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# Maths Topic 1: Basic Arithmetic and Algebra Quiz

### This quiz will be the first of several that will focus on individual topics from my first two quizzes. You may need a pen, paper and a calculator for this quiz. Good luck.

A multiple-choice quiz by dialga483. Estimated time: 4 mins.

Author
Time
4 mins
Type
Multiple Choice
Quiz #
365,973
Updated
Dec 03 21
# Qns
15
Difficulty
Difficult
Avg Score
8 / 15
Plays
454
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Question 1 of 15
1. What is 0.232323... as a fraction? Hint

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Question 2 of 15
2. What is (x+2)^-5 without a negative index? Hint

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Question 3 of 15
3. What is the expansion of (3x-2)(5x^2-7x+4)? Hint

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Question 4 of 15
4. What are the factors of 5y^2-13y+6? Hint

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Question 5 of 15
5. What are the factors of 27a^3-64b^3? Hint

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Question 6 of 15
6. Completing the square of x^2+2x, gives which result? Hint

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Question 7 of 15
7. What is 2sqrt(5) x 18sqrt(20) equal to? Hint

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Question 8 of 15
8. What is (sqrt(2)+3sqrt(5))(sqrt(2)-3sqrt(5)) equal to? Hint

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Question 9 of 15
9. Rationalising the denominator of sqrt(2)/(sqrt(3)-2) gives which result? Hint

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Question 10 of 15
10. For what value of x does 3(7x+6)=1-(x+5)? Hint

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Question 11 of 15
11. For what value of x does 2^(5x-1)=16? Hint

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Question 12 of 15
12. For what value of x does x^2-6x+3=0? Hint

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Question 13 of 15
13. What is abs(2)-abs(-1)+abs(-3)^2 equal to, where abs = absolute value? Hint

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Question 14 of 15
14. For what values of x does abs(2x+3)=7? Hint

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Question 15 of 15
15. For what values of p and q does 5p-q=11 and 2p+3q=1 when solved simultaneously? Hint

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Quiz Answer Key and Fun Facts
1. What is 0.232323... as a fraction?

To solve this question, we let x = 0.23232323... (equation 1)
Therefore, 100x = 23.23232323... (equation 2)
(equation 2)-(equation 1)
99x=23
Therefore x = 23/99
And so, 0.232323... as a fraction is 23/99
2. What is (x+2)^-5 without a negative index?

We can rewrite (x+2)^-5 using the index law x^-n = 1/x^n
Therefore (x+2)^-5 = 1/(x+2)^5
3. What is the expansion of (3x-2)(5x^2-7x+4)?

(3x-2)(5x^2-7x+4)
= 15x^3-21x^2+12x-10x^2+14x-8
= 15x^3-31x^2+26x-8
4. What are the factors of 5y^2-13y+6?

This quadratic can be factorised using the cross method. This gives the factors
(5y-3)(y-2). When the factors are expanded, they will then give the orginal quadratic 5y^2-13y+6
5. What are the factors of 27a^3-64b^3?

To factorise the equation, we can use the rule for the sum and difference of cubes, which is a^3-b^3 = (a-b)(a^2+ab+b^2).
In the equation, a=3 and b=4
Therefore, substituting these into the rule, gives (3a-4b)(9a^2+12ab+16b^2)
6. Completing the square of x^2+2x, gives which result?

To complete the square, we halve the coefficient of x and then square it
Therefore completing the square of x^2+2x, gives
= x^2+2x+1-1
=(x+1)^2-1
7. What is 2sqrt(5) x 18sqrt(20) equal to?

Multiplying these terms gives 36sqrt(100)
= 36 x 10
= 360
8. What is (sqrt(2)+3sqrt(5))(sqrt(2)-3sqrt(5)) equal to?

Using the FOIL expansion (first, outside, inside, last),
= 2 - 3sqrt(10) + 3sqrt(10) - 45
= 2 - 45
= -43
9. Rationalising the denominator of sqrt(2)/(sqrt(3)-2) gives which result?

To rationalise the denominator, we need to multiply it by its conjugate. In this case, the conjugate of sqrt(3)-2 is sqrt(3)+2. This give a rational result on the denominator.
So sqrt(2)/(sqrt(3)-2) x (sqrt(3)+2)/(sqrt(3)+2)
= (sqrt(6)+2sqrt(2))/(3-4)
= -(sqrt(6)+2sqrt(2)
= -sqrt(6)-2srqt(2)
10. For what value of x does 3(7x+6)=1-(x+5)?

3(7x+6)=1-(x+5)
21x+18=1-x-5
22x+18=-4
22x=-22
x=-22/22
x=-1
11. For what value of x does 2^(5x-1)=16?

To find the answer, we need to make both sides have the same base
Therefore, 2^(5x-1)=2^4
5x-1=4
5x=5
x=1
12. For what value of x does x^2-6x+3=0?

To solve this equation, we need to complete the square
So, x^2-6x+3=0
x^2-6x+9=-3+9
(x-3)^2=6
x-3=sqrt(6)
Therefore, x=3+sqrt(6)
13. What is abs(2)-abs(-1)+abs(-3)^2 equal to, where abs = absolute value?

Any numerical term within an absolute value bracket will give a positive value, so
abs(2)-abs(-1)+abs(-3)^2
=2-1+3^2
=2-1+9
=10
14. For what values of x does abs(2x+3)=7?

In a linear absolute value equation, the expression can always have up to two solutions, so
abs(2x+3)=7
2x+3=7
2x=4
x=2
or
2x+3=-7
2x=-10
x=-5
Therefore, the solutions are 2 and -5
15. For what values of p and q does 5p-q=11 and 2p+3q=1 when solved simultaneously?

To solve simoultaneous equations, we can use the elimination method
So, 5p-q=11 (equation 1)
2p+3q=1 (equation 2)
(equation 1) x 3
15p-3q=33 (equation 3)
(equation 2) + (equation 3)
17p=34
p=2
sub p=2 into equation 2
4+3q=1
3q=-3
q=-1
Therefore, p=2, q=-1
Source: Author dialga483

This quiz was reviewed by FunTrivia editor WesleyCrusher before going online.
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