# Core Mathematics 2019 WASSCE-Past Questions and Answers

“Core Mathematics 2019 WASSCE-Past Questions and Answer” – is an online learning resource for students.

Thus, it has been designed to help students to pass their Core Maths WASSCE and other relevant mathematics exams. So what does our site offer? Now read on and see for yourself. Read more.

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#### General Overview – Core Mathematics 2019 WASSCE

Core Mathematics 2019 WASSCE-Past Questions and Answers is an e-learning material we have prepared online.

This learning resource has been designed to help students to pass their Core Maths WEC exams. However, I must say that, we may not always provide a pdf download of this wassce past question.

This means that WASSCE Core Mathematics past questions and answers may not be available for a direct pdf download. If so, then what does our website offer? Just wait and see.

Also, have you had challenges trying to learn, write or pass your WAEC Maths exams? If the answer is yes, then I can assure you that educareguide is here to help and guide you. Furthermore, check from our site and find the novdec 2019 core mathematics questions.

We are here to encourage you that you can easily pass mathematics subject. Educareguide has made mathematics very easy for every student. It is actually not different from the following subjects or papers:

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Firstly, we have a lot of links to assist you to get enough details.  Truly, this will help you to gain enough knowledge and understanding to answer your waec maths past question.

Secondly, we have materials on various topics, sub-topics of Ghana Education Service (GES) core mathematics. Therefore, educareguide is very helpful to  Senior High School Student across the West African sub-region.

Notably, these countries are Nigeria, Ghana, Sierra Leone, The Gambia and Liberia. Our content is also helpful to people across other parts of the world preparing to write their various types of examination.

Moreover, these students rely on our guide to pass the WASSCE Core Maths exams. In detail, check the questions and the answers just below.

#### Other Relevant Examination

These mathematics questions and answer are not only for WASSCE. Rather, they are also relevant to the following examination:

• Kenya – Kenya Certificate of Secondary Education (KCSE)
• Uganda – Advanced Certificate of Education
• Tanzania-Certificate of Secondary Education Examination(C.S.E.E)
• South Africa – National Senior Certificate (NSC)
• Zimbabwe – ZIMSEC GCE Advanced Level
• ZIMSEC GCE Ordinary Level, a prerequisite to the GCE Advanced Level.
• Swaziland – Swaziland General Certificate of Secondary Education SGCSE
• USA High School Diploma
• Canadian High School Diploma Formerly the Canadian Diploma Certificate of Education (CDCE)
• General Educational Development (GED
• China – National Higher Education Entrance Examination
• Hong Kong – Hong Kong Diploma of Secondary Education
• Central Board of Secondary Education (CBSE) School Leaving Diploma in India
• Malaysia Higher School Certificate or International Baccalaureate Diploma or Cambridge A Levels
• Singapore – General Certificate of Education (GCE) A-level
• Australian Higher School Certificate
• New Zealand – National Certificate of Educational Achievement (NCEA)
• International Baccalaureate Diploma (IB Diploma)
• Advanced Placement International Diploma (APID)
• Advanced International Certificate of Education (AICE)

#### 1   (a)Mathematics question on standard Form

Without using mathematical tables or calculators, evaluate

$\frac{0.15×0.567}{0.05×0.189}$

, leaving the answer in standard form

Solution:

#### 1   (b) Mathematics question on Linear Equations and Inequalities

Solution:

This is a mathematics question on Linear Equations and Inequalities

The answer to the above question can be found below:

#### 2 (a) Mathematics question on variation

Z varies directly as x and inversely as twice the cube root of y. If Z = 8, when x = 4 and y =

$\frac{1}{8}$

find the relation for y in terms of x and Z.

Solution:

#### 2   (b)A mathematics question on Algebraic Expressions

Factorize completely:

Solution:

#### 3   (a)A mathematics question on Algebraic Expressions

Solve

$\frac{5x–7}{6}+\frac{2x–3}{4}=\frac{2}{3}$

Solution:

#### 3 (b) A mathematics question on Surds

Evaluate:

$\frac{\sqrt{\sqrt{28}+\sqrt{343}}}{2\sqrt{63}}+\frac{5}{3}$

Solution:

#### 4 Mathematics question on Percentages

A car dealer made a profit of 22.5% by selling a car for GH¢ 58,000.00. Find, correct to two decimal places, the percentage profit if the car had been sold for GH¢ 61,200.00

#### 5(a) Mathematics question on Probability

A number is chosen at random from Q = { 1, 2, 3, …, 10). Find the probability that the chosen number is either a prime factor of 42 or a multiple of 3.

Solution:

#### 5   (b)Mathematics question Number Bases

If

, find the value of x.

