10/7/14
Algebra class x cbse mathematics
NAVODAYA VIDYALAYA SAMITI,
CLASS-X PRACTICE PAPER SA-1 (Algebra) SUB:-MATHEMATICS
FULL MARKS-90 TIME-3 Hours
SECTION-A [1×4=4]
In the given figure the graph of polynomial p(x) is shown. The number of zeroes of p(x) is ____.
If the two zeroes of a quadratic polynomial 7x² – 15x – k are reciprocals of
each other, then find the value of k.
If the lines given by 3x + 2ky = 2 and 2x + 5y +1 = 0 are parallel, then find the value of k.
If a pair of equations x + y = √2 and x sin θ + y cos θ = 1 are consistent and dependent, then find the value of θ.
SECTION-B [2×6=12]
Check whether x² + 3x + 1 is a factor of 3x4 + 5x3 – 7x2 + 2x + 2.
If α and β are the zeroes of the quadratic polynomial p(x) = x² – (k – 6)x + (2k + 1). Find the value of k, if α + β = αβ.
If 2 and – 3 are the zeroes of the quadratic polynomial x² + (a + 1)x + b, then find the values of a and b.
Solve: 99x + 101y = 499, 101x + 99y = 501
For what value of k, the following system of linear equations has no solution?
3x + y =1; (2k ‒ 1)x + (k ‒ 1)y = 2k + 1
If 2x + y = 23 and 4x ‒ y = 19, find the value of 5y ‒ 2x.
SECTION-C [3×10=30]
If one of the zero of the quadratic polynomial 2x² + px + 4 is 2, find the other zero. Also find the value of p.
Find the zeroes of 3√2 x² + 13 x + 6√2 and verify the relationship between the zeroes and coefficients of the polynomial.
On dividing x3 ‒ 3x² + x + 2 by a polynomial g(x), the quotient and the remainder were x ‒ 2 and
‒ 2x + 4 respectively. Find g(x).
Form a quadratic polynomial whose one of the zeroes is (‒ 15) and product of the zeroes is (‒855).
Find the values of a and b for which the system of linear equations has infinite number of solutions:
(a + b)x ‒ 2by = 5a + 2b + 1; 3x ‒ y = 14
Solve the following system of linear equations graphically and find the points where these lines intersect the Y-axis: x ‒ 2y = 2; 3x + 5y = 17.
Solve for x and y: 3/y + 4/x = 10/xy ; 2/y ‒ 2/x = 2/xy
Nine times a two-digit number is the same as twice the number obtained by interchanging the digits of the number. If one digit of the number exceeds the other digit by 7, find the number.
Solve for x and y:`xy/(x+y) = 6/5 ; xy/(y-x) = 6, where x + y ≠ 0 and y ‒ x ≠ 0.
Four years ago, a father was six times as old as his son. Ten years later, the father will be two and a half times as old as his son. Determine the present ages of the father and the son.
SECTION-D [4×11=44]
Find all the zeroes of the polynomial 2x4 + 7x3 ‒ 19x² ‒ 14x + 30, if two of its zeroes are √2 and ‒√2.
Find all the zeroes of the polynomial p(x) = 2x3 + 3x² ‒ 11x ‒ 6, if one of its zeroes is ‒3.
If the polynomial x4 ‒ 6x3 + 16x² ‒ 25x + 10 is divided by another polynomial x² ‒ 2x + k, the remainder comes out to be x + a. Find the values of k and a.
Given that the zeroes of the cubic polynomial x3 ‒ 6x² + 3x + 10 are of the form a, a+b, a+2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.
If 1 and ‒1 are the zeroes of the polynomial Lx4 + Mx3 + Nx² + Rx + P, show that L + N + P = M + R =0.
A boat goes 64 km upstream and 72 km downstream in 14 hours. It goes 80 km upstream and
96 km downstream in 18 hours. Find the speed of the boat in still water and the speed of the steam.
5 books and 7 pens together cost Rs 285. 4 books and 4 pens together cost Rs220. Mona purchased 3 books and 5 pens and calculated total cost to be Rs 195. He paid Rs 195 to the shopkeeper. Shopkeeper rechecked and returned some money to Mona.
How much money did shopkeeper return to Mona?
What value is depicted by the shopkeeper?
Determine graphically, the coordinates of the vertices of a triangle whose sides are graphs of the equations 2x – 3y + 6 = 0; 2x + 3y – 18 = 0 and y – 2 = 0. Also find the area of this triangle.
Solve for x and y: (a – b)x + (a + b)y = a² − 2ab – b²
(a + b)(x + y) = a² + b²
Solve the following system of equations by using the method of cross-multiplication.
