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Quiz about Maths Topic 1 Basic Arithmetic and Algebra

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
dialga483

Time
4 mins

Type
Multiple Choice

Quiz #
365,973

Updated
Dec 03 21

# Qns
15

Difficulty
Difficult

Avg Score
8 / 15

Plays
454

One at a Time - Single Page

Question 1 of 15

1. What is 0.232323... as a fraction? Hint

20/99

23/9

26/99

23/99

NEXT>

Question 2 of 15

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

1/(x+2)^5

5(x+2)^5

(x+2)^5

5/(x+2)^5

NEXT>

Question 3 of 15

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

15x^3-31x^2+26x-8

15x^3-31x^2-2x-8

15x^3-11x^2+26x-8

15x^3-35x^2+2x-8

NEXT>

Question 4 of 15

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

(5y+3)(y-2)

(5y-3)(y-2)

(5y-3)(y+2)

(5y+3)(y+2)

NEXT>

Question 5 of 15

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

(3a-4b)(9a^2-12ab+16b^2)

(3a-4b)(9a^2+12ab+16b^2)

(3a+4b)(9a^2-12ab+16b^2)

(3a+4b)(9a^2+12ab+16b^2)

NEXT>

Question 6 of 15

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

(x-1)^2-1

(x-1)^2+1

(x+1)^2+1

(x+1)^2-1

NEXT>

Question 7 of 15

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

360

420

300

240

NEXT>

Question 8 of 15

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

-47

-43

NEXT>

Question 9 of 15

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

-sqrt(6)+2sqrt(2)

-sqrt(6)-2sqrt(2)

sqrt(6)+2sqrt(2)

sqrt(6)-2sqrt(2)

NEXT>

Question 10 of 15

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

1.1

-1.1

-1

NEXT>

Question 11 of 15

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

NEXT>

Question 12 of 15

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

-6+sqrt(3)

-3+sqrt(6)

3+sqrt(6)

6+sqrt(3)

NEXT>

Question 13 of 15

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

-8

NEXT>

Question 14 of 15

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

x= -2, 5

x= -4, 10

x= 4, -10

x= 2, -5

NEXT>

Question 15 of 15

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

p=2, q=-1

p=2, q=1

p=-2, q=1

p=-2, q=-1

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Quiz Answer Key and Fun Facts

1. What is 0.232323... as a fraction?

Answer: 23/99

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?

Answer: 1/(x+2)^5

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)?

Answer: 15x^3-31x^2+26x-8

(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?

Answer: (5y-3)(y-2)

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?

Answer: (3a-4b)(9a^2+12ab+16b^2)

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?

Answer: (x+1)^2-1

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?

Answer: 360

Multiplying these terms gives 36sqrt(100)
= 36 x 10
= 360

8. What is (sqrt(2)+3sqrt(5))(sqrt(2)-3sqrt(5)) equal to?

Answer: -43

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?

Answer: -sqrt(6)-2sqrt(2)

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)?

Answer: -1

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?

Answer: 1

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?

Answer: 3+sqrt(6)

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?

Answer: 10

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?

Answer: x= 2, -5

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?

Answer: p=2, q=-1

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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