Solution:

#### The answer to question to wassce 2019 core maths question 6a(i)

$r=a+\frac{1}{2}\left(a–b\right)\phantom{\rule{0ex}{0ex}}r=\left(\begin{array}{c}2\\ 3\end{array}\right)+\frac{1}{2}\left[\left(\begin{array}{c}2\\ 3\end{array}\right)–\left(\begin{array}{c}4\\ 5\end{array}\right)\right]\phantom{\rule{0ex}{0ex}}r=\left(\begin{array}{c}2\\ 3\end{array}\right)+\frac{1}{2}\left(\begin{array}{c}–2\\ –2\end{array}\right)\phantom{\rule{0ex}{0ex}}r=\left(\begin{array}{c}2\\ 3\end{array}\right)+\left(\begin{array}{c}–1\\ –1\end{array}\right)\phantom{\rule{0ex}{0ex}}r=\left(\begin{array}{c}1\\ 2\end{array}\right)$

#### The answer to question to wassce 2019 core maths question 6a(ii)

$\left|r\right|=\sqrt{{1}^{2}+{2}^{2}}\phantom{\rule{0ex}{0ex}}\left|r\right|=\sqrt{1+4}\phantom{\rule{0ex}{0ex}}\left|r\right|=\sqrt{5units}$

Solution:

#### Below is the answer to question to wassce 2019 core maths question 6b:

(i) Find the answer 2019 core mathematics, question, 6b(i)

#### 7  Mathematics question Trigonometry II

(a) Copy and complete the table of values for y =5sinx+9cosx for

$0\le x\le {150}^{o}$

 x ${0}^{o}$ ${30}^{o}$ ${60}^{o}$ ${90}^{o}$ ${120}^{o}$ ${150}^{o}$ y 10.3 -0.2

(b) Using a scale of 2 cm to 30° on the x-axis and 2 cm to 2 units on the y-axis, draw the graph of y = 5 sin x + 9cos x for 0° x 150°.
(c) Use the graph to solve the equations:
(i) 5sinx+9cosx= 0 ;
(ii) 5sinx+9cosx= 2.
(d) Using the graph, find, the value of y when x= 45°

#### Solution mathematics question9 wassce 2019

(a) y=5sinx+9cosx

 x ${0}^{o}$ ${30}^{o}$ ${60}^{o}$ ${90}^{o}$ ${120}^{o}$ ${150}^{o}$ y 9.0 10.3 8.8 5.0 -0.2 -5.3

Refer to the graph

(c) (i) 5 sin x+9 cos x …………….(1)
5 sin x+9 cos x= y (2)
Comparing (1) and (2): y=o
The line y = 0 cuts the curve at x =119°
x =119°
.
(ii) 5 sin x+9 cos x = 2 (1)
5 sin x+9 cos x= y (2)
Comparing (1) and (2):
y = 2
The line y = 2 cuts the curve at x =107.5° x =107.5°
(d) From the graph, when x = 45°, y = 9.9

#### 8 Mathematics question on Construction and Loci

(a) Using ruler and a pair of compasses only, construct;
(i) the quadrilateral ABCD such that

(ii) the perpendicular bisectors of

(b) Locate the point of intersection, T, of the two bisectors in (a)(ii).
(c) With the point T in (b) as centre, draw a circle to pass through the vertices B, C and D.
(d) Measure:
(i)

$\left|BT\right|$

(ii)

$\left|CD\right|$

Solution:

#### Answer – wassce 2019 core mathematics question 8

For answer a, b, and c, refer to the diagram below:

d(i)

$\left|BT\right|=4.9cm$

d(ii)

$\left|CD\right|=5.9cm$

#### 9 Mathematics question on Rigid Motion (Transformation)

(a) Using a scale of 2 cm to 1 unit on both axes, draw on a sheet of graph paper, two perpendicular axes Ox and Oy for

$–5\le y\le 5.$

(b) Draw on the same graph sheet, indicating clearly all vertices and their coordinates:
(i)

$∆$

ABC with vertices A(2, 1), B(1, 4) and C( —1, 2);
(ii) the image

under a reflection in the line y = 0, where

;

(iii) the image

under a translation by the vector

$\left(\begin{array}{c}–2\\ 1\end{array}\right)$

, where

(iv) the image

under an anticlockwise rotation of 90° about the origin, where

.

(c) What single transformation maps

Solution:

#### The answer to question to wassce 2019 core maths question 9

(a) Refer to the graph below:

(b) (i) Refer to the graph below:

(ii) Reflection  in the line y=0 or the x-axis

$\left(\begin{array}{c}x\\ y\end{array}\right)\to \left(\begin{array}{c}x\\ –y\end{array}\right)\phantom{\rule{0ex}{0ex}}A\left(\begin{array}{c}2\\ 1\end{array}\right)\to {A}_{1}\left(\begin{array}{c}2\\ –1\end{array}\right)\phantom{\rule{0ex}{0ex}}B\left(\begin{array}{c}1\\ 4\end{array}\right)\to {B}_{1}\left(\begin{array}{c}1\\ –4\end{array}\right)\phantom{\rule{0ex}{0ex}}C\left(\begin{array}{c}\\ \end{array}\right)\to {C}_{1}\left(\begin{array}{c}–1\\ –2\end{array}\right)\phantom{\rule{0ex}{0ex}}$

