Core Mathematics 2019 WASSCE-Past Questions and Answers

Core Mathematics 2019 WASSCE
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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 Inda
  • 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

0.15×0.5670.05×0.189

   , leaving the answer in standard form

Solution:

0.015 x 0.5670.05 x 0.189=15x103 x 567 x1035 x102 x189 x103=15 x567 x103 x1035 x189 x102 x103=3x3×1061x1x105= 9 x106(5)=9 x 104+5=9x101

1   (b) Mathematics question on Linear Equations and Inequalities

 

If 5yx8y+3x=15, find, correct to two decimal placesthe value of xy

Solution:

This is a mathematics question on Linear Equations and Inequalities

The answer to the above question can be found below:

5yx8y+3x=1518y+3x=55yx8y+3x=25y8y8x=17yDivide both sides by 8y, that gives us8x8y=17y8yxy=178xy=2.13 Answer corrected to two decimal places

 

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 = 

18

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

Solution:

Answer to question to wassce 2019 core maths question 2a:

Zx2y3 Z=kx2y3  ............(1)When Z=8,  x=4,  y=188=k42183     8=4k212     8=4k218=4k2     8=4k   k=84=2Putting k=2 into (1) gives youZ=2x2y3 Z= x2y3y3=xZy33=xZ3y=x3Z3  Ans.

 

2   (b)A mathematics question on Algebraic Expressions

Factorize completely:

4b2  ab + (a + 9b)2  a2

Solution:

4b2 ab + (a +9b)2 a2  = 4b2 ab+ (a +9b)(a +9b) a2 = 4b2 ab+a2 +9ab+9ab+81b2 a2 = 4b2 ab+ a2 +18ab +81b2  a2 =4b2 +81b2  ab+18ab+ a2 a2 = 85b2 +17 ab =17b(5b+ a)

 

3   (a)A mathematics question on Algebraic Expressions

Solve 

5x76+2x34=23

Solution:

5x76+2x34=23Multiplying through by 12, we will get125x76+122x34=2325x7+32x3=810x14+6x9=810x+6x=8+14+916x=15x=1516

 

3 (b) A mathematics question on Surds

Evaluate:

28+343263+53

Solution:

Below is the answer to question to wassce 2019 core maths question 3b:

28+343263+35=4×7+49×729×7+53=27+77237+53=9767+53=32+53=196316 Ans.

 

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

Find the answer 2019 core mathematics, question 4

At the first instance, Let P% represent profit percentage andSP represent selling priceCP=100100+P%×SPCP=100100+22.558,000CP=100122.5×58,000CP=47,346.94At the second instance:CP=47,346.94,  SP=61,200P=SPCPP=6120047346.94P=13,853.06P%=PCP×100%P%=13,853.0647,346.06×100%P%29.2586%P%=29.26%  Ans. (remember the question said to 2 decimal places.

 

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:

Solution to wassce 2019 core maths quuestion 5a

Q= {1, 2, 3, 4, 5, 6, 7, 8, 9, 10} n(Q) =10 Let A = {Prime factors of 42 in set Q} = {2, 3, 7} n(A)= 3 Let B = {Multiples of 3 in set Q) = {3, 6, 9} n(B)= 3 AnB= {3) n(A n B) = 1 P(A or B) = P(A) + P(B)  P(A n B) 310+31011051012

 

5   (b)Mathematics question Number Bases

If

110x =10204

, find the value of x.

Solution to Mathematics question wassce 2019 5b

110, =10204 (1xx2)+(lxx1)+(0xx0)=(1x43)+(1x42)+ (1x41)+(lx 40) X2 +X+ 0 =64+0+8+0 x2X = 72 x2+ x72=0 (x8)(x+ 9) = 0 x = 8, x = 9 x = 8

 

6(a) Mathematics question on vectors

If a=23,   b=45,  and r=a+12ab, find(i) r(ii) r

Solution:

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

r=a+12abr=23+122345r=23+1222r=23+11r=12

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

r=12+22r=1+4r=5units

 

6   (b) A mathematics question on Change of Subject and Substitution into Formulae

Given that a=bc and n=mkec,(i) express k in terms of a,b,e,m and n;(ii) find, correct to three significant figures, the value of k, whena=12,  b=4,   e=3,   m=7,   n=5.

Solution:

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

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

a=bc  ..............(1)n=mkec  ............(2)From (1)c=ab  ...............(3)Putting (3) into (2), we will getn=abn=mkaebn=mk×aaen=bmkaebmk=aenbm

 

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

 

When a=12,  b=4,  c=3,  m=7,  n=5k=123547=15228=152×128=1556 Ans.

