120^{\circ}\) and \(160^{\circ}\). The remaining angles are in the ratio \(2:3:5\). Calculate the size of the largest of the remaining angles.
Answer (b) $\_\_\_\_$ [3]
Question 21
It is given that \(\log x=6\) and \(\log y=-2\). Evaluate