4026Q1 SPECIMEN ADDITIONAL MATHS

Extracted Content: 4026Q1 SPECIMEN ADDITIONAL MATHS

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Candidate Name Centre Number Candidate Number

For Pe

ZIMBABWE SCHOOL EXAMINATIONS COUNCIL

General Certificate of Education Ordinary Level

ADDITIONAL MATHEMATICS 4026/1

PAPER 1

SPECIMEN PAPER 2 hours 30 minutes

Additional materials:
Graph paper
Mathematical tables
Data Booklet

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.

Write your centre and candidate number in the boxes on the top right comer of every page of this
paper.

Check if the booklet has all the pages and ask the invigilator for a replacement if there are
duplicate or missing pages.

Answer all questions in section A and any four in Section B.

Write your answers in the spaces provided on the question paper.

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.

Electronic calculators may be used.

INFORMATION FOR CANDIDATES

The number of marks is given in brackets [ ] at the end of each question or part question. If the
degree of accuracy is not specified in the question and if the answer is not exact, the answer
should be given to three significant figures. Answers in degrees should be given to one decimal
place.

This question paper consists of 14 printed pages and 2 blank pages.

Copyright: Zimbabwe School Examinations Council, Specimen paper.
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SECTION A [52 Marks] Answer all questions in this section. Given that the polynomial 2x? + x? + px — 4 has a factor x — 2.

(a) Find the value of p.

Answer [2]

(b) Show that 2x + 1 is another factor of the polynomial.

() Find the third factor.

Answer [3]

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2

The line y = x + 2 meets the curve y? = 4 (2x + 1) atA andB.
Find the coordinates of the midpoint of line AB.

Answer [5]

Find the range of values of x which satisfy the inequality

3x-1
2+Xx

>1

Answer [4]

Given that(a + b,/3)=(— 5

of a and the value of b.

),where a and b are integers. Find the value

Answer [5]

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(a) Solve the following pair of simultaneous equations: 3x2 —y? =3

ax-y=1

Answer x =

(b) Given that

Ax? +Bx? +x — 2C = (3x — 2)(x +1)(x + 2) + (x - 4).

Find the values of A, B and C.

ll

AnswerA

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6 Show that

+44 _ = 956629,

1tsin@ 1-sind

7 Given that f: x > “2; x + 3 and f(4) = 9,

x-3’
Find,

(a) the value of P,

Answer P = [2]

(b) f-*(-3),

Answer eee [3]
© — f?(x).
Answer [3]

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(a) A geometric series has a first term 1 and a common ratio r. Given that the sum to infinity of the series is 5, find the value of r.

Answer r = [3]

(b) Find the least value of nfor which the sum of the first n terms of the
series exceeds 4,9.

Answer n = [3]

(a) Express

logy + 2logq — 3logr as a single logarithm.

Answer [3]

(b) Solve the equation

2%421-*=3,

Answer x = [4]

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7

SECTION B [48 Marks]
Answer any four questions in this section

10 = (a) A curve has an equation y = x* — 4x3 + 27.

Find,
® 2
Answer [1]

di the coordinates of the stationary points on the curve.

Answer [3]

(iii) the nature of stationary points

Answer [5]

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10 (b) Find the equation of a curve which passes through the point (3;8) and has a gradient function

da.
SY = 2x2 —5,
dx

Answer

11 (a)_— Evaluate f V2x 7 dx.

Answer

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9

11 (b) —‘ The diagram shows the graph of y = 2 — x? and the line y = —x.

y

Find,

@ the coordinates of P and Q,

Answer P

Qe [4]

(ii) —‘ the shaded area, R.

Answer

oo [5]

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10 2 The straight line L has an equation 2y — x + 7 = 0. The straight line Mpasses through the point P (-1; 6) and is perpendicular to line L. (a) Find the,

(1) equation of line M, giving your answer in the form
ax+by+c=0,

Answer [3]

di coordinates of the point of intersection of line Land line M

Answer [3]

(b) Find the perpendicular distance from P to line L

Answer [3]

( Given that the points Q(-7;-7) and R(9 ; 1) lie on line L, find the exact
area of the triangle POR.

Answer [3]

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13

(a)

(i)

11

Express 3 cos @ + 5sin@ in the form
Rcos(@— a),
where R > O and 0° <a < 90°.

State the exact value of Rand give the value of a correct to 1
decimal place

Answer [3]

Hence, solve the equation

3cosé+5sin 0=1

giving all solutions in the interval 0° < @ < 360°

Answer [3]

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13 (b) The equation of a curve is x3 + y? = 6xy.

@ Show that

dy _ 2y-x?
dx y2—2x
Answer [4]

di Find the equation of the tangent to the curve at the point (2; 4),
giving your answer in the form ax + by =c

Answer [2]

14 (a) Evaluate the first 4 terms of each sequence whose r“" term is given and
determine the nature of the sequences, starting with r = 1

(i) Ur=

1
a

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14 (a) (id) Ur = 27

(ii) 9 Ur = (-1)"**4r

(b) — Evaluate "23 2" +n?

Answer [2]

() The first 3 terms of an arithmetic series are -2; 1; 4.
Find the number of terms for which the sum of the arithmetic series is

208.

Answer [4]

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ib) (a)

(b)

14

A particle P moves in a straight line such that t seconds after passing
through a fixed point O, its velocity Vms~? is given by V = 4 -t?.
Find the

@ acceleration of P after 4 seconds,

Answer [3]

di distance of P from O after 6 seconds,

Answer [3]

(iii) displacement of P from O when P is instantaneously at rest.

Answer [3]

The parametric equations of a curve are
x = 3t? andy = t* — 3¢? ford <t <3

_ 4 d
Find =.
dx

Answer [3]

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