 

7  Mathematics question Trigonometry II

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

0x150o

x 0o 30o 60o 90o 120o 150o
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 0o 30o 60o 90o 120o 150o
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

AB= 6.5 cm, BC = 9 cm, AD = 4 cm, ABC = 60° and BAD =120°

(ii) the perpendicular bisectors of 

BC and CD

(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) 

BT

(ii) 

CD

Solution:

Answer – wassce 2019 core mathematics question 8

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

 

 

 

 

 

 

 

d(i) 

BT=4.9cm

d(ii) 

CD=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 

5y5.

(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

A1B1C1 of ABC

under a reflection in the line y = 0, where

A A1 , B  B1, and C  C1

 ;

(iii) the image 

A2B2C2 of ABC

under a translation by the vector

21

, where

A  A2, B  B2 and C  C2 ;

(iv) the image 

A3B3C3 of ABC

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

A A3, B  B3 and C  C3

.

(c) What single transformation maps 

A1B1C1 onto A3B3C3,  where A1 A3,  B1 B3 and C1  C3 ?

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

xyxyA21A121B14B114CC112

(iii) Point +Translation Vector = image

A21+21=A202B14+21=B215C12+21=C233

(iv) 

90o

anticlockwise rotation about the origin

xyyxA21A312B14B341C12C321

(c) 

A121A312B114B341C112C321From the mappings above, it can be seen that:xyyx

Graph work- the answer to wassce 2019 core maths question 9

 

 

 

 

 

 

 

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:

Solution for wassce core maths 2019 question 10b

U2U1=U3U263a=75a63a75a=662115a7a+5a2=365a222a+2136=05a222a15=0a=5,  a=35sice r>0a=35

 

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 

87

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

 

Let the speed of train A = xSpeed of train B =87xDistance =Speed ×TimeTherefore, the distance covered by train A=x×2=2xAlso, distance covered by train B=87x×2=167xDistance covered by A+Distance covered by B=450kmTherefore:2x+167x=45014x+16x=315030x=3150x=315030=105Therefore, Speed of train A=105km1  Ans.                  Speed of train B=87×105kmh1=120kmh1

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.

[Take π =227

Solution:

Answer to question to wassce 2019 core maths question 11b:

Volume of cube = l3=83=512cm3Volume of cone = 13πr2h                              =13×227×42×h                               =16.762hVolume of the cone = volume of cube16.762h=512h=51216.762=30.545  Ans.

 

 

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,

BAE =

ECB = n and

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.

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

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

AEC =

ADC

2m =180m 2m + m =180° 3m =180° m = 60o

(ii)

AEC = 2m = 2(60°) =120°

AEC is isosceles. For this reason,

EAC =

ECA
Let

EAC =

ECA= x

From AEC: EAC + ECA+ AEC =180° x+x+120° =180° 2x =180°120° 2x = 60° x = 30° Therefore, EAC = ECA= 30° From ABC: ABC + BAC + BCA =180° m+ (n+ 30°) + (n + 30°) =180° 60°+n+30°+n+30°=180° 2n +120° =180° 2n =180° 120° 2n = 60° n = 30°

 

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

The functions f and g are defined as

f:x2x2   and    g:x1x1(i) g14; (ii)f2g3

 

Answer to wassce 2019 core mathematics quaestion 12(b)

gx=1x1g14=1141=154=45(ii) f2=222=24=2g3=131=12Therefore, f2g3=2122×21=4

 

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

Answer to wassce 2019 core mathematics quaestion 13(a)

U4 = 2U2 1 a +3d =2(a + d) 1 a +3d =2a +2d 1 a 2a +3d 2d = 1 a + d = 1 .............(1) U6 =7 a+5d =7 .............(2) (1) x 5: 5a +5d = 5 (3)(2)  (3): 6a =12 a = 2 Therefore, the first term is 2.

 

13 (b) Mathematics question on percentages

A clerk spends 

15,13 and 18

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:

Answer to wassce 2019 core mathematics quaestion 13(b)

Fraction spent =15+13+18=79120Fraction left=179120=41120Let the clerks annual salary be xBecause the amount left was GH¢4,100, we will get41120×x=4,10041x=120×4,10041x=492,000x=492,00041x=12,000Therefore, the clerks annual salary is GH¢12,000.00

 

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

Given that   

f : x  2x2  8x +5, g : x  x 2;

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

Solution:

Below is the answer to question to wassce 2019 core maths question 13c:

Find the answer  2019 core maths question 13c(i):

f (x)= 2x2  8x + 5 f (3) = 2(3)2  8(3) +5 =18+24+5 = 47

Find the answer  2019 core maths question 13c(ii):

f (x) = g(x) 2x2  8x + 5 = x2 2x2  9x 4 7 = 0 (x1)(2x7)=O x=1 and x=72

 

Conclusion – Core Mathematics 2019 WASSCE

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