(iii) Point +Translation Vector = image

$A\left(\begin{array}{c}2\\ 1\end{array}\right)+\left(\begin{array}{c}–2\\ 1\end{array}\right)={A}_{2}\left(\begin{array}{c}0\\ 2\end{array}\right)\phantom{\rule{0ex}{0ex}}B\left(\begin{array}{c}1\\ 4\end{array}\right)+\left(\begin{array}{c}–2\\ 1\end{array}\right)={B}_{2}\left(\begin{array}{c}–1\\ 5\end{array}\right)\phantom{\rule{0ex}{0ex}}C\left(\begin{array}{c}–1\\ 2\end{array}\right)+\left(\begin{array}{c}2\\ 1\end{array}\right)={C}_{2}\left(\begin{array}{c}–3\\ 3\end{array}\right)$

(iv)

${90}^{o}$

anticlockwise rotation about the origin

$\left(\begin{array}{c}x\\ y\end{array}\right)\to \left(\begin{array}{c}–y\\ x\end{array}\right)\phantom{\rule{0ex}{0ex}}A\left(\begin{array}{c}2\\ 1\end{array}\right)\to {A}_{3}\left(\begin{array}{c}–1\\ 2\end{array}\right)\phantom{\rule{0ex}{0ex}}B\left(\begin{array}{c}1\\ 4\end{array}\right)\to {B}_{3}\left(\begin{array}{c}–4\\ 1\end{array}\right)\phantom{\rule{0ex}{0ex}}C\left(\begin{array}{c}–1\\ 2\end{array}\right)\to {C}_{3}\left(\begin{array}{c}–2\\ –1\end{array}\right)$

(c)

#### 10(a) Mathematics question on Sets and Operations on Sets

In a class of 50 students. 24 like football, 21 basketball and 18 cricket. Six like football and basketball only, 3 like basketball only. 5 like all the three. games and 14 did not like any of the three games.

1. Illustrate this information on a Venn diagram.
2. Find the number of students who like:
1. football and cricket only;
2. exactly one of the games.

#### Solution to wassce core maths 2019 question 10a

n(U)= 50 , n(F) = 24, n(B) = 21, n(C) =18,

n(F n B only) = 25, n(B only) = 3, n(F nB nC) = 5, n(F u B u C)’ = 14

Let n(F n C only) = x, n(B nC only) = y n(F only) = m, n(C only) = b

(i) The Venn diagram is shown below.

U (50)

(ii) From set B: 6+5+3+y= 21

14+ y = 21

y =7

n(C)+m+6+3+14 =50

18+m+6+3+14=50 nz + 41= 50

m =9

From set F:

m + 6+5 = 24

9+x+6+5 = 24 x+ 20 = 24 x =4

From set C: x+5+ y+n =18.

4+5+7+b=18 b+16=18 b = 2

(a) The number of students who like football and cricket only

From the above calculations the answer = 4

(b) The number of students who like Exactly one of the games

= 9+3+2 = 14

#### 10(b) Mathematics question on Sequence

If (3-a), 6, (7 – 5a) are consecutive terms of a
Geometric Progression (G.P) with common ratio r > 0 , find the values of a.

Solution:

#### 11  (a) Mathematics question on Ratio, Proportion and Rates

Two passenger trains, A and B, 450 km apart, start to moves towards each other at the same
time and meet after 2 hours. If train B. travels

$\frac{8}{7}$

as fast as train A, find the speed of each train.

#### 11(b) Mathematics question on Mensuration II

A solid cube of side 8 cm was melted to form a solid circular cone. The base radius of the cone is 4 cm. Calculate, correct to one decimal place, the height of the cone.

Solution:

#### 12(a) Mathematics question on Plane Geometry II (Circle Theorems)

Pleas do note that the above diagram is not drawn to scale

The diagram shows a circle ABCD with centre E. Quadrilateral EADC is a rhombus,

$\angle$

BAE =

$\angle$

ECB = n and

$\angle$

ABC = m. Find:
(i) m;
(ii) n.

Solution

#### Answer to question to wassce 2019 core maths question 12a:

(i) Angle at the centre of a circle is twice the
angle at the circumference.

$\angle$

AEC =2m
Sum of angles at the circumference of opposite
segments of a circle is 180°.

$\angle$

ADC = 180° — m
Opposite angles of a rhombus are equal.

$\angle$

AEC =

$\angle$

(ii)

$\angle$

AEC = 2m = 2(60°) =120°

$∆$

AEC is isosceles. For this reason,

$\angle$

EAC =

$\angle$

ECA
Let

$\angle$

EAC =

$\angle$

ECA= x

#### 12(b) Mathematics question on Relations, Mappings and Functions

The functions f and g are defined as

#### 13(a) Mathematics question on Sequence

The fourth term of an Arithmetic Progression (A.P) is one less than twice the second term. If the sixth term is 7, find the first term.

Solution

#### 13 (b) Mathematics question on percentages

A clerk spends

of of his annual salary on rent, transport and entertainment respectively. If after all these expenses he had GH¢ 4,100.00 left, find how much he earns per annum.

Solution:

### 13 (c) A mathematics question on Relations, Mappings and Functions

Given that

find:
(i) f (-3) ;
(ii) the value of x such that f (x) = g(x) .

Solution:

#### Conclusion:

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