2x + y = 35 and 3x + 4y = 65
Solve for x and y: 6x + 3y = 8x + 9y – 5 = 10x + 12y – 8
******************************************************************************************
CLASS-X PRACTICE PAPER SA-1 (Algebra) SUB:-MATHEMATICS
FULL MARKS-90 TIME-3 Hours
SECTION-A [1×4=4]
In the given figure the graph of polynomial p(x) is shown. The number of zeroes of p(x) is ____.
If the two zeroes of a quadratic polynomial 7x² – 15x – k are reciprocals of
each other, then find the value of k.
If the lines given by 3x + 2ky = 2 and 2x + 5y +1 = 0 are parallel, then find the value of k.
If a pair of equations x + y = √2 and x sin θ + y cos θ = 1 are consistent and dependent, then find the value of θ.
SECTION-B [2×6=12]
Check whether x² + 3x + 1 is a factor of 3x4 + 5x3 – 7x2 + 2x + 2.
If α and β are the zeroes of the quadratic polynomial p(x) = x² – (k – 6)x + (2k + 1). Find the value of k, if α + β = αβ.
If 2 and – 3 are the zeroes of the quadratic polynomial x² + (a + 1)x + b, then find the values of a and b.
Solve: 99x + 101y = 499, 101x + 99y = 501
For what value of k, the following system of linear equations has no solution?
3x + y =1; (2k ‒ 1)x + (k ‒ 1)y = 2k + 1
If 2x + y = 23 and 4x ‒ y = 19, find the value of 5y ‒ 2x.
SECTION-C [3×10=30]
If one of the zero of the quadratic polynomial 2x² + px + 4 is 2, find the other zero. Also find the value of p.
Find the zeroes of 3√2 x² + 13 x + 6√2 and verify the relationship between the zeroes and coefficients of the polynomial.
On dividing x3 ‒ 3x² + x + 2 by a polynomial g(x), the quotient and the remainder were x ‒ 2 and
‒ 2x + 4 respectively. Find g(x).
Form a quadratic polynomial whose one of the zeroes is (‒ 15) and product of the zeroes is (‒855).
Find the values of a and b for which the system of linear equations has infinite number of solutions:
(a + b)x ‒ 2by = 5a + 2b + 1; 3x ‒ y = 14
Solve the following system of linear equations graphically and find the points where these lines intersect the Y-axis: x ‒ 2y = 2; 3x + 5y = 17.
Solve for x and y: 3/y + 4/x = 10/xy ; 2/y ‒ 2/x = 2/xy
Nine times a two-digit number is the same as twice the number obtained by interchanging the digits of the number. If one digit of the number exceeds the other digit by 7, find the number.
Solve for x and y:`xy/(x+y) = 6/5 ; xy/(y-x) = 6, where x + y ≠ 0 and y ‒ x ≠ 0.
Four years ago, a father was six times as old as his son. Ten years later, the father will be two and a half times as old as his son. Determine the present ages of the father and the son.
SECTION-D [4×11=44]
Find all the zeroes of the polynomial 2x4 + 7x3 ‒ 19x² ‒ 14x + 30, if two of its zeroes are √2 and ‒√2.
Find all the zeroes of the polynomial p(x) = 2x3 + 3x² ‒ 11x ‒ 6, if one of its zeroes is ‒3.
If the polynomial x4 ‒ 6x3 + 16x² ‒ 25x + 10 is divided by another polynomial x² ‒ 2x + k, the remainder comes out to be x + a. Find the values of k and a.
Given that the zeroes of the cubic polynomial x3 ‒ 6x² + 3x + 10 are of the form a, a+b, a+2b for some real numbers a and b, find the values of a and b as well as the zeroes of the given polynomial.
If 1 and ‒1 are the zeroes of the polynomial Lx4 + Mx3 + Nx² + Rx + P, show that L + N + P = M + R =0.
A boat goes 64 km upstream and 72 km downstream in 14 hours. It goes 80 km upstream and
96 km downstream in 18 hours. Find the speed of the boat in still water and the speed of the steam.
5 books and 7 pens together cost Rs 285. 4 books and 4 pens together cost Rs220. Mona purchased 3 books and 5 pens and calculated total cost to be Rs 195. He paid Rs 195 to the shopkeeper. Shopkeeper rechecked and returned some money to Mona.
How much money did shopkeeper return to Mona?
What value is depicted by the shopkeeper?
Determine graphically, the coordinates of the vertices of a triangle whose sides are graphs of the equations 2x – 3y + 6 = 0; 2x + 3y – 18 = 0 and y – 2 = 0. Also find the area of this triangle.
Solve for x and y: (a – b)x + (a + b)y = a² − 2ab – b²
(a + b)(x + y) = a² + b²
Solve the following system of equations by using the method of cross-multiplication.
2x + y = 35 and 3x + 4y = 65
Solve for x and y: 6x + 3y = 8x + 9y – 5 = 10x + 12y – 8
******************************************************************************************
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