# maths SA-1 question paper and answers

**Topics:**Triangle, Pythagorean theorem, Real number

**Pages:**25 (2765 words)

**Published:**October 10, 2013

Q1)

Use the following information to answer the next question.

The steps for finding the H.C.F. of 2940 and 12348 by Euclid’s division lemma are as follows. 12348 = a × 4 + b

a = b × 5 + 0

What are the respective values of a and b?

A.

2352 and 588

B.

2940 and 588

C.

2352 and 468

D.

2940 and 468

Answer

The steps to find the H.C.F. of 12348 and 2940 are as follows. 12348 = 2940 × 4 + 588

2940 = 588 × 5 + 0

Comparing with the given steps, we obtain

a = 2940 and b = 588

Thus, the value of a and b are 2940 and 588 respectively.

The correct answer is B.

Q2)

Use the following information to answer the next question.

The given figure shows the graph of polynomial,

p(x) = x2 + kx − 15

What is the value of k?

A.

3

B.

2

C.

−2

D.

−3

Answer

In the given figure, the graph intersects x-axis at two points, (−3, 0) and (5, 0). Therefore, x = −3 and x = 5 are the zeroes of the polynomial p(x). Substituting x = 5 in p(x), we obtain

p(5) = (5)2 + k(5) − 15 = 0

⇒ 25 + 5k − 15 = 0

⇒ 5k = −10

⇒ k = −2

Thus, the value of k is −2.

The correct answer is C.

Q3)

If the pair of linear equations, 7x + k1y = 2 and k2x + 2y = 3, has a unique solution, then which of the following relations is always correct? A.

kl ≠ 2 and k2 ≠ 7

B.

klk2 ≠ 9

C.

klk2 ≠ 14

D.

k1 ≠ 7 and k2 ≠ 2

Answer

We know that the pair of equations, and , will have a unique solution if . 7x + k1y = 2 and k2x + 2y = 3 will have a unique solution if

7 × 2 ≠ kl k2

kl k2 ≠ 14

Thus, the relation given in alternative C is correct.

The correct answer is C.

Q4)

Which of the following relations is correct for the three measures of central tendency? A.

Median = Mode + 2 Mean

B.

3 Median = Mode − 2 Mean

C.

Mode = 3 Median − 2 Mean

D.

3 Mode = Median + 2 Mean

Answer

The relation between the three measures of central tendency is given by, 3 Median = Mode + 2 Mean

⇒ Mode = 3 Median − 2 Mean

The correct answer is C.

Q5)

The HCF and LCM of two positive numbers are 26 and 910 respectively. If one of the numbers is 130, then what is the other number? A.

182

B.

264

C.

346

D.

428

Answer

It is given that the HCF and LCM of two positive numbers are 26 and 910 respectively. Let the two positive numbers be a and b, where a = 130

It is known that for any positive integers, a, b,

HCF (a, b) × LCM (a, b) = a × b

∴HCF (130, b) × LCM (130, b) = 130 × b

⇒ 26 × 910 = 130 × b

Thus, the other number is 182.

The correct answer is A.

Q6)

What is the value of the expression?

A.

−1

B.

0

C.

1

D.

2

Answer

The correct answer is B.

Q7)

Use the following information to answer the next question.

What is the number of zeroes of the polynomial represented by the given graph? A.

1

B.

2

C.

3

D.

4

Answer

The number of zeroes of a polynomial is equal to the number of points at which the graph of p(x) intersects x-axis. The graph of the polynomial intersects x-axis at three points. Thus, the polynomial has three zeroes.

The correct answer is C.

Q8)

What is the value of k for which the pair of linear equations kx + 5y − (k − 5) = 0 and 20x + ky − k = 0 has infinite many solutions? A.

10

B.

5

C.

−5

D.

−10

Answer

The given pair of linear equations is kx + 5y − (k − 5) = 0 and 20x + ky − k = 0. It is known that the pair of equations and has infinite many solutions, if . For the given pair of equations, a1 = k, b1 = 5, c1 = −(k − 5), a2= 20, b2= k, c2= −k

Equating the first two ratios:

k2 = 100

∴ k = ±10

Equating the last two ratios:

Thus, the value of k is 10.

The correct answer is A.

Q9)

Use the following information to answer the next question.

In the given figure, DE||BC, AB = 24 cm, AC = 20 cm, and AD = 10 cm.

What is the approximate length of EC?

A.

8 cm

B.

10 cm

C.

10.33 cm

D.

11.66 cm

Answer

It is given that DE||BC

By basic proportionality theorem, we obtain

AD = 10 cm, AC = 20 cm, and AB = 24 cm

∴...

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