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Worksheet

This document contains 30 math problems involving rational numbers, simplifying expressions, factoring polynomials, graphing points, and writing linear equations. The problems cover skills like finding rational numbers between given values, identifying rational numbers with terminating decimal expansions, expressing fractions in simplest form, rationalizing denominators, simplifying expressions with radicals, using the factor theorem to check for factors of polynomials, finding zeros of polynomials, factoring trinomials and more complex expressions, plotting points on a graph and finding the area of triangles formed, checking if points satisfy linear equations, and writing linear equations to represent word problems involving rates and collective contributions.

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89 views1 page

Worksheet

This document contains 30 math problems involving rational numbers, simplifying expressions, factoring polynomials, graphing points, and writing linear equations. The problems cover skills like finding rational numbers between given values, identifying rational numbers with terminating decimal expansions, expressing fractions in simplest form, rationalizing denominators, simplifying expressions with radicals, using the factor theorem to check for factors of polynomials, finding zeros of polynomials, factoring trinomials and more complex expressions, plotting points on a graph and finding the area of triangles formed, checking if points satisfy linear equations, and writing linear equations to represent word problems involving rates and collective contributions.

Uploaded by

veda
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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1.

Find 5 rational numbers between


i. 3/7 and 5/7 ii. 1.3 and 1.4 iii. -1 and ½ iv. -3/4 and -2/5
2. Without actual division, find which of the following rational numbers have terminating decimal expansions. In case
they have terminating decimal expansions, write their decimal expansions.
i. 31/375 ii. 18/125 iii. 7/12 iv. 19/27 v. 15/80
3. Express each of the following in the form of p/q, where p and q are integers and q≠0:
̅̅̅̅
i. 18. 48 ̅̅̅̅
ii. 0.0032 ̅̅̅̅̅
iii. 0.3178 iv. 0.407̅
4. Rationalise the denominator in each of the following:
5 √3 7 8 √11−√17 √19−√13
i. 𝑖𝑖. 𝑖𝑖𝑖. 𝑖𝑣. 11−√11 𝑣. 𝑣𝑖.
√2 √5 √3+√7 √13−√11 √2+√11
5. Simplify:
6+√7 6−√7 2 1 3 2√6 6√2 8√3
i. 6−√7 + 6+√7 𝑖𝑖. − + 𝑖𝑖𝑖. − +
√2+√3 √2−√3 √3−√2 √5+√7 √7−√5 √3
√21 1
6. If 𝑥 = 5 − , 𝑓𝑖𝑛𝑑
𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑥 + 𝑥
2
1
7. If 𝑎 = 2 − 3√3, 𝑓𝑖𝑛𝑑 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑎 2 − 2
𝑎
8. Simplify:
2 1 −3⁄ −4⁄
71⁄4 5 5
81 2 32 5
i. 33 × 35 𝑖𝑖. 71⁄5 𝑖𝑖𝑖. 78 × 58 𝑖𝑣. (99917 )1⁄17 𝑣. (64) 𝑣𝑖. (243)
9. Using factor theorem, check whether g(x) is a factor p(x) in the following:
i. p(x)=𝑥 3 − 𝑎𝑥 2 + 6𝑥 − 𝑎 ;g(x)=𝑥 − 𝑠
3
ii. p(x)=𝑥 3 − 6𝑥 2 + 2𝑥 − 4;g(x)=1 − 2 𝑥
1
iii. p(x)=2𝑥 3 + 3𝑥 2 − 11𝑥 − 3;g(x)=𝑥 + 2
10. Find the zero of the following polynomials:
i. p(x)=ax ii. P(x)=bx-d iii. P(x)=6x-2 iv. P(x)=3/2x-2/3
11. Find the value of a and b so that p(x)=𝑥 4 − 𝑎𝑥 3 − 7𝑥 2 − 8𝑥 + 𝑏 is exactly divisible by (𝑥 + 2) as well as (𝑥 + 3).
12. Find the value of k for which (𝑥 − 1) is a factor of (2𝑥 3 + 9𝑥 2 + 𝑥 + 𝑘)
Factorise the following:
13. (a+2b)2+101(a+2b)+100
14. 9x2+15xy
15. a3b-a2b+5ab-5b
16. px-5q+pq-5x
17. 5-20x2
18. 27a2-48b2
19. (3a+5b)2-4c2
20. x2+11x+30
21. x2+3√3x +6
22. 6-x-x2
23. 16x2+4y2+9z2-16xy-12yz+24zx
27 9𝑎 27𝑎2
24. 1 + 𝑎3 + +
125 5 25
25. 125x3-27y3-225x2y+135xy2
1
26. 125a3+ 8
27. a3-0.064
28. Write the quadrant or axis in which the following points lie:
i. (-6,3) ii. (-5,-6) iii. (9,-7) iv. (0,1) v. (5,2) vi. (-2,0) vii. (19,0) viii. (0,-101)
29. Plot the following points on a graph and find the aera of the triangle formed by these points:
i. (2,5); (-2,2); (4,2) ii. (-3,2); (2,2); (0,5)
30. check whether the following are the solutions of the equation 15x-5y=20
i. (0,5) ii. (1,-5) iii. (-1,-5)
31. Write a linear equation in 2 variables to represent the following:
i. The cost of 5 pencils is equal to the cost of 2 ballpoint pens.
ii. Two students A and B collectively contributed Rs 100 towards the Prime Minister’s Relief Fund to help the
earthquake victims.

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