### Challenging Questions on Various Secondary Math Topics

I have compiled some of the challenging questions I have covered with my students. For those who are interested, you are more than welcomed to give the questions below a try! Cheers =) .

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QUESTIONS:

\({\small 1.\enspace}\) Given that:

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\({\LARGE\frac{108}{17} \ = \ } {\LARGE a} + \huge{\frac{1}{b \ + \ \frac{1}{c \ + \ \frac{1}{d \ + \ 2}}}}\)

\(\\[1pt]\)

with

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\({\LARGE\frac{a^3 \ – \ 3a^2b \ + \ 3ab^2 \ – \ b^3}{c^3 \ – \ 3c^2d \ + \ 3cd^2 \ – \ d^3}} \)

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\({\small 2.\enspace}\) One year, 23 September was a Monday. What day of the week was 10 November that year?

\(\hspace{1.2em}\)(a). Sunday

\(\hspace{1.2em}\)(b). Monday

\(\hspace{1.2em}\)(c). Thursday

\(\hspace{1.2em}\)(d). Saturday

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\({\small 3.\enspace}\) In a rectangle

If

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\({\small 4.\enspace}\) Given that: \((3x\:+\:4y \:-\: 5z)^{3}\), find the sum of coefficients of the terms: \(x^2y,\:y^2z\) and \(x^2z\).

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\({\small 5.\enspace}\) Find the result of:

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\({\large\frac{5}{(2 \ \times \ 3)^{2}}}+{\large\frac{7}{(3 \ \times \ 4)^{2}}}+{\large\frac{9}{(4 \ \times\ 5)^{2}}} + \dots + {\large\frac{23}{(11 \ \times \ 12)^{2}}}\)

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\({\small 6.\enspace}\) Mr. Santoso has five kids. Each of them is given a different amount of pocket money per week. Adi gets half of what Edi receives, Beni gets $1 more from Adi, Citra gets $1.5 more than Adi and Doni gets $1.7 less that Edi. If the average of their pocket money is $5.2 in a week, what is the amount of pocket money that Doni received in a year?

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\({\small 7.\enspace}\) The same rule is applied to the top number in each box to give the bottom number.

\(\\[1pt]\)

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What number must box

(a). 30

(b). 32

(c). 34

(d). 40

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\({\small 8.\enspace}\) Oscar, Lily and Jack collect souvenir coins. Oscar has 44 more coins than Lily and 48 more coins than Jack. Oscar has 6 more coins than Lily and Jack combined. How many coins do Oscar, Lily and Jack have altogether?

(a). 196

(b). 166

(c). 156

(d). 146

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\({\small 9.\enspace}\) Sam had identical copies of these three paper shapes.

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He used them to create these designs.

\(\\[1pt]\)

\(\\[1pt]\)

What value must

(a). 10

(b). 11

(c). 12

(d). 13

\(\\[1pt]\)

\({\small 10.\enspace}\) In the equation below,

\(\\[1pt]\)

\({\large \frac{A}{3} \ + \ \frac{B}{4} \ = \ \frac{11}{12}} \)

\(\\[1pt]\)

\({\LARGE\frac{108}{17} \ = \ } {\LARGE a} + \huge{\frac{1}{b \ + \ \frac{1}{c \ + \ \frac{1}{d \ + \ 2}}}}\)

\(\\[1pt]\)

with

*a*,*b*,*c*and*d*are positive integers. Find the value of:\(\\[1pt]\)

\({\LARGE\frac{a^3 \ – \ 3a^2b \ + \ 3ab^2 \ – \ b^3}{c^3 \ – \ 3c^2d \ + \ 3cd^2 \ – \ d^3}} \)

\(\\[1pt]\)

\({\small 2.\enspace}\) One year, 23 September was a Monday. What day of the week was 10 November that year?

\(\hspace{1.2em}\)(a). Sunday

\(\hspace{1.2em}\)(b). Monday

\(\hspace{1.2em}\)(c). Thursday

\(\hspace{1.2em}\)(d). Saturday

\(\\[1pt]\)

\({\small 3.\enspace}\) In a rectangle

*ABCD*, point*F*and*E*are located at the side*AB*and*DC*in such a way a rhombus*BFDE*is formed, as shown in the picture.If

*AB*\(=\) 6.4 cm and*BC*\(=\) 4.8 cm, find*EF*.\(\\[1pt]\)

\({\small 4.\enspace}\) Given that: \((3x\:+\:4y \:-\: 5z)^{3}\), find the sum of coefficients of the terms: \(x^2y,\:y^2z\) and \(x^2z\).

\(\\[1pt]\)

\({\small 5.\enspace}\) Find the result of:

\(\\[1pt]\)

\({\large\frac{5}{(2 \ \times \ 3)^{2}}}+{\large\frac{7}{(3 \ \times \ 4)^{2}}}+{\large\frac{9}{(4 \ \times\ 5)^{2}}} + \dots + {\large\frac{23}{(11 \ \times \ 12)^{2}}}\)

\(\\[1pt]\)

\({\small 6.\enspace}\) Mr. Santoso has five kids. Each of them is given a different amount of pocket money per week. Adi gets half of what Edi receives, Beni gets $1 more from Adi, Citra gets $1.5 more than Adi and Doni gets $1.7 less that Edi. If the average of their pocket money is $5.2 in a week, what is the amount of pocket money that Doni received in a year?

\(\\[1pt]\)

\({\small 7.\enspace}\) The same rule is applied to the top number in each box to give the bottom number.

\(\\[1pt]\)

\(\\[1pt]\)

What number must box

*x*be ?(a). 30

(b). 32

(c). 34

(d). 40

\(\\[1pt]\)

\({\small 8.\enspace}\) Oscar, Lily and Jack collect souvenir coins. Oscar has 44 more coins than Lily and 48 more coins than Jack. Oscar has 6 more coins than Lily and Jack combined. How many coins do Oscar, Lily and Jack have altogether?

(a). 196

(b). 166

(c). 156

(d). 146

\(\\[1pt]\)

\({\small 9.\enspace}\) Sam had identical copies of these three paper shapes.

\(\\[1pt]\)

\(\\[1pt]\)

He used them to create these designs.

\(\\[1pt]\)

\(\\[1pt]\)

What value must

*x*be?(a). 10

(b). 11

(c). 12

(d). 13

\(\\[1pt]\)

\({\small 10.\enspace}\) In the equation below,

*A*and*B*represent natural numbers. What values of*A*and*B*will make the equation true?\(\\[1pt]\)

\({\large \frac{A}{3} \ + \ \frac{B}{4} \ = \ \frac{11}{12}} \)

\(\\[1pt]\)

As always, if you have any particular questions to discuss, leave it in the comment section below. Cheers =) .

Emma wants to plot every point on the number plane where:

– the coordinates are integers

– it is less than 4 units from the origin

– the sum of the coordinates is even or zero

Emma wants to plot every point on the number plane where:

– the coordinates are integers

– it is less than 3 units from the origin

– the sum of the coordinates is even or zero

Tala is sending three parcels. The middle-sized parcel is twice the mass of the smallest parcel and half the mass of the largest parcel. The total mass of the parcels is 840 grams. What is the mass of Tala’s largest parcel?