Construct a regular hexagon of side 5 cm. Construct a circle circumscribing the hexagon. All traces of construction must be clearly shown.

Concept: Circumscribing and Inscribing a Circle on a Regular Hexagon

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If a, b, c are in continued proportion, prove that (a + b + c) (a – b + c) = a^{2} + b^{2} + c^{2}

Concept: Compound Interest as a Repeated Simple Interest Computation with a Growing Principal

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A wholesaler buys a TV from the manufacturer for Rs. 25,000. He marks the price of TV 20% above his cost price and sells it to a retailer at a 10% discount on the market price. If the rate of the VAT is 8%, find the :

1) Market price

2) Retailer’s cost price inclusive of tax.

3) VAT paid by the wholesaler.

Concept: Introduction to Sales Tax and Value Added Tax

Appears in 1 question paper

ABC is a right angled triangle with ∠ABC = 90°. D is any point on AB and DE is perpendicular to AC. Prove that:

1) ΔADE ~ ΔACB

2) If AC = 13 cm, BC = 5 cm and AE = 4 cm. Find DE and AD.

3) Find. Area of ΔADE: area of quadrilateral BCED

Concept: Similarity of Triangles

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Sum of two natural numbers is 8 and the difference of their reciprocal is `2/15`. Find the numbers.

Concept: Quadratic Equations

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Calculate the ratio in which the line joining A(-4,2) and B(3,6 is divided by a point P(x, 3). Also, find (i) x (ii) Length of AP.

Concept: Ratios

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The numbers 6, 8, 10, 12, 13 and x are arranged in an ascending order. If the mean of the observations is equal to the median, find the value of x

Concept: Median of Grouped Data

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A shopkeeper bought a washing machine at a discount of 20% from a wholesaler, the printed price of the washing machine being Rs. 18,000. The shopkeeper sells it to a consumer at a discount of 10% on the printed price. If the rate of sales tax is 8%, find:

1) the VAT paid by the shopkeeper.

2) the total amount that the consumer pays for the washing machine

Concept: Introduction to Sales Tax and Value Added Tax

Appears in 1 question paper

In Δ ABC, ∠ABC = ∠DAC. AB = 8 cm, AC = 4 cm, AD = 5 cm.

1) Prove that Δ ACD is similar to Δ BCA.

2) Find BC and CD

3) Find- area of Δ ACD : area of Δ BCA

Concept: Similarity of Triangles

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If (x - 9) : (3x + 6) is the duplicate ratio of 4: 9, find the value of x.

Concept: Ratios

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At what rate % p.a. will a sum of Rs. 4000 yield Rs. 1324 as compound interest in 3 years?

Concept: Compound Interest as a Repeated Simple Interest Computation with a Growing Principal

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The median of the following observations

11, 12, 14, (x - 2), (x + 4), (x + 9), 32, 38, 47 arranged in ascending order is 24.

Find the value of x and hence find the mean.

Concept: Median of Grouped Data

Appears in 1 question paper

If (x – 2) is a factor of the expression 2x^{3} + ax^{2} + bx – 14 and when the expression is divided by (x – 3), it leaves a remainder 52, find the values of a and b.

Concept: Factor Theorem

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Solve the following equation and calculate the answer correct to two decimal places:

x^{2} – 5x – 10 = 0.

Concept: Quadratic Equations

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In the given figure, AB and DE are perpendicular to BC.

1) Prove that ΔABC ∼ ΔDEC

2) If AB = 6 cm; DE = 4 cm and AC = 15 cm. Calculate CD.

3) Find the ratio of area of ΔABC: area of ΔDEC

Concept: Similarity of Triangles

Appears in 1 question paper

A shopkeeper sells an article at the listed price of Rs. 1500 and the rate of the VAT is 12% at each stage of the sale. If the shopkeeper pays a VAT of Rs. 36 to the Government, what was the price, inclusive to TAX, at which the shopkeeper purchased the article from the wholesaler?

Concept: Introduction to Sales Tax and Value Added Tax

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Without solving the following quadratic equation, find the value of ‘p' for which the given equation has real and equal roots:

x^{2} + (p – 3)x + p = 0.

Concept: Quadratic Equations

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A shopkeeper purchases a certain number of books for Rs. 960. If the cost per book was Rs. 8 less, the number of books that could be purchased for Rs. 960 would be 4 more. Write an equation, taking the original cost of each book to be Rs. x, and solve it to find the original cost of the books.

Concept: Quadratic Equations

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On what sum of money will the difference between the compound interest and simple interest for 2 years be equal to Rs. 25 if the rate of interest charged for both is 5% p.a.?

Concept: Compound Interest as a Repeated Simple Interest Computation with a Growing Principal

Appears in 1 question paper

ABC is an isosceles right-angled triangle with ∠ABC = 90°. A semi-circle is drawn with AC as the diameter. If AB = BC = 7 cm, find the area of the shaded region. [Take Π = 22/7]

Concept: Perimeter and Area of a Circle

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