PRELIMINARY CONTEST 2024
Contest 28
St. John’s Grammar School – 38 pts (Winner)
Accra High School – 32 pts
St. Francis Girls’ SHS – 13 pts
Contest 29
Kumasi Academy – 56 pts (Winner)
Saviour SHS – 16 pts
Battor SHS – 14 pts
Contest 30
Ghana SHS, Koforidua – 49 pts (Winner)
Sefwi Wiawso SHS – 15 pts
Northern School of Business – 09 pts
ROUND 2
SPEED RACE
QUESTION
A binary operation star is defined on the set R of real numbers by $m*n=m+n\sqrt{3}$, where m and n are real numbers. Evaluate $3*(2*1)$
SOLUTION
$m*n=m+n\sqrt{3}$
$3*(2*1)=3*(2+\sqrt{3})$
$=3+(2+\sqrt{3})(\sqrt{3})$
$=3+3+2\sqrt{3}$
$ANSWER:6+2\sqrt{3}$
PRACTICE QUESTIONS
1. A binary operation is defined on the set of real numbers by $m*n=m+n\sqrt{3}$. Evaluate $3*(2*1)$.
ANSWER: $6+2\sqrt{3}$
SOLUTION
$m*n=m+n\sqrt{3}$
$2*1=2+1\sqrt{3}$
$3*(2+1\sqrt{3})=3+(2+1\sqrt{3})\sqrt{3}$
$=3+2\sqrt{3}+1(3)$
$=6+2\sqrt{3}$
2. A binary operation is defined on the set of real numbers by $m*n=m+n\sqrt{5}$. Evaluate $2*(3*4)$.
ANSWER: $22+3\sqrt{5}$
SOLUTION
$m*n=m+n\sqrt{5}$
$3*4=3+4\sqrt{5}$
$2*(3+4\sqrt{5})=2+(3+4\sqrt{5})\sqrt{5}$
$=2+3\sqrt{5}+4(5)$
$=22+3\sqrt{5}$
3. A binary operation is defined on the set of real numbers by $m*n=m+n\sqrt{2}$. Evaluate $5*(1*2)$.
ANSWER: $9+\sqrt{2}$
SOLUTION
$m*n=m+n\sqrt{2}$
$1*2=1+2\sqrt{2}$
$5*(1+2\sqrt{2})=5+(1+2\sqrt{2})\sqrt{2}$
$=5+1\sqrt{2}+2(2)$
$=9+\sqrt{2}$
4. A binary operation is defined on the set of real numbers by $m*n=m+n\sqrt{7}$. Evaluate $(4*3)*2$.
ANSWER: $4+5\sqrt{7}$
SOLUTION
$m*n=m+n\sqrt{7}$
$4*3=4+3\sqrt{7}$
$(4+3\sqrt{7})*2=(4+3\sqrt{7})+2\sqrt{7}$
$=4+5\sqrt{7}$
5. A binary operation is defined on the set of real numbers by $m*n=m+n\sqrt{3}$. Evaluate $(1*2)*3$.
ANSWER: $1+5\sqrt{3}$
SOLUTION
$m*n=m+n\sqrt{3}$
$1*2=1+2\sqrt{3}$
$(1+2\sqrt{3})*3=(1+2\sqrt{3})+3\sqrt{3}$
$=1+5\sqrt{3}$
6. A binary operation is defined on the set of real numbers by $m*n=m+n\sqrt{5}$. Evaluate $(6*4)*1$.
ANSWER: $6+5\sqrt{5}$
SOLUTION
$m*n=m+n\sqrt{5}$
$6*4=6+4\sqrt{5}$
$(6+4\sqrt{5})*1=(6+4\sqrt{5})+1\sqrt{5}$
$=6+5\sqrt{5}$